A Proposed Heuristic for a Computer Chess ProgramComputer chess programs have historically been weak...

A Proposed Heuristic for a Computer Chess Program

copyright (c) 2010John L. Jerz

[email protected], Virginia

Independent ScholarMS Systems Engineering, Virgina Tech, 2000

MS Electrical Engineering, Virgina Tech, 1995BS Electrical Engineering, Virginia Tech, 1988

June 12, 2010

Abstract

How might we manage the search efforts in a computer chess program in orderto play a stronger positional game of chess? A new heuristic for estimating thepositional pressure produced by chess pieces is proposed. We evaluate the ’health’of a game position from a Systems perspective, using a dynamic model of theinteraction of the pieces. The identification and management of stressors and theconstruction of resilient positions allow effective cut-offs for less-promising gamecontinuations due to the perceived presence of adaptive capacity and sustainabledevelopment. We calculate and maintain a database of potential mobility for eachchess piece 3 moves into the future, for each position we evaluate in our searchtree. We determine the likely restrictions placed on the future mobility of thepieces based on the attack paths of the lower-valued enemy pieces. Initial searchefforts are based on goals obtained from the lowest-scoring of the vital diagnosticindicators. Initial results are presented.

keywords: complexity, chess, game theory, constraints, heuristics, planning,measurement, diagnostic test, resilience, orientor

1

A Proposed Heuristic - copyright (c) 2010 John L. Jerz

Contents

1 Overview 4

2 Introduction 4

3 Principles of Positional Chess 5

4 Systems Engineering 6

5 Systems Thinking 7

6 Goldratt’s Theory of Constraints and Thinking Process 8

7 Soft Systems Methodology 9

8 Measurement 10

9 Vulnerability 11

10 Resilience 11

11 Inventive Problem Solving 14

12 The Strategic Plan 15

13 From Orientors to Indicators to Goals 20

14 Shannon’s Evaluation Function 23

15 The Positional Evaluation Methodology 23

16 All Work and No Play... 29

17 John Boyd’s OODA Loop 30

18 Results 31

19 Conclusions 34

2


20 Appendix A: Related Quotations 37

References 38

3


1 Overview

The complexity present in the game of chess of-ten hinders planning efforts and makes simplequestions like ”what’s going on?” and ”whichside has the better position?” difficult to answer.

Indeterminate and unexpected events in thenear future might make revisions necessary forthese plans, often after only a few moves havebeen played.

We theorize that dynamic planning modelsbased on perceptions of constraints, the man-agement of stress, the readiness of resourcesto support strategy, resiliency, sustainable de-velopment, and sensitivity to both incrementalprogress towards goals and the emergence of newopportunities can be used with greater success.We seek positions which can serve as a platformfor future success, in a future that is often un-certain.

A proposed heuristic for a machine playingthe game of chess, taking advantage of conceptsfrom multiple disciplines, can be used to bet-ter estimate the potential of resources to supportstrategy and to offer better insight for determin-ing whether progress is being made towards re-mote goals. In a future that is uncertain, thereis a benefit to develop a strategic position fullof resilience, flexibility, and structures with thepotential for seizing new opportunities as theyemerge.

As we evaluate each game position and ori-ent our search efforts, we now consider the poten-tial to exploit and respond to new opportunitiesas time passes and new situations emerge frombeyond our initial planning horizon. Our flexibil-ity ideally allows a smooth and resilient responseto concurrent events as they unfold. We theo-rize that our focus on the constraints, as well as

the development of a resilient position, is a moreuseful level of abstraction for our game-playingmachine.

We examine concepts and values useful forplaying a positional game of chess, we developa perception useful for measuring incrementalprogress towards goals, and then look at po-sitions in chess games where the heuristic of-fers insight not otherwise obtainable. We con-clude that our orientation/evaluation heuristicoffers promise for a machine playing a game ofchess, although our limited evidence (at present)consists of diagrams showing the strategic (dy-namic) potential of the game pieces and an ex-ample of how these ’building blocks’ can be com-bined into vital indicators.

We see the chess position as a complex adap-tive system, full of opportunities of emergencefrom interacting pieces. Our aim in this paperis to reengineer the work performed by our ma-chine, mindful of the values commonly adoptedby experts and the principles of Systems think-ing, so that it might be done in a far superiorway [hammer95].

2 Introduction

This paper is concerned with heuristic algo-rithms. According to [koen03] a heuristic is any-thing that provides a plausible aid or direction inthe solution of a problem but is in the final anal-ysis unjustified, incapable of justification, andpotentially fallible. Heuristics help solve unsolv-able problems or reduce the time needed to finda satisfactory solution.

A new heuristic is proposed which offersbetter insight on the positional placement ofthe pieces to a chess-playing computer program.

4


The heuristic will have usefulness in the orienta-tion/evaluation methodology of a computer pro-gram, or as part of a teaching tool which explainsto a human user the reasons that one side or theother has an advantage in a chess game.

The heuristic involves constructing a tableof the future mobility for each piece, taking intoaccount the other pieces on the board, as wellas the likely constraints that these other piecesplace on this future movement. The heuristicconcept is described, and then examples are pre-sented from a software application constructedto demonstrate this concept.

Computer chess programs have historicallybeen weak in understanding concepts relating topositional issues. The proposed heuristic offers amethod to potentially play a stronger positionalgame of chess.

3 Principles of Positional Chess

Understanding the principles of positional chessis a necessary starting point before designingconcepts useful for a machine implementation.We select the relevant concepts of positionalchess which have been addressed by multiple au-thors.

[stean02] declares that the most importantsingle feature of a chess position is the activ-ity of the pieces and that the primary con-straint on a piece’s activity is the pawn structure.[znoskoborovsky80] generalizes this principle bydeclaring that if a piece attacks another, it isnot the weaker but the stronger one which hasto give way. [reshevsky02] notes that a good orbad bishop depends on placement of the pawns.Pieces should be ”working” and engaged, deliv-ering the full force of their potential and avoiding

influences which constrain. [levy76] discusses agame where a computer program accepts a posi-tion with an extra piece out of play, making a windifficult, if at all possible. Our evaluation shouldtherefore consider the degree to which a piece isin play or is capable of forcefully contributing tothe game.

Stean defines a weak pawn as one which can-not be protected by another pawn, therefore re-quiring support from its own pieces. This isthe ability to be protected by another pawn, notnecessarily the present existence of such protec-tion. Stean declares that the pawn structurehas a certain capacity for efficiently accommo-dating pieces and that exceeding that capacityhurts their ability to work together.

[aagaard03] declares that all positional chessis related to the existence of weakness in ei-ther player’s position. This weakness becomesreal when it is possible for the weakness to beattacked. The pieces on the board and theirconstraining interactions define how attackablethese weaknesses are.

[emms01] declares that is an advantage if apiece is performing several important functionsat once, while a disadvantage if a piece is not par-ticipating effectively in the game. Emms teachesthat doubled pawns can be weak if they are at-tackable or if they otherwise reduce the mobilityof the pawns. Doubled pawns can control vitalsquares, which might also mean denying mobil-ity to enemy pieces. Isolated pawns require thepresence of pieces to defend them if attacked.

[dvoretsky96] argues that creating multiplethreats is a good starting point for forming aplan. Improving the performance of the weakestpiece is proposed as a good way to improve yourposition as a whole.

5


[mcdonald06] gives an example of good dou-bled pawns which operate to restrict the mobil-ity of the opponent’s pieces and are not easilyattackable. His view is that every position needsto be evaluated according to the unique featurespresent.

[capablanca02] and [znoskoborovsky80]speak of how the force of the chess pieces actsin space, over the chessboard, and through time,in sequential moves. Critical is the concept ofposition, which is valued by greater or lesser mo-bility plus the pressure exerted against pointson the board or against opponent’s pieces. Pre-eminence, according to Capablanca, should begiven to the element of position. We are alsoinstructed that the underlying principle of themiddle game is co-ordinating the action of ourpieces.

[heisman99] discusses the important ele-ments of positional evaluation, including globalmobility of the pieces and flexibility.

[albus01] has written that the key to build-ing practical intelligent systems lies in our abilityto focus attention on what is important and toignore what is not. [kaplan78] says that it is im-portant to focus attention on the few moves thatare relevant and to spend little time on the rest.

The positional style is distinguished by po-sitional goals and an evaluation which rewardspieces for their future potential to accomplish ob-jectives. [ulea02] quotes Katsenelinboigen as say-ing that the goal of the positional style of chessis the creation of a position which allows for de-velopment in the future. By selecting appropri-ate placement of pieces, combinations ideally willemerge. [katsenelinboigen92] further describesthe organizational strategy of creating flexiblestructures and the need to create potential inadaptive systems that face an unpredictable en-

vironment.

