Introduction to Cognition and Gaming

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, raiseat 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. Hand Combinations Probability Odds Royal Flush 4 .00000154 1 in 649740 Straight Flush 36 .00001385 1 in 72193 4 of a Kind 624 .00024010 1 in 4165 Full House 3,744 .00144058 1 in 694 Flush 5,108 .00196540 1 in 509 Straight 10,200 .00392465 1 in 255 3 of a Kind 54,912 .02112845 1 in 47 2 Pair 123,552 .04753902 1 in 21 Pair 1,098,240 .42256903 1 in 2.366 Five Card Stud

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