with a two-headed snake that winds from 1 to 34, and the bet can be placed on the head at either end of the body. In the United Kingdom, the farthest outside bets (low/high, red/black, even/odd) result in the player losing only half of his/her bet if a zero comes up. Bet odds table The expected value of a $1 bet (except for the special case of Top line bets), for American and European roulette, can be calculated as where n is the number of pockets in the wheel. The initial bet is returned in addition to the mentioned payout: it can be easily demonstrated that this payout formula would lead to a zero expected value of profit if there were only 36 numbers (that is, the casino would break even). Having 37 or more numbers gives the casino its edge. Top line (0, 00, 1, 2, 3) has a different expected value because of approximation of the correct -to-1 payout obtained by the formula to 6-to-1. The values 0 and 00 are not odd or even, or high or low. En prison rules, when used, reduce the house advantage. House edge The house average or house edge or house advantage (also called the expected value) is the amount the player loses relative to any bet made, on average. If a player bets on a single number in the American game there is a probability of that the player wins 35 times the bet, and a chance that the player loses their bet. The expected value is: −1 × + 35 × = −0.0526 (5.26% house edge) For European roulette, a single number wins and loses : −1 × + 35 × = −0.0270 (2.70% house edge) For triple-zero wheels, a single number wins and loses : −1 × + 35 × = −0.0769 (7.69% house edge) Mathematical model As an example, the European roulette model, that is, roulette with only one zero, can be examined. Since this roulette has 37 cells with equal odds of hitting, this is a final model of field probability , where , for all . Call the bet a triple , where is the set of chosen numbers, is the size of the bet, and determines the return of the bet. The rules of European roulette have 10 types of bets. First the 'Straight Up' bet can be imagined. In this case, , for