[botvinnik84] and [botvinnik70] attempt ingeneral terms to describe a vision for implement-ing long range planning, noting that attackingthe paths that pieces take towards objectives isa viable positional strategy. Positional play aimsat changing or constraining the attack paths thatpieces take when moving towards objectives - ineffect, creating or mitigating stress in the posi-tion.

[hubbard07] identifies procedures which canbe helpful when attempting to measure intangi-ble values, such as the positional pressure pro-duced by chess pieces. [spitzer07] declares thatwhat gets measured get managed, that every-thing that should be measured, can be measured,and that we should measure what is most impor-tant.

4 Systems Engineering

A system [kossiakoff03] is a set of interrelatedcomponents working together toward a commonobjective. A complex engineered system is com-posed of a large number of intricately interre-lated diverse elements. von Bertalanffy is of theopinion [vonbertalanffy68] that the concept ofa system is not limited to material entities butcan be applied to any whole consisting of inter-acting components. This description could alsoapply to the situation faced by an agent play-ing a game, where the pieces represent the in-terrelated diverse elements. von Bertalanffy fur-ther identifies dynamic interaction as the cen-tral problem in all fields of reality (which wouldinclude playing a game), identifying system ele-ments in mutual interaction as the very core is-sue. Additionally, we are told to suspect systems

6


or certain systems conditions at work wheneverwe come across something that appears vitalis-tic or human-like in attribution. We thereforesee an opportunity to apply principles of SystemTheory, and in particular, Systems Engineering,to game theory.

How would we begin? We now applybasic principles of Systems Engineering from[kossiakoff03]:

A needs analysis phase defines the need fora new system. We ask ”Is there a valid needfor a new system?” and ”Is there a practical ap-proach to satisfying such a need?” Critically, canwe modify existing designs, and is available tech-nology mature enough to support the desiredcapability? The valid need would be to playa stronger positional game of chess, and exist-ing technology has struggled with the conceptof positional chess, as reflected in recent corre-spondence games which use Shannon-based pro-grams. It would seem that we need a differentapproach, which might be as simple as attempt-ing to emulate the style of play performed bystrong human players.

The concept exploration phase examines po-tential system concepts in answering the ques-tions: ”What performance is required of the newsystem to meet the perceived need?” and ”Isthere at least one feasible approach to achiev-ing such performance at an affordable cost?” Wewould answer the first question as simply thatour software function as an adequate analysistool, capable of selecting high-quality positionalmoves (with quality of move proportional to theanalysis time spent) when left ”on” for indefi-nite periods of time. As far as the second ques-tion, we might speculate that a new approachis needed, which feasibly we could model afterhumans playing the game.

The concept definition phase selects the pre-ferred concept. It answers the question: ”Whatare the key characteristics of a system conceptthat would achieve the most beneficial balancebetween capability, operational life, and cost?”To answer this question a number of alterna-tive concepts might be considered and their rel-ative performance, operational utility, develop-ment risk, and cost might be compared. The firstconcept we might consider would be the Shannonapproach, which has been the backbone of mostsoftware computer chess programs. We presentin this paper, defined in another section, anotherapproach. We therefore decide to explore theconcept definition phase in more detail, as welook for key system characteristics which con-ceptually could serve as the base of such a newsystem.

5 Systems Thinking

The heart of Systemsthinking, which is differentfrom analytical thinking,is the attempt to simplifycomplexity.

Systems think-ing is a disciplinefor observing wholes[senge06]. It is aframework for ob-serving interrelation-ships rather than

things, for observing the effects of change ratherthan static snapshots. The heart of Systemsthinking, which is different from analyticalthinking, is the attempt to simplify complex-ity [gharajedaghi06]. We see an opportunity toapply principles of Systems thinking to gametheory. [gharajedaghi06] discusses how inde-pendent variables are the essence of analyticalthinking. We might find, on closer inspection,

7


that our independent variables are not truly in-dependent - that the whole is more than a simplesum of the parts. Emergent properties of a sys-tem are a product of interactions and cannot[gharajedaghi06] be analyzed or manipulated byanalytical tools, and do not have causal explana-tions. We must instead attempt to understandthe processes that produce them by managingthe critical interactions. One might think ofemergent properties as being in the process ofunfolding. What makes it possible to turn thesystems approach into a scientific approach isour belief that there is such a thing as approxi-mate knowledge [capra88].

[gharajedaghi06] informs us that under-standing consequences of actions (both short-and long-term, in their entirety), requires build-ing a dynamic model to simulate the multiple-loop, nonlinear nature of the system. Our modelshould aim to capture the important delays andrelevant interactions among the major variables,but need not be complicated.

We therefore attempt to approach the ori-entation/evaluation methodolgy from a Systemsperspective. We will look at the interactions ofthe pieces and their ability to create and miti-gate stress. We adopt constraints, vulnerability,dynamic modeling, and resiliency as higher levelconcepts which will help cut through the com-plexity and steer search efforts along the linesof the most promising moves. The technique ofmodeling [kossiakoff03] is one of the basic toolsof systems engineering, especially in situationswhere complexity and emergence obscure the ba-sic facts in a situation.

From [anderson97], we apply Systems think-ing to look at the web of interconnected, circularrelationships present in a chess position, confi-dent that this is the proper tool for doing so.

Our reason for believing this is that everythingin a chess position is [anderson97] dynamic, com-plex, and interdependent. Things are changingall the time, analysis is messy, and the interac-tions of the pieces are all interconnected.

we apply Systems think-ing to look at the webof interconnected, circularrelationships present in achess position, confidentthat this is the proper toolfor doing so.

As we attemptto construct resilientgame positions, wefollow [tierney07]and identify 4 systemlevel components ofresiliency: Robust-ness - the ability of

our game-playing agent to withstand our op-ponent’s forces without degradation or loss ofperformance; Redundancy - the extent to whichpieces, structures or moves are substitutable,that is, capable of sustaining operations, if degra-dation or a surprise move occurs; Resourceful-ness - the ability of our agent to diagnose andprioritize candidate moves and to initiate solu-tions by identifying and mobilizing appropriateamounts of search time and game resources; andRapidity - the capacity to restore or sustainfunctionality in a timely way, containing lossesby graceful failure and avoiding other disrup-tions.

6 Goldratt’s Theory of Con-straints and Thinking Pro-cess

[goldratt04] has developed a Theory of Con-straints which postulates that organizations andcomplex systems are hindered from reachingtheir goals by the constraints placed on that sys-tem. Identifying those constraints and remov-

8


ing them can speed progress towards these goals.[scheinkopf99] describes how Golratt’s institutebegan to modify the original concepts to servethe needs of clients who wanted more generalizedprocedures to solve a wider variety of problemsoutside of a factory production environment.

Goldratt’s ideas, while seemingly original,can be properly classified as a Systems thinkingmethodolgy which emphasizes raw human think-ing over the construction and implementationof computer models. Each approach is useful.Also emphasized is a vocabulary and terminol-ogy which allows groups to construct and discussanalytical diagrams of feedback loops and iden-tify root causes.

[dettmer07] explores Goldratt’s ThinkingProcess and identifies procedures to logicallyidentify and eliminate undesirable effects fromsystems and organizations.

[dechter03] explains that a model of realitybased on constraints helps us to achieve an effec-tive focus for search efforts, and is similar to theheuristic process that humans use to search foreffective solutions in complex situations. Remov-ing the constraints partially solves the problem,and measured progress towards removing theseconstraints can steer and prune our search effortswhen identifying positions and lines of analysiswhich are promising.

[hollnagel06] speaks of identifying and mon-itoring the ”barriers” which keep the system re-sponse within safe margins. Also, the use of ”au-dit tools” is envisioned as a method to measurethe effectiveness of the containment.

7 Soft Systems Methodology

[checkland06] presents a modified Systemsmethodology where complexity and confusionare tackled through organized exploration andlearning. We envision the continuous changepresent in the game of chess as a complex statethat needs to be (at least partially) understoodin order to make exploration efforts (of an expo-nentially growing search tree) more efficient.

We conceptualize a learning agent whichgathers relevant information as it seeks to de-termine the cumulative stress present in the po-sition, in order to determine the paths of ex-ploration - the ones of promise and the onesof risk mitigation. Our Systems model (makingup our orientation/evaluation methodology) willideally suggest to us what moves are promisingor worth our time exploring, as well as to rec-ommend which paths can, justifiably, wait untillater. The heuristics which make up this learn-ing and decision making process will be discussedin a later section. Critical to these heuristics isthe concept that all dynamic behavior emergesfrom a combination of reinforcing and balancingfeedback loops [anderson97].

what we really need is aninsightful and informed di-rection for exploration anda notion for how press-ing this direction becomesstrategically.

Curiously, ourorientation/ evalua-tion ’function’ willbecome a method-olgy rather than aformula. We shareBotvinnik’s puzzle-

ment with an evaluation ”number” [botvinnik70]when what we really need is an insightful andinformed direction for exploration (orientation)and a notion for how pressing this direction be-comes strategically.

