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The payout given by the casino for a win is based on the roulette wheel having 36 outcomes, and the payout for a bet is given by . For example, betting on 1-12 there are 12 numbers that define a win, p = 12 {\displaystyle p=12} , the payout is 36 12 = 3 {\textstyle {\frac {36}{12}}=3} , so the bettor wins 3 times their bet.
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 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.
American Roulette: This variation includes an extra “double-zero” pocket, raising the house edge to 5.26 per cent, making it less favourable for players.
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 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]
Parimutuel betting differs from fixed-odds betting in that the final payout is not determined until the pool is closed – in fixed-odds betting, the payout is agreed at the time the bet is sold. Parimutuel gambling is frequently state-regulated, and offered in many places where gambling is otherwise illegal.
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related to: american roulette payouts