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## Is it possible to win with mathematics knowledge?

A mathematician will often tell a gambler that abstinence from gambling is the best strategy. Many mathematicians believe that strategies that don’t involve too much risk are the best theory of probability or theory of games can offer a gambler.

It’s hard to say if Edward Thorp, an American mathematician, shared this view. While on winter vacations in Las Vegas, Thorp decided to gamble in the game of twenty-one after he had entered a casino. It turned out that “Dame Fortune” was very unkind to him. Although we don’t know how much the math teacher at one of America’s universities lost on that cold winter night in the 50-s, the beginning of the 60s of the past century, it is evident from the events that the amount was substantial. How can we explain that our hero spent many years developing an optimal strategy for this game? The problem was not just in the amount of money that the mathematician lost. Thorp may have been a risk-averse person, and his pride as a gambler and expert-mathematician hurt him. He could also suspect a croupier for dishonesty since he noticed that They didn’t shuffle cards after every game. It didn’t make him feel uneasy during the game. After visiting casinos several times, he realized that the rules didn’t require any shuffling of cards at the end of each game. It was hard to accuse a croupier. He managed to devise a winning strategy for the fun of twenty-one.

This strategy was, among other things, based on the same aspect that had put a defeated mathematician under his guard: cards weren’t shuffled too often. They did this to avoid unnecessary slowdowns and not due to evil intent. Edward Thorp published the results of his research in 1962 in Thorp E.O. Beat the Dealer. The winning strategy in the game of twenty-one. – New York: Blaisdell,1962.) owners of Nevada gambling houses effectively changed the rules of the game of Twenty-one. But we must not ride ahead of the hounds.

According to the game rules of twenty-one, one croupier dealt two cards to gamblers from a 52-card pack. Gamblers did not reveal their cards to the dealing croupier. One official from a casino also took two cards and showed one to the gamblers. