House Advantage or Edge
Casino games generally provide a predictable long-term advantage to the casino, or "house", while offering the player the possibility of a large short-term payout. Some casino games have a skill element, where the player makes decisions; such games are called "random with a tactical element." While it is possible through skilful play to minimize the house advantage, it is extremely rare that a player has sufficient skill to completely eliminate his inherent long-term disadvantage (the house edge or house vigorish) in a casino game. Such a skill set would involve years of training, an extraordinary memory and numeracy, and/or acute visual or even aural observation, as in the case of wheel clocking in Roulette.
The player's disadvantage is a result of the casino not paying winning wagers according to the game's "true odds", which are the payouts that would be expected considering the odds of a wager either winning or losing. For example, if a game is played by wagering on the number that would result from the roll of one die, true odds would be 5 times the amount wagered since there is a 1/6 probability of any single number appearing. However, the casino may only pay 4 times the amount wagered for a winning wager.
The house edge (HE) or vigorish is defined as the casino profit expressed as a percentage of the player's original bet. In games such as Blackjack or Spanish 21, the final bet may be several times the original bet, if the player doubles or splits.
Example: In American Roulette, there are two zeroes and 36 non-zero numbers (18 red and 18 black). If a player bets $1 on red, his chance of winning $1 is therefore 18/38 and his chance of losing $1 (or winning -$1) is 20/38.
The player's expected value, EV = (18/38 x 1) + (20/38 x -1) = 18/38 - 20/38 = -2/38 = -5.26%. Therefore, the house edge is 5.26%. After 10 rounds, play $1 per round, the average house profit will be 10 x $1 x 5.26% = $0.53. Of course, it is not possible for the casino to win exactly 53 cents; this figure is the average casino profit from each player if it had millions of players each betting 10 rounds at $1 per round.
The house edge of casino games vary greatly with the game. Keno can have house edges up to 25%, slot machines can have up to 15%, while most Australian Pontoon games have house edges between 0.3% and 0.4%.
The calculation of the Roulette house edge was a trivial exercise; for other games, this is not usually the case. Combinatorial analysis and/or computer simulation is necessary to complete the task.
In games which have a skill element, such as Blackjack or Spanish 21, the house edge is defined as the house advantage from optimal play (without the use of advanced techniques such as card counting or shuffle tracking), on the first hand of the shoe (the container that holds the cards). The set of the optimal plays for all possible hands is known as "basic strategy" and is highly dependent on the specific rules, and even the number of decks used. Good Blackjack and Spanish 21 games have house edges below 0.5%.
Read more about this topic: Gaming Mathematics
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