Russell Thomas

Transcription

1 From Actuarial Science to Poker Russell Thomas

2 Agenda Playing poker vs. Being an Actuary Rules of No Limit Texas Hold em Poker skills Conclusions 2

3 How does Poker relate to being an Actuary? Deal with uncertainty Guess work with incomplete information Combination of science and art Calculate and assess risks Claim Probability Distribution table, stochastic simulations vs. expected value, pot odds and Bayesian's theorem Actuarial judgment - instincts Collect and Analyze data historical claims vs. opponents hand history Develop accurate assumptions Trends, interest rates, risk scores vs. opponent s hand ranges and betting patterns 3

4 Rules of No Limit Texas Hold em Card game played between 2 and 10 players One player acts as the dealer. The two players to his left are forced to put out bets known as the small blind and big blind ($1 and $2 for example). Everyone gets dealt two hole cards that only they are allowed to see. Example The person to the left of the big blind starts the action: raise (increase the price to call), call (match the raise), or fold (forfeit your hand) No Limit means you are allowed to choose to do so: All in wager all of your remaining chips if you 4

5 Rules of the game (cont d) After the first betting round finishes, three community cards that everyone can use are dealt. This is known as the flop. Example: The players who did not fold their hand before the flop engage in another betting round Can check if it s your turn and you do not want to bet A 4 th community card is dealt, known Another betting round between players left in the hand A 5 th community card is dealt, known as the turn as the river Final betting round between players left in the hand Showdown: Using your 2 hole cards plus the 5 community cards in the middle you make your best 5 card hand. Player with the best hand wins. 5

6 Hand rankings 6

7 Cash Games Formats of No Limit Texas Hold em Sit down, play as long as you like, and then leave with your winnings/losses at any point Tournaments Entry fees create a prize pool Play continues until one player has all of the chips Blind levels increase antes also in play Fixed, top heavy payout structure Top ~10% get paid First place gets between 10-20% of the prize pool 7

8 Isn t poker gambling? Casinos Games - Played against the house - Negative expected value Poker - Played against other people - A zero sum game -Your opponent s mistake is your profit - Large skill edges between experienced and inexperienced player 8

9 I offer you a proposition - + Expected Value coin flip Let s say there is a weighted coin when it is flipped it has a 55% chance of landing on heads You have an opportunity to bet $100 to win $100 on the coin coming up heads. If the coin ends up tails, you lose your $100. How many of you would take the bet? Expected Value (betting on heads) =.55(100)-.45(100) = $10 9

10 Skill vs. Chance 10

11 Skill vs. Chance (Cont d) 11

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14 What is skill in poker? Knowing the probabilities Taking good risks Trial and error Making good assumptions about your opponent Gaining poker tells on your opponent Being able to constantly adjust to new situations Every hand is different 14

15 What is skill in poker? poker (Cont d) Different styles and strategies in poker Tight vs Loose What percentage of hands you play Aggressive vs Passive How frequently you bet as opposed to check or call Winning strategies Putting a lot of money in the pot with a high percentage chance of winning (Maximize EV) 15

16 First, let s do the numbers Basic probability Pot Odds Assumptions Data 16

17 Some Probabilities for All Ins before the flop You hold Your opponent holds Probability of Winning Higher pair Lower Pair 80% Two high cards Lower Pair 45% Two high cards Two lower connected cards 61% Two high cards Same highest card but different low card 75% Pair in between those two cards 30% High card and low card Example hands Vs. Vs. Vs. Vs. Vs. 17 High pair Unconnected low cards 89% Vs.

18 Pot Odds Definition The ratio of the current size of the pot to the cost of a contemplated call Important concept relating the amount you have to risk to win the pot Example The pot is $40 after your opponent bets You ou need to call a bet of $10, therefore, you are getting 4 to 1 pot odds or 20% pot odds (($10/($40+$10)) = 20%) Problem Let s say you are holding and your opponent is holding. Because you have a 30% chance to win the hand, and you are getting 4 to 1 or 20% pot odds, you should call because your probability to attain the best hand exceeds your pot odds and therefore is a positive expected value call. 18

19 Assumptions One of the most important skills in poker A key differentiator to separate winning players and losing players The correct play is always dependent on your opponent What actions is your opponent going to take? What reactions is your opponent going to have to respond to your action? Does your opponent like to bluff or not? 19

20 Assumptions (Cont d) Live game Population tendencies Age/Gender/Area 60 year old business man from America 21 year old European professional player Comfortable at the table Online Databases History 20

21 Poker Tells Generally unreliable for me unless they are really obvious from an inexperienced player. Jay Farber is bluffing the river in one of these pictures which one? 21

22 Poker Tells (Cont d) 22

23 Data in Poker Past 10 years - data revolution in the game All hand histories saved Allows you to keep statistics on opponents for next time you play Large sample size Hundreds of statistics on players tendencies The best strategies have evolved much faster since data was introduced in the game 23

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25 Hold em Manager Most good online poker players use a HUD (Heads Up Display) Programs like Hold em Manager track stats on of your opponents How often do they raise preflop? Do they limp in/call preflop? From what positions at the table? How often do they reraise preflop? How often do they fold to reraises? How often do they bet the flop when checked to? Concerns How credible is the data? Topflop12 we only have 66 hands on. Don t over rely on the stats I chose a mix of general stats and specific stats that I felt were useful

26 Raising from 1 Range v Raising from 4 range 16% range 56% range 26

27 All in or Fold problem A 9 player tournament table Small Blind (SB) 100, Big Blind (BB) 200, Ante 25 You are SB (the 8th player) with 1900 Chips left after anteing and posting the small blind The 7 players before you all fold their hand The BB (the 9th player) with 2000 chips left after anteing and posting the big blind Amount in the pot preflop = (9*25) = 525 Two options are to go all-in or fold. Assume our opponent will be calling us with the top 25% of hands: Quiz: What do we do with A) 22 B) QT suited C) 65 suited D) 72 off suit? suit 27

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29 Amateurs vs Pros weigh in 22 QT suited 65 suited 72 offsuit Amateur 1 Fold All in Fold Fold Amateur 2 All in All in Fold Fold Amateur 3 Fold All in Fold Fold Pro 1 All in All in All in All in Pro 2 All in All in All in Fold Pro 3 All in All in All in All in 29

30 The Math behind the decision For us to want to go all in: EV(All In) > EV(folding your hand) Scenario 1: We fold then EV of folding = 1900 Scenario 2: We go all in then Possibility 1: He will fold and we will win the small blind, the big blind, and the antes in the pot Possibility 2: He will call,, creating a bigger pot, and we win the pot Possibility 3: He will call,l, creating a bigger pot, and we lose the pot EV(All In) = A + B + C where A= P(he folds)*(new chip stack if he folds) B= P(he calls)*p(our hand wins the all in)*(new chip stack if he calls and we win) C= P(he calls)*p(our hand loses the all in)*(our new chipstack=0) =0 30

31 P(our hand wins the all in) 31

32 The Math behind the decision (Cont d) A= = P(he folds)*(new chip stack if he folds) = (1-0.25)*( )= (1 (.75)*2425 = B= P(he calls)*p(our hand wins the all in)*(new chip stack if he calls and we win) =0.25* 27.95%*( )= EV(All In) = A + B + C = = > 1900 Therefore EV(All In) >EV(folding your hand) hand On average, going all in increases our chip stack by 214 or 11.25% Breakeven decision when he calls top ~45% ~45 of hands 32

33 Conclusions Play poker requires similar skills as being an actuary Both are a combination of science and art Data, assumptions, uncertainty, probability, judgments Poker is a strategy game, not pure luck in a long run Make accurate assumptions and maximize EV Practice, practice, practice! 33

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