9


The insight we obtain by this method is usedas a spring for action [checkland06], as our soft-ware agent decides what to do next, after com-pleting the current evaluation. Our ”evaluation”ideally produces candidate directions for explo-ration, as part of a carefully constructed strate-gic plan, and indicates which paths are criti-cal and which can wait until later. For Check-land, our model is an intellectual device we useto richly explore the future, using stress trans-formation as our chosen strategy, or worldview.Simply put, our model tells us which paths toexplore.

Our estimate of the winning chances of acandidate position critically depends on the iden-tification and exploration of the critical candi-date sequences of moves, and the correct classifi-cation of the worthiness (for timely exploration)of such candidate positions. A heuristic estimateof the cumulative stress present in the position,at the end of our principal variation, can be cor-related, if desired, with winning chances. How-ever, our operational use of this value is for (cy-bernetically) steering search efforts.

8 Measurement

What gets measured gets managed. [spitzer07]speaks about the critical need to develop metricswhich are predictive and which measure strate-gic potential. We seek to measure how ”ready”our pieces are (and the structures they form) forsupporting strategy [kaplan04], especially whenthe future positions we face are not entirely de-terminable. An asset (such as a game piece) thatcannot support strategy has limited value. Partof our orientation/evaluation of the promise of aposition should ideally include the readiness ofthe pieces and structures to support future de-

velopments. We embrace the principle that whatyou look for is what you find.

For [zeller80], measurement clarifies our the-oretical thinking and links the conceptual withthe observable. For measurement to be effective,we must first construct a valid sensor. In our at-tempts at measurement, we seek empirical indi-cators which are valid, operational indicators ofour theoretical concepts. We desire to constructa diagnostic indicator which gives, as a result, auseful predictive measure of future promise anda direction for future exploration.

Although it would seem that a perceptionbased on simplicity would yield the best all-around results, [blalock82] points out the diffi-culties trying to simultaneously achieve simplic-ity, generality, and precision in our measurement.If we have to give up one of these three, it isBlalock’s opinion that parsimony, or the scien-tific idea that the simplest explanation of a phe-nomenon is the best one, would have to be sac-rificed in order to achieve the other two. There-fore, our attempts to describe a complex orien-tation/evaluation methodology are grounded inthe two-fold goals of generality (it must be ap-plied to all positions we encounter) and preci-sion (otherwise, search efforts are wasted on lesspromising lines).

The alternative view is presented by[gunderson10], who declares that his experiencehas suggested to be as ruthlessly parsimoniousand economical as possible while still retainingresponsiveness to the management objectives andactions appropriate for the problem. Addition-ally, we are advised that the variables selectedfor system description must be the minimumthat will capture the system’s essential qualita-tive behavior in time and space. We are furthercautioned that the initial steps of bounding the

10


problem determine whether the abstract modelwill usefully represent that portion of reality rel-evant to policy design. We must therefore aim tosimplify, but not so much as to impact the use-fulness of the tool for predicting promising pathsof exploration.

9 Vulnerability

Critical to the success of a computer chess pro-gram that attempts to play in the positionalstyle is the concept of vulnerability. The piecesand structures that are or have the potential tobecome vulnerable will become a focus of oursearch and exploration efforts and will serve astargets for our long-range planning.

We follow [mccarthy01] and conceptualizevulnerability as a function of exposure, sensi-tivity, and adaptive capacity. Consequently, thesensor we develop should attempt to measure ex-posure to threats, the sensitivity to the effects ofstimuli, and the ability to adapt and cope withthe consequences of change. We envision a sensorthat produces a forecast of potential vulnerabil-ity as an output. This forecast can guide explo-ration efforts by identifying targets for the usefulapplication of stress and serve as one indicatorof a promising position.

Additionally, we predict that any machine-based attempt to zero-in on vulnerability thatdoes not address this conceptual base runs therisk of missing opportunities in exploring theexponentially growing tree of possibilities thatexist for each game position. A missed oppor-tunity might equally prevent us from increas-ing positional pressure on our opponent, or in-stead, might dissipate the pressure that we havecarefully accumulated over time. Our orienta-

tion/evaluation of the winning chances presentin the position might not be as accurate as itcould be unless we explore the promising posi-tions and consider the vulnerabilities that arepresent.

We conceptualize that the reduction of vul-nerability and the pursuit of sustainable devel-opment are interrelated aims [smith03].

10 Resilience

Vulnerability is the condition that makes adap-tation and resilience necessary as a mitigation[worldwatch09]. The scientific study of resiliencebegan in the 1970s when Norman Garmezy stud-ied well-adapted children who had overcomethe stress of poverty [lukey08]. Resilience isalso an important research area in military sci-ence [friedl07] and in the study of ecosystems[folke02]. We find this concept useful in gametheory.

In our view, adapted from [luthar03], re-silience refers to an ongoing, dynamic develop-mental process of strategically positioning re-sources that enables the player in a game tonegotiate current issues adaptively. It also pro-vides a foundation for dealing with subsequentchallenges, as well as recovering from reversalsof fortune.

We desire a generic, con-tinuous ability (both duringcrisis and non-crisis gamesituations) to cope with theuncertain positions that ar-rive from beyond our plan-ning horizon.

We desire ageneric, continuousability (both duringcrisis and non-crisisgame situations) tocope with the uncer-tain positions thatarrive from beyond

11


our planning horizon. Ideally, we seek to createa useful positional pressure to force these arriv-ing positions to be in our favor, or minimally,to put a ”cage” of constraints around the enemypieces. Flexibility, adaptive capacity, and effec-tive engagement of available resources will beour weapons against the dynamic changes whichwill unfold in our game [hollnagel08].

Ideally, we will look for and manage theheuristic early warning signs of a position ap-proaching a ”tipping point”, where a distinct,clear advantage for one side emerges from anunclear array of concurrent piece interactions.We agree with [walsh06] that resilience cannotbe captured as a snapshot at a moment in time,but rather is the result of an interactive processthat unfolds over time.

The failure to include resilience measure-ments like this in planning efforts might causea house-of-cards effect, as the weakest link inour plan might collapse, due to effects we cannotinitially perceive. This might create a situationfrom which we cannot recover, or from which wecannot continue to mount increasing positionalpressure on our opponent.

A central concept is the construction of aresilient position, one that ideally 1. possesses acapacity to bounce back from disruption in theevent of an unforeseen move by our opponent, 2.produces advantageous moves in light of smallmistakes by our opponent, or 3. permits us topostpone our search efforts at early points forless promising positions, with greater confidencethat we have sufficient resources to handle futureunforeseen developments if the actual game playproceeds down that route. In simplest form, wemight just measure the ability to self-organize.

When change occurs, the components thatmake up resilience provide the necessary capac-

ity to (minimally) counter and (ideally) seizenew opportunities that emerge [folke02]. Re-silience is (minimally) insurance against the col-lapse of a position and (ideally) an investmentthat pays dividends in the form of better posi-tions in the future. With no pun intended, wesee the struggle to control the unknown, emerg-ing future positions as a ”Red Queen’s Race”,where in tough-fought games against a talentedopponent, it might take all the effort possible tomaintain equal chances. Extraordinary effortsinvolving hundreds of hours of analysis per move(such as in correspondence games) might be re-quired to maneuver to an advantage [jerz07].

For [reivich02], resilience is the basicstrength. [hollnagel06] suggests that ”incidents”,which for us might be the construction of shortsequences of just the top few promising moves(diagnostic probing), might reveal insight toboundary conditions in which resilience is eithercausing the system to stretch to adapt, or buckleand fail. Emergency response teams use prac-tice incidents to measure resilience as unforeseenevents emerge during operations. Fire drills, ran-dom audits and security searches, even surprisetests are diagnostic tools used to detect and cor-rect situations lacking in resilient capabilities.

We acknowledge the reality that our abilityto handle an unexpected move or critical situa-tion in a game depends on the structures alreadyin place [weick07]. We desire [weick07] to payclose attention to weak signals of failure that arediagnostic indicators of potential problems in thesystem. We also perform diagnostic probing touncover and steer game play towards positionswhere there are multiple good moves - an addi-tional sign of resilience.

12


We speculate that the abil-ity to construct a resilientposition and the ability toperceive stress in a posi-tion are two primary con-ceptual differences betweena game-playing man andmachine.

We speculatethat the ability toconstruct a resilientposition and the abil-ity to perceive stressin a position are twoprimary conceptualdifferences betweena game-playing manand machine. We believe that these abilities canbe emulated through the use of custom diagnos-tic tests.

Humans construct resilient positions (instrategic situations) almost by instinct and oftenwithout conscious thought [fritz03], in diversesituations such as driving automobiles, playingsports games, conducting warfare, social inter-action, and managing resources in business orwork situations. Humans have such refined abili-ties [laszlo96] to make predictions, interpret cluesand manipulate their environment, that usingthem is frequently effortless, especially if per-formed daily or over extended periods of time.[aldwin07] points out that humans appear to behard-wired physiologically to respond to theirperceptions of stress - so much so that effectiveresponses can be generated continuously withlittle conscious thought. We therefore see themachine-based perception of stress as critical tosuccessful performance in a game.

