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By Root 710 0

this is true or not, the wheel was certainly of French origin, and by the end of the eighteenth century roulette was a popular attraction in Paris. The rules are as follows: a ball spins around an outer rim before losing momentum and falling towards an inner wheel, which is also rotating. The inner wheel has 38 pockets, marked by the numbers 1 to 36 (alternately red and black) and the special spots 0 and 00 (green). The ball reaches the wheel and bounces around before coming to rest in an individual pocket. Players can make many bets on the outcome. The simplest is to bet on the pocket where the ball will land. If you get it correct, the house pays you back 35 to 1. A £10 bet, therefore, wins you £350 (and the return of your £10 bet).

Roulette is a very efficient money-making machine because every bet in roulette has a negative expected value. In other words, for every gamble you make you can expect to lose money. Sometimes you win and sometimes you lose, but in the long run you will end up with less money than you started with. So, the important question is, how much can you expect to lose? When you bet on a single number, the probability of winning is , as there are 38 potential outcomes. For each single number bet of £10, therefore, a player can expect to win:

(chance of landing on a number)(what you win) + (chance of not landing on a number)(what you win)

or

In other words, you lose 52.6p for every £10 wagered. The other bets in roulette – betting on two or more numbers, on sections, colours, or columns, all have odds that result in an expected value of –52.6p, apart from the ‘fnumber’ bet on getting either 0, 00, 1, 2 or 3, which has even worse odds, with an expected loss of 78.9p.

Despite its bad odds, roulette was – and continues to be – a much-loved recreation. For many people, 52.6p is a fair payment for the thrill of potentially winning £350. In the nineteenth century casinos proliferated and, in order to make them more competitive, roulette wheels were built without the 00, making the chance of a single-number bet and reducing the expected loss to 27p per £10 bet. The change meant that you lost your money about half as quickly. European casinos tend to have wheels with just the 0, while America prefers the original style, with 0 and 00.

All casino games involve negative-expectation bets; in other words, in these games gamblers should expect to lose money. If they were arranged in any other way, casinos would go bust. Mistakes, however, have been made. An Illinois riverboat casino once introduced a promotion that changed the amount paid out on one type of hand in blackjack without realizing that the change moved the expected value of the bet from negative to positive. Instead of expecting to lose, gamblers could expect to win 20 cents per $10 bet. The casino reportedly lost $200,000 in a day.

The best deal to be found in a casino is at the craps table. The game originated from a French variant of an English dice-rolling game. Players throw two dice and the outcome depends on which numbers land and how they add up. In craps, your chances of winning are 244 out of 495 possible outcomes, or 49.2929 percent, giving an expected loss of just 14.1p per £10 bet.

Craps is also worth mentioning because of the possibility of making a curious side bet in which you can bet with the house; that is, against the player throwing the dice. The side bettor wins when the main bettor loses, and the side bettor loses when the main bettor wins. Since the main bettor loses, on average, 14.1p per £10 bet, the side bettor stands to win, on average, 14.1p per £10 bet. But there is an extra rule preventing this neat outcome in craps side bets. If the main player rolls a double six on his first roll (which means that he loses), the side bettor does not win either, but only receives his money back. This seems like a very insignificant change. There’s only a 1-in-36 chance of throwing a double six. Yet less of a chance of winning decreases the expected value by 27.8p per £10 bet, which shifts the expected value of the bet into