1. Introduction to Cognition and Gaming 9/22/02: Bluffing

2. Bluffing A special form of lying or deception Bluffing is about behavior, not language Try to get opponent to draw erroneous conclusions  that the causes that would normally produce such behavior are really there No untrue statement is actually made CIA: white propaganda Essence is found in inexpressive behavior

3. Bluffing If you come to class unprepared, and look at me as if you know the lesson for today, you’re bluffing If you openly tell me you did your homework, you’re lying The real difference is in how I react to each situation if I discover your deception If you were bluffing, next time I will challenge you and give you a chance to let me change my opinion of you If you were lying, I will label you as a liar and won’t believe you again, even if you’re telling the truth

4. Bluffing and the Categorical Imperative Lies should ethically be condemned under the categorical imperative If everyone lied continually, this would contradict the notion that statements have meaning, and that conclusions can be drawn from them  While it’s true that lies often contain information from which true conclusions can be drawn, it’s an unreliable strategy However, certain types of optimal mixed strategies necessitate the use of bluffing (!!)

5. Bluffing and Motivation Bluffers have different motivations than liars A liar aims to have others believe his lie, have things rearranged accordingly, and directly profit from it A bluffer sometimes wants his bluff called, for next time, he can gamble for high stakes One who bluffs for immediate gain is no different from a liar and will suffer in the long run Bluffing is a long-term strategy – while a bluff can win, it’s really only a happy side effect. The chief goal is to leave doubt regarding future bluffs

6. Poker It’s terribly boring to play poker with people who never bluff Those who don’t bluff can only lose Following the cards exclusively will allow opponents to see right through you Everybody has lucky and unlucky streaks, but long term results don’t depend on luck-of-the-draw One doesn’t lose much from a bad hand – the greatest loss is when you have a good hand, but an opponent has a better hand when you thought they were bluffing – because previous bluffs sowed doubt!

7. How much Should you Bluff? Like just about anything else – use in moderation Essential in small amounts, harmful if used excessively Those who bluff too much invest too much in later profit, and loses in the long run Two ways to look at it – through the eyes of philosophy, or the eyes of game theory

8. A Simple Poker Model Two players, A and B – A is the challenger, B is the challenged  Roles can be interchanged throughout play if desired A rolls a d6 – if it rolls a 6, A wins, but if A rolls anything else, B wins Well, okay – it’s not that simple

9. The Rules A the beginning of each round, A puts $10 on the table, B puts down $30 A rolls the die so B cannot see the result Having seen the result, A either folds or raises. If A folds, B wins and takes A’s $10. If A raises, A must add $50 to the table If A raises, B can either fold or call. If B folds, a gets B’s $30. If B calls, B must also put down $50 (A: $60, B: $80) If A raises and B calls, A must reveal the die. If it’s a six, A wins B’s $80, if A bluffed, B wins A’s $60

10. A Game about Bluffing If A never bluffs, B will eventually always believe him – A would lose 5 x $10 for every 1 x $30 won If A bluffs poorly (B sees through him), it’s even worse – if bluff succeeds, A wins $30, if bluff fails, A loses $60 If A bluffs too much, B will eventually never fold – A would lose 5 x $60 for every 1 x $80 won Which position would you prefer?

11. The Strategy It’s better to play A (really!) – all things being equal, it’s preferable mathematically When you throw a six, raise. If not, raise at random with a probability of 1 in 9 Do not simulate emotion, remain expressionless – do not explicitly falsify any facts

12. Why 1 in 9? Balance sheet of a 54-round game using this strategy (makes the calculation easier) First, we calculate how much A is expected to win or lose if B accepts or declines all challenges

13. B Calls A is expected to roll a six 9 times in the 54 rounds If B accepts all challenges, X will win $80 each time (9 x $80 = $720) In one-ninth of the remaining 45 rounds, A bluffs (5 times total) B accepts, and A loses $60 each time (5 x -$60 = - $-300) A folds first in the remaining 40 rounds (40 x -$10 = -$400) In the end, A profits $20 ($720 - $300 - $400)

14. B Folds A’s 9 sixes will yield him 9 x $30 = $270 With the 5 bluffs, A wins 5 x $30 = $150 A folds first in the remaining 40 rounds – (40 x -$10 = -$400) A’s balance at the end is $270 + $150 - $400 = $20 Thus, provided A provides B no additional information, long term profit is ensured!

15. Equilibrium Point If A bluffs more often, B calls more often, resulting in a deficit for A If A bluffs less often, B won’t risk the additional $50, and A winds up with a deficit again If A is satisfied with a $20 profit, B is essentially hosed. What should B do?

16. B’s Strategy Accept every challenge with a probability of 4/9 If A always raises, of the 9 sixes, A will win $80 for each of the 4 challenges B calls, and $30 for each of the 5 folds (4 x $80 + 5 x $30 = $470) Of the remaining 45 rounds, A will win 25 x $30 = $750 (since B folds 5/9 of the time), and will lose 20 x $60 = $1200 (when B calls his bluff). A winds up with $470 + $750 - $1200 = $20 If A never raises, he will win $470 with his 9 sixes, and will lose 45 x $10 = $450 in the remaining rounds, for a total of $20

17. Unbalanced! To make the game more just, change the raise amounts of each player from $50 to $40 A’s strategy changed to bluff 1 in every 10 non-six rounds B’s strategy changes to accept ½ of all challenges

18. Poker Much more complex French, German, early Hindu? Countless variations Dealer’s rules!

19. Poker High Card Pair Two Pair Three of a Kind Straight

20. Poker Flush Full House 4 of a Kind Straight Flush Royal Flush

21. Five Card Stud HandCombinationsProbabilityOdds Royal Flush4.000001541 in 649740 Straight Flush36.000013851 in 72193 4 of a Kind624.000240101 in 4165 Full House3,744.001440581 in 694 Flush5,108.001965401 in 509 Straight10,200.003924651 in 255 3 of a Kind54,912.021128451 in 47 2 Pair123,552.047539021 in 21 Pair1,098,240.422569031 in 2.366

22. Novice Poker Bluffers Player tries to create a false impression Manipulate appearance of confidence, overcompensates, bets too quickly. Players deliberate over a good hand Confidence speaks for itself Insecurity breeds boastful behavior