Additionally, much has been written[fagre09] [folke02] concerning ecosystems, re-silience, and adaptive management that has di-rect application to game theory.

Conceptually, we desire the equivalent of a”mindset” that can successfully cope with prob-lems as they arise, as we attempt to 1. exam-ine the promising positions, 2. evaluate the cor-

responding winning potential and 3. steer oursearch efforts through an exponentially grow-ing ”tree” of strategically important move se-quences. This process is aided by the heuristicmeasurement of adaptive capacity, as the thou-sands of unexamined positions that lie just be-yond the point of our search cut-offs must beresilient enough to counter whatever unknownevents emerge. Before we cut-off our search ef-forts, we might choose to search the less resilientpositions a little deeper as a mitigation of un-foreseen events.

Rather than thinking about resilience as”bouncing back” from a shock or stress, it mightbe more useful to think about ”bouncing for-ward” to a position where shocks and stresseshave less effect on vulnerabilities [walsh06][worldwatch09]. Integral to the definition of re-silience are the interactions among risk and pro-tective factors [verleye-prepub] at an agent andenvironmental level. Protective factors operateto protect assets, such as pieces in a game, atrisk from the effects of the risk factors.

We agree and conceptualize that, while riskfactors do not automatically lead to negativeoutcomes, their presence only exposes a game-playing agent to circumstances associated witha higher incidence of the outcome; protective ormitigating factors such as constraints can con-tribute to positive outcomes - perhaps regardlessof the risk status.

We accept as an operational concept of re-silience, the fourth proposal of Glantz and Slo-boda [glantz99], which involves the adoption ofa systems approach. We consider both posi-tive and negative circumstances and both in-fluencing and protecting characteristics and theways in which they interact in the relevant situ-ations. Additionally, this conceptualization con-

13


siders the cumulation of factors and the influ-ences of both nearby and distant forces. In ad-dition, [elias06] discusses a model of resiliencein which specific protective influences (which wesee as constraints) moderate the effect of riskprocesses over time, in order to foster adaptiveoutcomes.

We propose [gunderson10] an approachbased on resilience, which would emphasize theneed to keep options open, the need to viewevents in a larger context, and the need to em-phasize a capacity for having a large number ofstructural variations. From this we recognize ourignorance of, and the unexpectedness of futureevents. The resilience framework does not re-quire a precise ability to predict the future, butonly a capacity to devise systems that can absorband accommodate future events in whatever un-expected form they may take. If we could cramMacGyver into our software, we would certainlydo so.

11 Inventive Problem Solving

Our chess program attempts to be, like Mac-Gyver, an inventive problem solver. We see ef-fective problem solving as an adaptive processthat unfolds based on the nature of the prob-lem, rather than as a series of specific steps[albrecht07]. We agree with [browne02] thatknowing the difference between what’s impor-tant and what isn’t is a basic starting point.

We attempt to navigate an exponentiallygrowing search tree, selecting those paths for ex-ploration that are promising, interesting, risk-mitigating, and resilient in the face of an un-known future. We are concerned at all timeswith the potential of a position to serve as an ad-

vancing platform for future incremental progresstowards positional goals [fritz07]. We will accom-plish this by knowing the outcomes we want andlooking tirelessly for them. [savransky00] liststhree major requirements for a problem-solvingmethodology, which we modify slightly for thepurposes of a machine playing a game:

1. It should focus on the most appropriateand strongest solutions

2. It should produce, as an output, the mostpromising strategies

3. It should acquire and use important, well-organized, and necessary information at all stepsof the process

[savransky00] additionally suggests that weshould focus on gathering the important in-formation, information which characterizes theproblem and makes it clear, including contra-dictions. Any simplifications we perform shouldaim at reducing the problem to its essence andbe directed towards our conceptual, strategic so-lution.

As an example, typical American news re-ports each day announce the results of the DowJones index of stocks. This index serves as agood indicator of overall market performanceand can help answer the question ”How didthe markets do today?”. We seek an equiva-lent summary numerical representation of reality[march94] which can serve as a guiding light anda measure of progress towards our distant posi-tional goals. We are not restricted to the use of asingle scoring metric, and can combine multiple,critical metrics in creative ways, including theselection of the lowest score from several indica-tors to provide a search focus. We should firstform a concept of what should be measured, thencreate a sensor array which allows us to measure

14


and perform search efforts (in an exponentiallygrowing tree of possible continuations) with rea-sonable efficiency.

12 The Strategic Plan

We see a strategic plan [bradford00] as a sim-ple statement of the few things we really needto focus on to bring us success, as we define it.It will help us manage every detail of the game-playing process, but should not be excessivelydetailed. It will encapsulate our vision and willhelp us make decisions as we critically choose,or choose not, to explore future positions in oursearch tree. We see the formation and executionof the strategic plan as the most effective way toget nearer to the goal state, especially in a com-petitive environment where our opponent is alsoattempting to do the same.

We see the role of themachine as merely that ofan executor of a strategicplan... we simply ask themachine to do what it istold.

We see the roleof the machine (inplaying a game suchas chess) as merelythat of an executorof a strategic plan,where we have previ-ously defined (through programmed software in-structions) the specific answers to the questions”Where do we want to be?” ”How will we knowwe have reached it?” ”What is changing in theenvironment that we need to consider?” ”Whereare we right now?” and ”How do we get fromhere to our desired place?” [haines98]. In our vi-sion, the intelligence is located in the strategicanswers to these questions and in the skill of theprogrammer in implementing them - we simplyask the machine to do what it is told.

If one game-playing computer program isbetter than another, as demonstrated in a tour-nament of many games played, we speculate thatthe reason is either a better strategic plan ora better software implementation of that plan.Therefore, improvements in computer chess pro-grams ideally should focus on these two areas,including answers to the questions presentedabove. For Haines, all types of problems andsituations (which include selecting a move in agame) can benefit from a strategic approach.

Before we develop our strategic plan, weask ourselves and ponder three critical questions[jorgensen07]: 1. what are the underlying prop-erties that can explain the responses we see onthe game board to perturbations and interven-tions, 2. are we able to formulate at least build-ing blocks of a management theory in the form ofuseful propositions about processes and proper-ties, and 3. can we form a theory to understandthe playing of chess that is sufficiently developedto be able to explain observations in a practicalway for choosing a move? We do not see the needto construct mathematical proofs - the concept ofa useful proposition allows us flexibility in choos-ing an approach and allows us to consider multi-ple options before settling on one with the mostpromise. We return to these critical questionswhenever we seek direction or clarification in anapproach, or consider starting over. We look toother disciplines (as suggested by [boyd87]) andto other professionals who have sought answersto the same questions, which must be asked in ageneral way to any management problem.

Central to our strategic plan are the follow-ing concepts [jorgensen07]: system behavior fre-quently arises out of indirect interactions thatare difficult to incorporate into connected mod-els, that we may not know exactly what happens,

15


but approximately what happens, and that wecan use holistic metrics to measure the growthand development of a position in a game. We ac-knowledge that systems have a complex responseto disturbances, and that constraints play a ma-jor role in interactions. As a strategy we seek amethod to determine (and to resolve uncertaintyconcerning) 1. the promising candidate moves ina given position, and 2. the chances of sustain-able development in a position, allowing us topostpone (if necessary) the exploration of futureconsequences.

In a building block for ourstrategic plan, we examinethe position under evalu-ation for the presence ofstressors

In a buildingblock for our strate-gic plan, we exam-ine the position un-der evaluation for thepresence of stressors[glantz99] and determine their contribution tothe cumulative stress in the position. A stressoris a real object on the game board, such as apiece, or an object or property that might be-come real in the future, such as a Queen from apromoted pawn, a stone in the game of Go, ora King in the game of draughts/checkers. Usingour stressors, we seek to establish a structuraltension [fritz89] that, if resolved, leads to posi-tions that favor us.

The stress we seek to place on our opponent[glantz99] is the kind that interferes with or di-minishes the development of our opponent’s cop-ing repertoire, search and planning abilities, ex-pectations and potential resilience. This stress isideally so effective that we create a platform fromwhich we can apply even more stress. We forceour opponent to divert additional resources tocontaining our threats, making fewer resourcesavailable for threats of his own.

