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If a player bets on a single number in the American game there is a probability of 1 ⁄ 38 that the player wins 35 times the bet, and a 37 ⁄ 38 chance that the player loses their bet. The expected value is: −1 × 37 ⁄ 38 + 35 × 1 ⁄ 38 = −0.0526 (5.26% house edge) For European roulette, a single number wins 1 ⁄ 37 and loses 36 ⁄ 37:
Following is an analysis of the expected value of one round. Let q be the probability of losing (e.g. for American double-zero roulette, it is 20/38 for a bet on black or red). Let B be the amount of the initial bet. Let n be the finite number of bets the gambler can afford to lose. The probability that the gambler will lose all n bets is q n ...
The mathematics of gambling is a collection of probability applications encountered in games of chance and can get included in game theory.From a mathematical point of view, the games of chance are experiments generating various types of aleatory events, and it is possible to calculate by using the properties of probability on a finite space of possibilities.
The wheel is divided into 18 pockets which are numbered from 1 to 9, each number occurring twice. The numbers 1, 3, 6 and 8 are black, while the numbers 2, 4, 7 and 9 are red, and 5 is yellow. Instead of the ivory ball used in roulette, a rubber ball is used in Boule.
The most commonly played game is roulette. The minimum amount wagered per spin is £1 and the maximum is £2. The largest single payout cannot exceed £500 and this can limit the wager size e.g. the maximum wager on a single number on roulette at odds of 35:1 is £2. [2]
In probability theory, odds provide a measure of the probability of a particular outcome. Odds are commonly used in gambling and statistics.For example for an event that is 40% probable, one could say that the odds are "2 in 5", "2 to 3 in favor", or "3 to 2 against".
The Labouchère System is meant to be applied to even money Roulette propositions such as Even/Odd, Red/Black or 1–18/19–36. When any of these bets are made in the game of Roulette, a spin resulting in a "0" or "00" results in a loss, so even though the payout is even money, the odds are clearly not 50/50.
E.g. £100 each-way fivefold accumulator with winners at Evens ( 1 ⁄ 4 odds a place), 11-8 ( 1 ⁄ 5 odds), 5-4 ( 1 ⁄ 4 odds), 1-2 (all up to win) and 3-1 ( 1 ⁄ 5 odds); total staked = £200 Note: 'All up to win' means there are insufficient participants in the event for place odds to be given (e.g. 4 or fewer runners in a horse race).