Blackjack: An Analysis of Probability By: John Theobald

So, How Do I Play? Start with 2 cards: one face down, one face up. Objective: Closest to 21 without going over. Decks normally interchanged every hand or so in order to prevent cheating “Draw/Hit” to take one card “Stand/Stay” to stop drawing cards; ends turn 2 through 9 represented by self-values, all face cards worth 10, aces worth 1 or 11.

Sounds Easy Enough… Right? Dealer wins all ties (including 21), but loses if he busts. Dealer always goes last, so all moves by players must be made before the dealer plays. At a casino, the odds are stacked against the players, due to these dealer rules. Casinos use multiple decks to prevent card counting.

Great… Then How Do I Win? Form a basic strategy. Basic strategy - the strategy which maximizes the player's average gain, or expectation, playing one hand against a complete pack of cards (Griffin 12) Assess the probabilities of your hand to the remaining cards and determine whether you should hit or stay. Bet smart: proper betting can be the difference between profit and loss. Higher bets compensate for lost hands, but variance in betting is key to not losing too much.

Strategy Variations Hard draw/stand: Never hit 17 or higher. Soft draw/stand: Draw up to 17, stand on 18. Hit on 18 only if against dealer with 9 or 10 “Mimic the Dealer”: mimic the dealer’s strategy. Odds still in the dealers favor, but can be useful as strategy variation. Still worse than a basic strategy though.

Hit or Stand? 21: Stay; you win unless dealer also has : Very unlikely to get 21, stay : Depends on strategy chosen. 1-14: Hit or pair split Use your basic strategy or use a combination of probabilities/luck to determine your next action. Observe the dealer’s “up card” to help make a decision.

Dealer’s Chance to Bust TA Up Card % Bust

Conditional Probability

Multiple Decks vs. Single Decks

Betting Betting is performed at the beginning of each round. Payouts for winning hands vary by casino. Winning odds are normally 3:2. ($2 bet, $3 payout). Bets should be high enough to make up for lost hands, yet low enough to not go into debt. Variance is vital.

Betting Probabilities

Blackjack Theory: Gambler’s Ruin

Sources ndit.htm ndit.htm Beat The Dealer, Edwin O. Thorp The Theory of Blackjack, Peter Griffin Blackjack Essays, Mason Malmuth The Casino Gambler’s Guide, Allen Wilson