Bank advantage

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As a bank advantage , engl. Edge (Eng. Advance, advantage), House edge , House or Percentage for short , is the term used to describe the expected loss of the player based on his stake in games of chance .

example

If a player, for example, an amount of 100 € in the roulette on a group of four figures, it receives with a probability of 4/37 a gain of 800 € (the win ratio is in a set on four numbers 8: 1) and there is a 33/37 chance of losing his € 100 bet.

The player's expected profit is therefore 4/37 × 800 € + 33/37 × (-100 €) = -2.70 € or -2.70% of his stake or, in other words, the expected loss of the player or the expected winning the banker 2.70% of the player's bet.

In the USA, the term percentage is sometimes interpreted to mean that the banker's expected profit is related to the banker's stake. In the previous example the result is the significantly lower value of 0.3375%, since the profit of 2.70 € is divided by the much higher stake of the banker, namely 800 €.

Problems with definition

  • In some games of chance, such as baccarat , it is possible for a game to end in a draw. In general, undecided games are not taken into account when calculating the bank advantage (cf. e.g. Baccarat - Punto Banco ) - but this is by no means always the case, with more complex games such as blackjack , this is not done in order to avoid additional definition problems.
  • In some games of chance, such as Black Jack, but also Red Dog , Tropical Stud , Easy Poker , the player may change his stake during the game. When specifying the bank advantage, it should therefore be noted whether the expected profit of the casino is related to the stake at the beginning of the game or to the expected total stake of the player: If, for example, a player starts a round of blackjack with a stake of € 100, so his expected stake in this game is € 111.67 due to the possibility of splitting or doubling with an optimal game (see article Black Jack ).
  • In games of chance, which leave certain options open to the player in the course of a single game, when determining the bank advantage it is generally assumed that the player always makes the optimal decision in terms of probability theory.

Relationship between payout ratio and bank advantage

While it is common practice in games of chance such as roulette, baccarat or blackjack to indicate the bank advantage, in lotteries and sports betting it is common to calculate the payout percentages. These two terms are very closely related: the payout ratio plus bank advantage always results in 100%; if the payout ratio is 98%, the bank advantage is 2%.

literature

  • Albert H. Morehead, Richard L. Frey, Geoffrey Mott-Smith: The New Complete Hoyle Revised. Doubleday, New York 1991.