We attempt to cope withthe stressors of our oppo-nent by weakening them orreducing their influence toa manageable level

We attempt tocope with the stres-sors of our opponentby weakening themor reducing their in-fluence to a manage-able level [snyder01] -

there is no compelling need to make their ef-fects go away completely. For [vonbertalanffy68],stress is a danger to be controlled and neutralizedby adaptive mechanisms. We gather diagnosticinformation that is used to determine the readi-ness of the pieces to inflict stress on the oppo-nent and lessen the stress imposed by the enemypieces on our weak points. The creation of ef-fective stress and the perceived mobilization offorces to mitigate it will become a central con-cept in our orientation/evaluation. Our orienta-tion/evaluation looks not so much to goal seek-ing/optimizing a ”score” as to sustaining rela-tionships between/among the pieces and learn-ing what happens as stress is moved from onearea of the board to another.

Figure 1: Simplified model (dynamic hypothesis) of posi-tional pressure for each piece

Figure 1 shows a simplification of the pro-posed model of positional pressure for each piece,based on principles of system dynamics. Thefuture mobility of each piece targets opponentpieces, the trajectories taken by these pieces, and

16


certain other weaknesses such as weak pawns,the opponent’s king, or undefended pieces. Thisthreat is mitigated (but not reduced completely)by the protective factor of constraints imposedby the lower-valued enemy pieces. The residual”Stock” is the effective stress that can be felt byour opponent, and which we seek to increase. For[warren08], the management of critical resourcesis part of an emerging theory of performance:performance depends on resource contribution,resource contribution accumulates and depletes,and this depends on existing resource contribu-tion levels.

Figure 2 shows the plan for managing theperceived stress by incentivizing a coping strat-egy, such as the placement of constraints, in or-der to control the effects of the overall cumulativestress. We seek to maintain a resilient positionfull of adaptive capacity.

Figure 2: As perceived stress increases, we increase the in-centive to cope with the stress

Things start to get complicated when weremove stress (and the associated constraints)from one area of the board and apply it to

other areas. The short- and long-term effectsof these stress-exchanging maneuvers are exam-ined through prioritized search efforts, and in ouropinion represent the essence of playing a gamesuch as chess. This conceptual model will formthe basis of the machine’s perception. We relyon the simplifying principles of system dynam-ics to predict and anticipate the effects of suchstress transformation.

From [friedl07] we define a stressor as anychallenge to a player in a game that evokes aresponse. Coping is the set of responses thatsustain performance in the presence of stressors.Resilience is the relative assessment of copingability. We desire to create in our opponent’sposition a condition similar to fatigue, definedby Friedl (and modified for game theory) as thestate of reduced performance capability due tothe inability to continue to cope with stressors.We follow [fontana89] and define stress as a de-mand made upon the adaptive capacity of aplayer in a game by the other. We theorize acorrelation between the state of stress-inducedreduced performance capability and an ”advan-tage”, or favorable chances for the more capableplayer winning the game.

we are dealing with a pro-cess whose effects taketime in revealing them-selves

Strategically, weseek to identify thestress present in theposition by 1. exam-ining the demands of

each stressor, 2. the capacity of each player torespond to those demands, and 3. the conse-quences of not responding to the demands.

17


we will predict the win-ning chances at some fu-ture point in time, afterthe present circumstancesprogress and the structuresin place are allowed to un-fold

We carefully de-fine weakness so thatthe stress and tensionwe create is focusedand effective. The in-formation we gatherfrom the interactingpieces should be pre-cise enough to get results - it does not needto be perfectly accurate. Information is power[bradford00], especially in strategic planning.Along the way, we will need to make assumptionsabout whether or not the stress we are inflictingon our opponent is increasing or decreasing, andwhether it is effective or not effective. We mightexplore promising paths in detail to confirm ourassumptions, or we might just rely on our mea-surements of resilience.

Critical is our ability to focus our search ef-forts on lines that are promising, with regard tothe oriented application of stress and the pre-dicted effects on future lines of play. In our opin-ion [schumpeter08], we are dealing with a pro-cess whose effects take time in revealing them-selves - we will predict the winning chances atsome future point in time, after the present cir-cumstances progress and the structures in placeare allowed to unfold, including the newly emer-gent features which we are not currently able toperceive. We establish a portfolio of promisinglines, and see where they go. We invest our timeand processor resources in the most promising,but only after investigating the promising via aswarm of lower-risk experiments [hamel03]. Wedefine a concept of stress which lets us focus oursearch efforts on anticipated promising lines. Werely on the promise of adaptive capacity presentin resilient positions to sustain our efforts inlines where the perception of weaker cumulative

stress, time constraints, and our model of pur-poseful activity do not permit us to explore.

Figure 3: Conceptual Framework, from Chapin, 2009, p.21,(placeholder until new diagram is created)

We theorize that the dynamic forces ofchange during the playing of a game have anadaptation cost associated with them [kelly04][zeidner96]. This might come from a shift in ex-pectations, or from a required recovery from dis-ruptions. We make ”payments” for these adap-tation costs from our ”bank” of resilience. If welose our positional resilience, we lose our flex-ible ability to adapt to the unknown require-ments of change. Likewise, we can make ”de-posits” to our resilience account during quietperiods of maneuver, if we choose, and if wevalue resilience as an element of our orienta-tion/evaluation methodology. [friedl07] refers tothis concept as pre-habilitation. We seek to at-tack our opponent’s capacity to respond and tostrengthen our own, so that the dynamic forcesof change that drive the game continuation willcause the unknown positions arriving from be-yond our planning horizon to be in our favor.

We seek a resilient mindset. Specifically, wefollow [coutu03] and aim for three fundamental

18


characteristics: we identify and face the realityof the stresses and constraints present in the po-sitions we evaluate, we identify and reward thevalues of positional chess, and we develop anability to improvise solutions based on whateverresources are available to us. We seek to preparefor an unknown future that can be influencedby the strategic placement of resources in thepresent.

In the generalized exchange of pieces,squares, and opportunities encountered in gameplaying [botvinnik70], we seek to establish apressure that has a realistic chance to resolvein our favor, as determined by heuristic probingand the examination of promising future gamesequences. We desire to create and sustain aweb of stress which threatens to become real andtherefore has the property that [vonneumann53]has called ”virtual” existence. Our opponentmust ”spend” or dedicate resources to containor adapt to the threats. Even if a particularthreat is contained, it nevertheless has partici-pated in the dynamic shaping and influencing ofthe events that emerge and unfold in the game.

We will succeed at forming an effectivestrategic plan when we have identified our values,determined the key drivers to performance, de-veloped a sensor which is effective at measuringthem, and have focused on the lines of play thatare promising. At all times we wish to maintaina resilient position, which increases our ability toeffectively handle the unknown positions whichlie beyond the horizon of our explorations.

We will use two key strategies [maddi05] tobecome and remain resilient: we will develop thevision to perceive changes in the promise of a po-sition (as they emerge from our heuristic explo-rations), and we seek flexibility to act quickly,while remaining focused on our goals of estab-

lishing and maintaining a useful structural ten-sion. We seek [kelly04] a balanced portfolio of re-silience skills, where ideally we are focused, flex-ible, organized, and proactive in any given situa-tion. We believe that resilient responses [kelly04]are the result of resilience characteristics operat-ing as a system, as we evaluate and predict theemergent results of change.

Following [jackson03], we avoid placinga complete reliance on specific predictions ofthe future, concentrating on relationships, dy-namism and unpredictability as much as we doon determinism. In our plan, we will adapt asnecessary and seize new opportunities as theyemerge from the ”mess”. We seek to focus onidentifying and managing the structures that willdrive the behavior of the game, and acknowledgethe reality that large portions of the future pos-sibilities will go unsearched and unexplored (un-til they emerge from beyond our planning hori-zon and into our perception). As we deepen ourexploration and learning, we see new opportu-nities emerging as much for us as for our op-ponent, and requiring us to re-direct our search(and planning) efforts. We see the widest pos-sible spectrum of adaptive responses competingfor the fittest solution [bossel98]. Diversity is animportant prerequisite for sustainability.

Where possible, we follow the advice ofFrench military strategist Pierre-Joseph Bourcet[alexander02] and spread out attacking forcesover multiple objectives, forcing an adversary todivide his strength and prevent concentration.Such divided forces - a ”plan with branches”, canbe concentrated at will, especially if superior mo-bility is present, as recommended by French mil-itary strategist Guibert. As an end result of allthis positional pressure and maneuver, we seekwhat Napoleon sought, that is [alexander02], the

19


nature of strategy consists of always having (evenwith a weaker army) more forces at the pointof attack or at the point where one is being at-tacked than the enemy. Such positions have thepossibility of the win of material, and are thenapproached from a more tactical perspective -one that current heuristics handle well.

