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

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.

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.

Rules of Blackjack Player Dealer

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

Example x2 Player Dealer

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.

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).

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

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

Maple Simulation  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  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.

Maple Simulation  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 (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.

Normal Distributions 10,000 trials of 500 hands

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

Conclusions 6.09

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

0.55

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.

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.

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