Online Poker

James Gilman

Topics● Hand Probabilities● Betting Odds● Odds of winning● Expected Value● Decision Making● Poker Statistics● Variance

Hand Probabilities

How often will you get dealt AA?

P(Ace,Ace) = (4/52)x(3/51) = 12/2625 = 1/221 = .00452

Betting Odds

● A normal bet (1:1) - You need to win 50% to break even

● You bet with two people at once(2:1) - You need to win 33.3% to break even

● A number on a roulette wheel (35:1) - You need to win 2.77% to break even

Odds of Winning

44 unknown cards

Duhamel’s outs to win:

4 Eights, 4 Kings, 2 Jacks

10/44 = .227

Expected Value

Total Pot = 41.6M

Affleck EV = .773 x 41.6M = 32.2M

Duhamel EV = .227 x 41.6M = 9.4M

Simplified Example

$10 in the potYou and your opponent have $10 each.You are first to act and can only fold or bet $10.

Your Decision

Fold

Bet $10

Outcome = $0

Opponent folds, outcome = $10Opponent Calls and you lose, outcome = -$10Opponent Calls and you win, outcome = $20

Back To The Example

What is the worst hand you would want to bet with?

What if you had to bet $20 or $30 instead of $10?

What if you could bet any amount you want?

What if your opponent could re-raise you?

Tracking Program

Checking on My Own Statistics

Variance

You can think of a poker hand, session, tournament as an event that will end in as either Success or Failure.

Bernoulli trial / Binomial Distribution

Var = p(1-p) or np(1-p)

A look at long run variance

Implied Odds

34% 66%

Bankroll Management

Kelly CriterionUsed to maximize your growth rate

Example: One on One Tournament

You think you are a 60% favorite to win. After the rake you will get 10/11 odds on your money if you win.[(10/11) x .6 - .4] / (10/11) = .16

Multi-Table Tournament

8074 players

Lottery Example Using Kelly Criterion

Assume you are getting a good bet that pays out 2/1 in the long run.Odds of jackpot 1/175,000,000

[350,000,000 x (1/175,000,000) - (1 - (1/175,000,000)] / 2 = 0.000000002857

If tickets are $1, you would need a $35 million dollar bankroll to make this bet.