-:Fat Chance:-Risk and Reward

Paul Taylor 2010

What is chance?

Why do we need chance?

• We balance risk / rewards in everyday life– What is the danger of a building collapsing?– A train being delayed?– Showing up to class vs Failing the Exam?

Roll of the Die...

• What are the odds?

http://www.edcollins.com/backgammon/diceprob.htm

http://www.extrabit.com/dice/d6-06.jpg

What are the odds?

http://www.extrabit.com/dice/d12-12.jpg

What do you do if you don’t have a 12 face die?

• Roll 2x 6 face die?• Roll 1x 6 face die and double the answer?• Roll 1x 6 face die and flip 1x coin?

http://www.serenapowers.com/img/dice.jpg

Rolling 2x 6 face diehttp://www.edcollins.com/backgammon/diceposs.gif

http://www.upscale.utoronto.ca/cgi-bin/ErrorAnalysis/HistogramExample.cgi

• 1x Die = 1-6• 1x Coin = H / T = +0 / +6

C# / XNA Randomness

Random randNumber;randNumber = new Random();int diceRoll = randNumber.Next(1, 7);

int dice12face = randNumber.Next(1, 7) + randNumber.Next(1, 7);

Complex Chance

• Suppose we have 184 different enemies for the player to face

• We want to be able to estimate the difficulty of the game without knowing the exact enemies chosen

A hierarchy of chance

• We have 184 different enemies– All must be easy, difficult, or normal– (We categorise the enemies)

• Now we can set probabilities for each category

Now what is the probability:

• That your game is fun?• That your game is too difficult?• That your game is too easy?

• Now to add some balance....

Adding some Balance

• We can’t just throw risk around without considering how it affects the balance of the game

http://blog.wineenthusiast.com/wp-content/uploads/2008/12/balance.jpg

Balancing Asymmetrical games

• Commonly achieved via Resource and Power balance– Vampire Guinea Pig Apocalypse

– Three main character classes:• Normal Guinea Pig• Vampire Guinea Pig• Exorcist Guinea Pig

Powers of Pigs

Exorcist Vampire GP Guinea PigDefence High Medium LowAttack Low High MediumAvoid Medium Low High

Checking the balance of powerExorcist Vampire GP Guinea Pig

Defence High Medium LowAttack Low High MediumAvoid Medium Low High

Exorcist Vampire GP Guinea PigDefence High (3) Medium (2) Low (1)Attack Low (1) High (3) Medium (2)Avoid Medium (2) Low (1) High (3)Total Power 6 6 6

Rock Paper Scissors

This is the circle of life version of fairnessUsed extensively by games such as Pokémon • There is no most powerful piece• For every power there is a weakness

Paper Scissors Rock has no probabilityPlayer: Paper Scissors Rock

Vs Paper Draw Win Lose

Vs Scissors Lose Draw Win

Vs Rock Win Lose Draw

When is probability a good choice?

• For small frequent challenges– Item Dropping– ??– ??

• When the player can estimate the risk

When is probability a bad choice?

• When the risk is high• When the player has no control over the

amount of risk• Irreversible actions

References

• Fundamentals of Game Design