Blackjack: A Beatable Game

1. Blackjack: A Beatable Game Amber Guo Adapted from: David Parker Advisor: Dr. Wyels California Lutheran University ‘05

2. Why is Blackjack Beatable? • Only game in a casino where the probabilities change from game to game. • If a player can take full advantage of favorable probabilities, they might be able to win more money then the dealer over a period of time.

3. Rules of Blackjack • Player(s) vs. Dealer • Object: Closest to 21 without going over • Card Values • Face Cards = 10 • Aces = 1 or 11 (Player’s choice) • 2,3,4,5,6,7,8,9,10 = Numerical value of card drawn.

4. Rules of Blackjack Player Dealer

5. Basic Strategy S = Stand H = Hit D = Double Down P = Split Pair Dealer Card Up Dealer Card Up Player Player

6. Example x2 Player Dealer

7. How to Count Cards • Dr. Edward Thorp (1962) • High cards are good for the player. • Card Counting • Cards 2,3,4,5,6 are worth +1 • Cards 10,J,Q,K,A are worth -1 • Cards 7,8,9 are neutral and are worth 0 • Player keeps a running total of cards played in their head. Once the deck is reshuffled the count is reset to zero.

8. True Count • Player still keeps track of count. • Player keeps track of total number of cards played. • Complete Count = Count divided by the number of decks have not been completely exhausted. • True count = Floor (Complete Count).

9. True Count (Cont.) • Higher the true count, the greater the advantage to the player • 6 deck shoe • Shuffled  running count = 0, dealer advantage of 0.5% • +1 count  even with the dealer • Each +1 after +1 count, additional 0.5% player advantage

10. True Count in Blackjack Strategy • True count < or = +1, bet base amount • True count +2 or +3, bet 2 times base unit • True count +4 or +5, bet 3 times base unit • True count +6 or +7, bet 4 times base unit • True count > or = +8, bet 5 times base unit

11. Dealer Card Up Player Cards Final Player Cards Outcome Count Probability of winning at count Number of Cards Played Truecount Probability of Winning at Truecount Maple Simulation

13. 6 Deck Shoe

14. Betting Strategies • Bet Count • Bet Truecount • Hi-Low • When the truecount is in the player’s favor (>2), bet 20 chips, otherwise bet 1 chip. • MIT Team • Pick a betting unit. • When there is a favorable truecount (>2), bet the [truecount x (betting unit)]. • Otherwise bet half the betting unit.

15. Dealer Card Up Player Cards Final Player Cards Outcome Count Probability of winning at count Number of Cards Played Truecount Probability of Winning at Truecount Betting Consistently Thorp Braun Hi-Low MIT Blackjack Team Amount Bet Amount Won/Lost Total amount Won/Lost Maple Simulation

16. Maple Simulation (Cont.) • Study was conducted with the same rules as if we were playing at a 5 dollar minimum Las Vegas blackjack table. • 6 deck shoe. • Single player vs. dealer. • Trials of 500 hands • 500 hands takes between 7.5 – 10 human hours to play.

17. Normal Distributions10,000 trials of 500 hands -10.41 0.55 -5.87 -7.59 6.09

19. Max Amount Won10,000 Trials of 500 Hands 95% Confidence Intervals

20. Conclusions 6.09

21. Conclusions • Hi-Low strategy wins the most money. • Chances of getting caught are high. • High Standard Deviation. • Need to buy 860 Chips.

22. 0.55

23. Conclusions • Hi-Low strategy wins the most money. • Chances of getting caught are high. • High Standard Deviation. • 860 Chips to Play. • MIT Strategy is the only other strategy in which the player wins money • Proven to work. • Good Standard Deviation. • 366 Chips to Play.

24. Conclusions • Not many chips (0.55) earned for number of hours spent playing (7-10 hours). • Dealers are taught the betting strategies to spot card counters. • Casinos take measures to improve their odds. • Not allowing the player to double down with certain hands. • Dealer has to hit on 17. • Reshuffling with cards left in the shoe.

25. Double-Deck Basic Strategy We will be playing with Hits, Stands, Doubles, and Splits. Double after Splits are allowed. Surrendering is not allowed.