13 From Orientors to Indica-tors to Goals

We have found six basicsystem orientors (existenceand subsistence, effective-ness, freedom of action, se-curity, adaptability, coex-istence) that apply to allautonomous self-organizingsystems -Hartmut Bossel

We identifyand adapt the ap-proach of [bossel76][bossel77] [bossel94][bossel98] [bossel99][bossel07] and[muller98] to concep-tualize the ’health’and evaluation of achess position, which in our vision shares muchwith that of an ecosystem. We seek indicatorswhich realize Bossel’s 6 basic high-level orientingproperties of existence and subsistence, effective-ness, freedom of action, security, adaptability,and coexistence. We theorize with Bossel thatthese properties are each vital diagnostic indi-cators of successful system development, andwe aim to steer our initial search efforts alongpaths which seek to improve the weakest of theseproperties. These indicators must give a fairlyreliable and complete picture of what really mat-ters [bossel98]. If a system is to be viable inthe long run, a minimum satisfaction of each ofthese basic orientors must be assured [bossel94].We theorize with Bossel that the behavioral re-sponse of the system is conditional on the chosenindicator set: problems not perceived cannot be

attacked and solved [bossel77]. Meaningful non-routine behavior can only occur by referenceto orientors, which are therefore key elementsof non-routine behavior [bossel77]. The possiblesuccesses of unoriented non-routine behavior canbe only chance successes [bossel77].

We directly follow [lockie05] in our concep-tual foundation of indicators, in which we di-rectly quote due to the importance of the con-cept. Indicators are instruments to define andmonitor those aspects of a system that providethe most reliable clues as to its overall well-being.They are used, in other words, to provide costand time-effective feedback on the health of asystem without necessarily examining all compo-nents of that system. According to proponents,the validity of indicators is based on the degreeto which the wider network of components andrelationships in which they are situated link to-gether in a relatively stable and self-regulatingmanner, and the degree to which the indicatorsthemselves represent the most salient or criti-cal aspects of the system that can be monitoredover time. [maslow87] notes that needs, alongwith their partial goals, when sufficiently grati-fied cease to exist as active determinants or or-ganizers of behavior.

We see a value in the two-phased approach of[bossel94]: first, a certain minimum qualificationmust be obtained separately for each of the basicorientors. A deficit in even one of the orientorspotentially threatens our long-term survival fromour current position. Our computer software willhave to focus its attention on this deficit. Onlyif the required minimum satisfaction of all basicorientors is guaranteed is it permissible to try toraise system satisfaction by improving satisfac-tion of individual orientors further - if conditions,in particular our opponent, will allow this.

20


Health and fitness of a sys-tem require adequate satis-faction of each of the sys-tem’s basic orientors. Plan-ning, decisions, and actionsin societal systems musttherefore always reflect atleast the handful of basicorientors (or derived crite-ria) simultaneously. Com-prehensive assessments ofsystem behavior and devel-opment must also be multi-criteria assessments...

We see goal func-tions as operating totranslate the funda-mental system needsexpressed in the ba-sic orientors into spe-cific objectives link-ing system responseto properties ob-served on the chessboard. We conceptu-alize that goal func-tions emerge as gen-eral properties in thecoevolution of the chess position and dynamic,future development. They can be viewed as spe-cific responses to the need to satisfy the basicorientors. For example, mobility is related toadaptability, constraints relate to coexistence,king safety is related to the orientors of secu-rity and existence, virtual existence and stressare related to effectiveness, material is relatedto existence, security and adaptability, etc. Wecan creatively come up with new indicators forour search orientation, but we see them fittingwithin the proposed framework and ’dimensionof concern’ as outlined previously.

We see the vital orientors, which express ourvalues, as operating together to create a selec-tion method for our immediate goals. We seean interesting similarity with the ”ABC” (air-way, breathing, circulation) priority system usedin emergency room and rescue operations whendeciding what to do next with an accident vic-tim. The rescue team performs the set of vitaldiagnostic tests and then focuses their immedi-ate attention on the critical indicator that scoresthe lowest. The ”health” of the victim (and infact the direction to take next) would not be

based on an average or summation score of thevital indicators, but instead on the vital indi-cator which scores the lowest. The goal, thenwould be to do something which improves thescore returned by that indicator. If more thanone indicator is below a certain critical threshold(such as, the patient is not breathing and thereis no circulation), then Cardiopulmonary Resus-citation (CPR) would need to be performed - im-provement of the airway, breathing and circula-tion indicators are all simultaneously attempted.

...a system’s developmentwill be constrained by theorientor that is currently’in the minimum’. Par-ticular attention will there-fore have to focus on thoseorientors that are currentlydeficient. -Hartmut Bossel

We also see asimilarity to the com-mon yearly perfor-mance evaluationwhich is traditionallyperformed by Amer-ican management oneach company em-ployee, or even a re-

port card given to a student. The ritual evalua-tion will list strengths, weaknesses, and expecta-tions, and it is also common to list improvementsnecessary to reach the next performance level.The smart worker will examine his vital, multi-criteria diagnostic assessment and orient his orher efforts (during the next year) towards im-proving the weakest scoring of these indicators,while continuing to leverage strengths and meetthe listed expectations.

We see similarities to Festinger’s principle ofcognitive dissonance [festinger57], where a per-ception of dissonance between an observed indi-cator and a desired value leads to activity ori-ented towards reduction of the perceived disso-nance. Festinger believes that reduction of dis-sonance is a basic process in humans, precededfirst by perception and identification.

21


Our experience in computerchess over the past fewyears seems to indicate thatfuture chess programs willprobably benefit from eval-uation functions that alteras the general chess envi-ronment changes. -PeterFrey, Chess Skill in Manand Machine, 1977

We see the chessprograms of the fu-ture as addressingthis conceptual foun-dation, in creativeways and approachesthat cannot yet beenvisioned by today’sdevelopers. Ourconceptualization ofstress managementand the construction of resilient positions asindicators are, ideally, part of an operational re-alization of the six orientors. If our concept failsas an orientor or focus of search efforts, thenit needs to be modified or itself re-engineered.Perfectly usable indicators might overlap, or re-quire too much processor time to implement.Perhaps what is required is the art of a talentedprogrammer/chess player to select a set of indi-cators which also orient with effective insight.

Our immediate goals,therefore, emerge from theweakest indicators (results)of the vital diagnostictests, and operate tofocus the search effortsalong lines that allowsustainable development inthe uncertain future.

What we are say-ing is simply thatwe must pay at-tention to each ofthese orientatingqualities separately- we should not justroll them up intoa grand, universal”number” and ex-pect to effectively and efficiently drive our searchefforts in that fashion. A weakness in one of the6 orientors critically impacts sustainable devel-opment in the uncertain future and cannot be”made up for” with a higher score from the oth-ers. A simple mechanism for scoring, such asaveraging the lower 2 indicators (of 6 total, one

for each orientor), or using the lowest if it is farbeneath the others, will make sure that the ma-chine pays attention to (and focuses attentionon) those orienting parameters that are in needof improvement.

Our orienting indicators, which help us toconstruct a picture of the state of our environ-ment on which we can base intelligent decisions[bossel98], can all be based on a common foun-dation, such as cumulative stress, but with aweighting that aims to highlight the particulardimension of concern.

Our present [evaluationfunction] is blind to thesimplest phenomena. Theevaluator gladly acceptsa position in which thecomputer is a knight aheadalthough its king is out inthe center of the boardsurrounded by hostileenemy queens and rooks.-David Slate and LawrenceAtkin, Chess Skill in Manand Machine, 1977

What good is be-ing a piece up if yourKing is in the cen-ter of the board, sur-rounded by hostileenemy pieces? Bet-ter to see if we canreturn the King toa safe place, even atthe price of material,so that we can con-tinue the sustainabledevelopment of ourposition in the fu-

ture. We therefore orient our future searchingin ways to improve King safety. Our immediategoals, therefore, emerge from the weakest indica-tors (results) of the vital diagnostic tests, and op-erate to focus the search efforts along lines thatallow sustainable development in the uncertainfuture. The orientors represent our intentions- an intention doesn’t exactly require any deepcalculation or plan. We can follow them and seewhere they lead.

22


14 Shannon’s Evaluation Func-tion

Shannon proposed [shannon50] a simple evalua-tion to be performed in relatively quiescent po-sitions. While recent tournaments have shownthat such evaluations (combined with alpha-betapruning and the null-move heuristic) can be usedto produce world-class chess programs, we seekan alternate approach with the capability of evenbetter performance. Programs that use Shan-non’s evaluation often have trouble figuring outwhat to do when there is no direct sequence ofmoves leading to the placement of pieces on bet-ter squares (such as the center), or the acquisi-tion of a ”material” gain.

Networks are comprised ofa set of objects with directtransaction (couplings)between these objects...these transactions viewedin total link direct andindirect parts together inan interconnected web,giving rise to the networkstructure...

We see a gen-eral correlation be-tween the placementof a piece on a”good square” andthe ability of thatpiece to inflict stresson the opponent, andto mitigate the ef-fects of stress causedby well-placed oppo-nent’s pieces. We even see that the concept ofmobility has value in a general sense. However,we see problems with this technique being usedto build positional pressure, such as the kindneeded to play an effective game of correspon-dence chess. The long and deep analysis pro-duced by the machine is often focused in thewrong areas, as determined by the actual courseof the game.

