March 31st, 2009 - 8:02am PST
Game of Blackjack - Probability of Getting 21
Many people head to Las Vegas or Atlantic City in search of their big score. Furthermore, many amateur bettors and gamblers choose to play blackjack because of the simple nature of the game. People often make decisions at the blackjack table solely based upon "feel" or whether or not they think the card they need is going to come. This strategy, however, will never yield long term success in blackjack.
Another way to play the game is through a more analytic mind. That is, there is a clear way to play blackjack based upon the mathematical principles involved. One of the statistics that seems to be often wondered about is the actual probability of getting a blackjack. Calculating the probability of one card is fairly simple. However, when we begin to calculate the probability of two cards, it can get more complex.
The first thing that needs to be calculated is the probability of drawing 1 card that is worth a 10 in blackjack. In one deck there are 16 cards that will yield a 10 (4 10's, 4 jacks, 4 queens, 4 kings). The next step is calculating the probability of drawing a card that is worth 11. There are 4 Aces in a deck of 52 cards that are worth 11.
The easiest way to determine the probability to draw a blackjack, then, is to multiply the simple probabilities. (16/52) * (4/52)= 64/2704 or 2.37%. This answer, of course, is going to be more complicated when you factor in the cards that have already been played. That is, if you are dealt one 10 card to begin, the probability of drawing an ace changes slightly to 4/51, because 1 card has already been played. Further, if there are multiple players at the table, calculating the probability of getting a blackjack is nearly impossible.
Even more complicated is the calculation of blackjack on the initial deal. In this case the probability shrinks to .048%.