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Card counting is a card game strategy used to determine when a player has a probability advantage. The term is used almost exclusively to refer to the tracking of the ratio of high cards to low cards in blackjack, although theoretically card counting can be used in some other card games.
The probability of being dealt various starting hands can be explicitly calculated. In Texas Hold 'em, a player is dealt two down (or hole) cards. The first card can be any one of 52 playing cards in the deck and the second card can be any one of the 51 remaining cards. This gives 52 × 51 ÷ 2 = 1,326 possible starting hand combinations. (Since the order of the cards is not significant, the 2,652 combinations are divided by the 2 ways of ordering two cards.) Alternately, the number of possible starting hands is represented as the binomial coefficient
(52/2) = 1,326
which is the number of possible combinations of choosing 2 cards from a deck of 52 playing cards.
In poker, the probability of many events can be determined by direct calculation. This article discusses how to compute the probabilities for many commonly occurring events in the game of Texas hold 'em and provides some probabilities and odds[1] for specific situations. In most cases, the probabilities and odds are approximations due to rounding.
When calculating probabilities for a card game such as Texas Hold 'em, there are two basic approaches.
The chances of winning a lottery jackpot are principally determined by several factors: the count of possible numbers, the count of winning numbers drawn, whether or not order is significant and whether drawn numbers are returned for the possibility of further drawing.
In a typical 6 from 49 lotto, 6 numbers are drawn from 49 and if the 6 numbers on a ticket match the numbers drawn, the ticket holder is a jackpot winner - this is true regardless of the order in which the numbers are drawn. The odds of being a jackpot winner are approximately 1 in 14 million (13,983,816 to be exact).
Boxcars is the outcome of rolling the dice in a game of craps and getting a 6 on each die. The pair of 6 pips resembles a pair of box cars on a freight train. In modern parlance, it refers to such a roll in any game involving 6 sided dice which are marked with pips. The probability of this roll is 1 in 36, or about 2.8%. One of the 4 bets on any common craps table. It is on the 'high side' of the horn bet in which the player can either bet on the 2,3,11, or 12. When the player throws in money and calls out "midnight" or "Boxcars", the dealer will usually 'book' the bet as a bet on the 12, so as to not create confusion.
Also called Midnight.
The house average or house edge is the amount the player loses relative to a bet, on average. If a player bets on a single number in the American game there is a probability of 1/38 that the player receives 36 times the bet (35 times the bet plus the return of the bet itself), so the player ends up, on average, losing 5.26% on each bet:
( (probability * payout) / bet ) - 1 = expected value as fraction of bet
For example, betting $10 on a single number on an American wheel:
( ((1/38) * 360) / 10 ) - 1 = -0.0526
The subject of gambling is all encompassing. It combines man's natural play instinct with his desire to know about his fate and his future. (Franz Rosenthal)
Poker is a godless game, full of random pain.