The stress produced by the Shannon methodis not of the type that reduces the coping ca-

pacity of the opponent, or increases our own re-silience, in certain game situations where posi-tional play is required. For example, in positionsthat are empty of tactical opportunities, the ma-chine can be effectively challenged by opponentswho know how to play a good positional gameof chess [nickel05]. The terms of the Shannonevaluation function do not seem suitable metricsfor guiding search and planning efforts, in thesecases.

...The connectivity of na-ture has important impactson both the objects withinthe network and our at-tempts to understand it.If we ignore the web andlook at individual uncon-nected organisms... wemiss the system-level ef-fects. -Jorgensen, Fath, etal., A New Ecology, p.79

[fontana89] ad-vises us to ask: whatare the stressors,what needs to bedone about them,and what is stop-ping us from doingit? There is littleto be gained fromgeneralizing, if ourgoal is to identify thestressors, accurately

assess the levels of stress present, and mobilizeaccording to the results.

15 The Positional EvaluationMethodology

We propose that an approach which attempts toincrease the oriented positional pressure or cu-mulative stress on the opponent, even if unre-solved at the terminal positions in our searchtree, is a viable strategy and has the potentialto play a world-class game of chess. Our strate-gic intent is to form targeted positional pressure(aimed at weakpoints defined by chess theoryand at constraining the movement of the enemy

23


pieces) that will resolve at some future point intime into better positions, as events unfold andgameplay proceeds. At minimum, this pressurewill allow for sustainable development as onecomponent of a resilient position. We will notjudge pieces by the ”squares” they occupy, butinstead, by our heuristic estimate of the level offocused stress they can contribute (or mitigate)in the game.

We construct an orientation/evaluationmethodology with the goal of making our ma-chine more knowledgeable with regard to thepositional concepts discussed earlier. In de-signing our orientation/evaluation methodology,we heed the advice of [dombroski00] that thismethodology is our test of effects and conse-quences and is our guiding light in our searchfor the consequences of our choices.

So we need something likea map of the future. A mapdoes not tell us where wewill be going, or where weshould be going - it merelyinforms us about the pos-sibilities we have... Wetherefore need a descriptionof the possibilities ahead ofus...

Our orienta-tion/evaluation cen-ters on a heuristic ap-praisal of the stresswe inflict on the op-ponent’s position,and our mitigationof the stress createdby the opponent. Weaim to reduce our op-ponent’s coping abil-ity through careful targeting of stress. The dy-namic forces of change, acting over time and ina future we often cannot initially see, transformthe reduced coping ability of our opponent, ourcarefully targeted stress, and our resilient posi-tion full of adaptive capacity, to future positionsof advantage for us.

Perhaps this concept is what inspired BobbyAllison to race most of the 1982 Daytona 500

without a back bumper - it fell off after con-tacting another car early in the event [nascar09].Some drivers accused Allison’s crew chief of rig-ging the bumper to intentionally fall off on im-pact. Allison’s car without the bumper had im-proved aerodynamics, and the forces of dynamicchange operating over the 500 mile race suppliedthe driver with an advantage he used to win.Other examples (the winged keel of the AustraliaII yacht and the new loop-keel design, hingedice skates and performance enhancing swimsuitscome to mind) show how small changes, com-bined with other critical abilities and interactingwith a dynamic environment over time, can cre-ate a performance advantage.

...Such a map would nothave to give us very de-tailed information... But itshould give us a useful im-age of what may be ahead,and allow us to comparethe relative merits of dif-ferent routes... before weembark on our journey. -Hartmut Bossel

We seek, in sim-ilar fashion, to fa-vor certain inter-acting arrangementsof pieces, such thatthe dynamic forcesof change (operat-ing during the play-ing of a game) causefavorable positionsto emerge over time,

from beyond our initial planning horizon. Weseek to re-conceptualize the ”horizon effect” toour advantage. We cannot arrange for a bumperto fall off during a chess game, but we can dothe equivalent - we can actively manage the dy-namics of change to improve the chances forpersistence or transformation [chapin09]. Thiswould include the general approaches of reduc-ing vulnerability, enhancing adaptive capacity,increasing resilience, and enhancing transforma-bility [chapin09]. We manage the exposure tostress, in addition to the sensitivity to stress[chapin09].

24


We adopt the vision of [katsenelinboigen92],that we define a ”potential” which measures astructure aimed at forcing events in our favor.Ideally, one which also absorbs or reduces theeffects of unexpected events.

We follow the suggestion in [pearl84] to useas a strategy an orientation/evaluation based ona relaxed constraint model, one that ideally pro-vides (like human intuition), a stream of tenta-tive, informative advice for managing the stepsthat make up a problem-solving process, and usethe insight from [fritz89] and [sterman00] thatstructure influences behavior.

Sustainability... means, assaid before, that only theriverbed, not the exact lo-cation of the river in it, canand should be specified -Hartmut Bossel

In order to moreaccurately estimatethe distant positionalpressure produced bythe chess pieces, aswell as to predict thefuture capability ofthe pieces in a basic form of planning [lakein74][shoemaker07] we create the software equivalentof a diagnostic probe which performs a heuris-tic estimate of the ability of each piece to causeand mitigate stress. The objectives we select forthis stress will be attacking enemy pieces, con-straining enemy pieces, and supporting friendlypieces (especially those pieces that are weak). Tosupport this strategy, we calculate and maintainthis database of potential mobility for each chesspiece 3 moves into the future, for each positionwe evaluate.

We update this piece mobility database dy-namically as we evaluate each new leaf positionin our search tree. This database helps us de-termine the pieces that can be attacked or sup-ported in the future (such as 2 moves away fromdefending a piece or 3 moves away from attack-

ing a square next to the enemy king), as well asconstrained from accomplishing this same activ-ity. Note that the piece mobility we calculate isthe means through which we determine the pres-sure the piece can exert on a distant objective.We can therefore see how mobility (as a generalconcept) can become a vital holistic indicator ofsystem health and one predictor of sustainabledevelopment.

We reduce our bonus for each move that ittakes the piece to accomplish the desired objec-tive. We then consider restrictions which arelikely to constrain the piece as it attempts tomake moves on the board.

For example, let’s consider the pieces in thestarting position (Figure 4).

Figure 4: White and Black constraint map, pieces at thestarting position Legend: Red: pawn constraints, Yellow: Mi-nor piece constraints, Green: rook constraints, Blue-green:Queen constraints, Blue: King constraints

What squares can our knight on g1 influencein 3 moves, and which squares from this set arelikely off-limits due to potential constraints fromthe enemy pieces?

25


Figure 5: Influence Diagram and Simulation Diagram, Ng1at starting position Legend: Red - 1 move influence, Yellow- 2 move influence, Green - 3 move influence, Dark Red - 1move influence possibly constrained by opponent piece, DarkYellow - 2 move influence possibly constrained by opponentpiece, Dark Green - 3 move influence possibly constrained byopponent piece, Blue - no influence possible within 3 moves, X- presence of potential constraint ”it is what it does... how cansomething exercise any efficacy by means of its mere existencein space, without any motion?” - Johann Gottlieb Fichte

We now construct the influence diagram[shoemaker07] and the simulation diagram[bossel94] (Figure 5), which are interpreted inthe following way. If a piece is on our influ-ence diagram for the knight, then it is possibleto attack it or defend it in 3 moves (this includeswaiting moves or moves which move a piece outof the way). We label this kind of map an influ-ence diagram because it shows the squares thatthe piece can influence in 3 moves, provided thatit is unconstrained in movement by the enemy.

Keep in mind that we need to take into ac-count the location of the other pieces on thechessboard when we generate these diagramsfor each piece. If we trace mobility through afriendly piece, we must consider whether or notwe can move this piece out of the way before wecan continue to trace mobility in that particu-lar direction. If we trace mobility through anenemy piece, we must first be able to spend 1move capturing that piece.

Comparing this 3-move map with a diagram

of the starting position, we can determine thatthe white knight on g1 can potentially attack 3enemy pieces in 3 moves (black pawns on d7, f7and h7). We can defend 8 of our own pieces in 3moves (the knight cannot defend itself).

We decide to reward pieces for their poten-tial ability to accomplish certain types of worth-while positional objectives: attacking or con-straining enemy pieces, defending friendly pieces,attacking squares near our opponents king (es-pecially involving collaboration), minimizing ouropponent’s ability to attack squares near our ownking, attacking pieces that are not defended orpawns that cannot be defended by neighboringpawns, restricting the mobility of enemy pieces(specifically, their ability to accomplish objec-tives), etc. In this way, we are getting real aboutwhat the piece can do. The bonus we give thepiece is 1. a more precise estimate of the piece’sability to become strategically engaged with re-spect to causing or mitigating stress and 2. op-erationally based on real things present on thechessboard. In this way, our positional orienta-tion/evaluation methodology will obtain insightnot usually obtained by a computer chess pro-gram, and allow our machine to take positive,constructive action [browne02]. It is still an esti-mate, but the goal here is to focus our search ef-forts on likely moves in a positional style of play,and to evaluate positions from a more positionalpoint of view.

