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House Edge
03-29-2009, 09:26 PM
Post: #1
House 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. The house edge is the casino's average profit from a player's bet. 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 skillful 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. Let's look at an example; say all the roulette players collectively gamble $1 million on Saturday night. Based on the odds, the casino expects them to receive $950,000 on winning bets and to lose the other $50,000. That's how the casino makes its money. They don't have to give you terrible odds - they give you an almost even game and make just a few percent on each bet on average. In roulette, casino achieves it’s advantage by placing number 0 on the wheel.

This doesn’t mean that players from our example will always lose. The 5% figure is the mathematical average of how much the players will lose, based on the odds of the game.

The longer you play, the more likely your loss will get close (equal) to the house edge. If you make one $1 000 bet on red or black (“even chance”) you can't lose exactly 5%, you'll either double your money or lose the whole thing if zero comes. But if you make that bet 100 times and you might win 48 times and lose 52 times, winning $48 000 and losing $52 000, for a net loss of $4 000 or 4% of the $10 000 you wagered.

How it’s Calculated

The house edge (HE) or vigorish is defined as the casino profit expressed as a percentage of the player's original bet.
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. On a given night the casino expects the players to win back 95% of what they bet and to lose the other 5%. The 5% the players lose is the casino's profit.

Other Games

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), 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%.

Here's the House Edge for various games:

[Image: house_edge_table.JPG]

"Depend on the rabbit's foot if you will, but remember it didn't work for the rabbit." - R. E. Shay
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