Blackjack A Beatable Game Amber Guo Adapted from

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

Why is Blackjack Beatable? o Only game in a casino where the probabilities change from game to game. o 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.

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

Rules of Blackjack Player Dealer

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

Example x 2 Player Dealer

How to Count Cards o o o Dr. Edward Thorp (1962) High cards are good for the player. Card Counting n n n o 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.

True Count o o 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).

True Count (Cont. ) o o Higher the true count, the greater the advantage to the player 6 deck shoe n n n 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

True Count in Blackjack Strategy o o o 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

Maple Simulation o o o o o 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

6 Deck Shoe

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

Maple Simulation o o o o o 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 o o o o Betting Consistently Thorp Braun Hi-Low MIT Blackjack Team Amount Bet Amount Won/Lost Total amount Won/Lost

Maple Simulation (Cont. ) o Study was conducted with the same rules as if we were playing at a 5 dollar minimum Las Vegas blackjack table. o 6 deck shoe. o Single player vs. dealer. o Trials of 500 hands n 500 hands takes between 7. 5 – 10 human hours to play.

Normal Distributions 10, 000 trials of 500 hands -10. 41 0. 55 -7. 59 -5. 87 6. 09

Max Amount Won 10, 000 Trials of 500 Hands 95% Confidence Intervals

Conclusions 6. 09

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

0. 55

Conclusions o Hi-Low strategy wins the most money. n n n o 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 n n n Proven to work. Good Standard Deviation. 366 Chips to Play.

Conclusions o o o 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. n n o Not allowing the player to double down with certain hands. Dealer has to hit on 17. Reshuffling with cards left in the shoe.

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