What does the orientation/evaluationmethodology look like for the proposed heuris-tic? We model (and therefore estimate) thepositional pressure of our pieces, by following atwo-step process:

1. We determine the unrestricted future mo-bility of each chess piece 3 moves into the future,then

26


2. We estimate the operating range or levelof engagement of the pieces by determining thelimiting factors or constraints that bound the un-restricted mobility.

The concept of using limiting factors isbriefly mentioned [blanchard06] in the contextof Systems Engineering. [lukey08] argues that animportant aspect of cognitive appraisal is the ex-tent to which stress-causing agents are perceivedas controlled. Balancing processes such as con-straints [anderson97] seek to counter the rein-forcing loops created by a piece creating stress,which, if unconstrained, can potentially createeven more stress (perhaps in combination withother pieces). Once we have identified the lim-iting factors, we can more easily examine themto discover which ones can be altered to makeprogress possible - these then become strategicfactors.

The consideration of constraints is a part ofthe decision protocol of Orasanu and Connolly[orasanu93] and [plessner08] which also includesthe identification of resources and goals facingthe decision maker. We therefore reduce thebonus for accomplishing objectives (such as, at-tacking an enemy piece or defending a friendlypiece) if the required moves can only be tracedthrough squares that are likely to result in thepiece being captured before it can accomplishits objective. We also reduce the engagementbonus for mobility traced through squares wherethe piece is attacked but not defended. Wemay use another scheme (such as probability)for determining stress-application reduction forpiece movement through squares attacked bothby friendly and enemy pieces where we cannoteasily resolve whether or not a piece can tracemobility through the square in question (andtherefore create stress). We think in terms of

rewarding a self-organizing capacity to createstress out of the varied locations of the piecesand the constraints they face [costanza02].

We reward each piece for its predicted abil-ity to accomplish strategic objectives, exert po-sitional pressure, and restrict the mobility of en-emy pieces, based on the current set of pieceson the chess board at the time we are callingour orientation/evaluation methodology. Usinganticipation as a strategy [vanwezel06] can becostly and is limited by time constraints. It canhurt our performance if it is not done with com-petence. An efficient compromise between an-ticipative and reactive strategies would seem tomaximize performance.

We give a piece an offensive score based onthe number and type of enemy pieces we can at-tack in 3 moves - more so if unconstrained. Wegive a piece a defensive score based on (1) howmany of our own pieces it can move to defend in 3moves and (2) the ability to mitigate or constrainthe attacking potential of enemy pieces. Again,this bonus is reduced for each move it takes toaccomplish the objective. This information is de-rived from the influence diagram and simulationdiagram we just calculated. Extra points can begiven for weak or undefended pieces that we canthreaten.

The proposed heuristic also determines kingsafety from these future mobility move maps.We penalize our king if our opponent can movepieces into the 9-square template around ourking within a 3 move window. The penalty islarger if the piece can make it there in 1 or 2moves, or if the piece is a queen or rook. We pe-nalize our king if multiple enemy pieces can at-tack the same square near our king. Our king isfree to move to the center of the board - as long asthe enemy cannot mount an attack. The incen-

27


tive to castle our king will not be a fixed value,such as a quarter pawn for castling, but ratherthe reduction obtained in the enemy’s ability tomove pieces near our king (the rook involved inthe castling maneuver will likely see increasedmobility after castling is performed).

The king will come out of hiding naturallywhen the number of pieces on the board is re-duced and the enemy does not have the poten-tial to move these reduced number of pieces nearour king. We are likewise free to advance thepawns protecting our king, again as long as theenemy cannot mount an attack on the monarch.The potential ability of our opponent to mountan attack on our king is the heuristic we use asthe basis for king safety. Optionally, we will con-sider realistic restrictions that our own pieces canmake to our opponent’s ability to move piecesnear our king.

Pawns are rewarded based on their chance toreach the last rank, and what they can do (piecesattacked and defended in 3 moves, whether ornot they are blocked or movable). The piecemobility tables we generate should help us iden-tify pawns that cannot be defended by otherpawns, or other pieces - it is this weakness thatwe should penalize. Doubled or isolated pawnsthat cannot be potentially attacked blockaded orconstrained by our opponent should not be pe-nalized. Pawns can be awarded a bonus basedon the future mobility and offensive/ defensivepotential of a queen that would result if it madeit to the back rank, and of course this bonus isreduced by each move it would take the pawn toget there.

The information present in the future mo-bility maps (and the constraints that exist onthe board for the movement of these pieces) al-low us to better estimate the positional pres-

sure produced by the chess pieces. From thesecalculations we can make a reasonably accu-rate estimate of the winning potential of a posi-tion, or estimate the presence of positional com-pensation from a piece sacrifice. This orienta-tion/evaluation score also helps steer the searchprocess, as the positional score is also a measureof how interesting the position is and helps usdetermine the positions we would like to searchfirst.

In summary, we have created a model ofpositional pressure which can be used in theorientation/evaluation methodology of a com-puter chess program. [michalewicz04] remindsus that models leave something out, otherwisethey would be as complicated as the real world.Our models ideally provide insight and identifypromising paths through existing complexity.

[starfield94] emphasizes that problem solv-ing and thinking revolve around the model wehave created of the process under study. We canuse the proposed model of positional pressure todirect the machine to focus the search efforts onmoves which create the most stress in the posi-tion as a whole. For our search efforts, we desirea proper balance between an anticipatory and areactive planning strategy. We desire our fore-cast of each piece’s abilities to help us anticipateits effectiveness in the game [vanwezel06], insteadof just reacting to the consequences of the moves.

By identifying the elements and processes inour system [voinov08], identifying the limitingfactors from the interactions of the elements, andby answering basic questions about space, timeand structure, we describe and define the con-ceptual model of our system.

28


16 All Work and No Play...

...makes ”Jack” a dull boy. We follow [brown09]and [suttonsmith01] in a conceptualization ofplay that will form one foundation of our au-tomated search/exploration efforts.

Humans adopt play as a foundational behav-ior that guides exploratory activity and in somecases becomes a basis for acquiring knowledge.Play is the basis of all art, games, books, sports,movies, fashion, fun, and wonder [brown09].Play is the vital essence of life - it is what makeslife lively [brown09]. However, a machine doesnot know how to play. It simply does what wetell it to do, so we must tell it how to play withthe pieces on the board and the relationshipsamong these pieces. Why must our machineplay? because, Play is the answer to the ques-tion, How does anything new ever come about?(Jean Piaget).

We further conceptualize play [suttonsmith01]as the extrusion of internal mental fantasy intothe web of external constraints. Additionally,we adopt the practical aspect that play seemsto be driven by the novelties, excitements, oranxieties that are most urgent to the perceptionsof the players [suttonsmith01]. Finally, we notethat the imagination makes unique models ofthe world, some of which lead us to anticipateuseful changes - the strategic flexibility of theimagination, of play, and of the playful is theultimate guarantor of our game-based survival[suttonsmith01]. Play lies at the core of creativ-ity and innovation [brown09].

We desire our machine to always be busymaking up its own work assignments [paley91].Specifically, the ”work assignments” involvechoosing our courses of action and adjustingthose courses based on the internal satisfactions

we receive [henricks06]. We desire from our ma-chine a behavior similar to ”playfulness”, and aset of creative, inquisitive, exploratory orienta-tions centered on an object-based model of thegame-world [henricks06]. We desire an activityof constant exploration, manipulation and ap-praisal.

We agree with [brown09] that movement isprimal and accompanies all the elements of playwe are examining. Through movement play,we think in motion - movement structures ourknowledge of the world, space, time, and our re-lationship to others [brown09].

Our exploration of future game positionstherefore must take into account piece movementthat is likely, critical, interesting, stress induc-ing/relieving, or otherwise ”lively”. Children atplay engage other children or contemplate waysto engage their playmates. We therefore desireto create a heuristic which playfully examinesthe future consequences of the transformation ofstress on the board, as the pieces move about orare constrained by objects on the board, such asblocked pawns or lower-valued enemy pieces.

We begin our efforts by conceptualizing thebuilding of a principal variation a few moves intothe future, by first examining the single movethat creates the most perceived stress for our op-ponent (or mitigates the perceived stress causedby his pieces). We then look at the most likelyresponse.

After ”sliding forward” a few moves in thisfashion, we then work backwards in our princi-pal variation, examining the consequences of thenext most likely move, and so on. We establisha few simp

A Proposed Heuristic for a Computer Chess ProgramComputer chess programs have historically been weak...

Documents

Transcript of A Proposed Heuristic for a Computer Chess ProgramComputer chess programs have historically been weak...