Online Poker James Gilman. Topics ●Hand Probabilities ●Betting Odds ●Odds of winning...
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Transcript of Online Poker James Gilman. Topics ●Hand Probabilities ●Betting Odds ●Odds of winning...
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.