There are a couple of hubs published about using statistics or probability theory to enhance your chances of winning at 21 (also known as blackjack), but I'm not sure either actually answer this question.
The basic idea is simple - you have a dealer and at least one player, the dealer gives one card face down and one card face up to each player and to himself and the object of the game is to beat the dealer's hand without going over 21. I've seen the game played with anywhere from 1 to 6 shuffled 52 card decks. Each card 2-10 is worth face value; J,Q, and K are worth 10; and an Ace can be either worth 1 or 11 at the discretion of the player. Once the dealer has given each player the first two cards, each player has several choices depending on what their hand looks like compared to what they think the dealer has based on his one card that is showing (this is where probability begins to play a role). The two basic options for players are a 'stand' or 'stay' in which players do not take another card if they are satisfied with their hand or they can 'hit' and take another card to try and better their hand. The player could also 'split' or 'double down', but I'm not going to go into these because they aren't necessary to play the game.
If the player or dealer goes over 21 they 'bust' and immediately lose the hand. The best case for a player is to see the dealer bust because you automatically win (providing you have not already busted out of the hand). A natural 'blackjack' occurs when a player has a face card and an Ace as their first two cards. This is the best hand in the game, but unfortunately it can be tied by the dealer (a tie between the dealer and a player is known as a 'push') and the player neither wins nor loses his bet.
The strategy of the game involves probability as the players' and dealer's card values determine whether the player should hit or stay. For example, if the player has a Q and a J and the dealer has an 8 showing, the odds are in favor of the player and thus he should stay. However, if the player has a 10 and a 2 and the dealer is showing a K, the odds are in favor of the dealer and the player should hit. There are published blackjack tables that show the odds and what players should do in given situations.
Hope this helps. Have fun, it's a great game!
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