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 pot You 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 = $10 Opponent Calls and you lose, outcome = -$10 Opponent 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 Criterion Used 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 = If tickets are $1, you would need a $35 million dollar bankroll to make this bet.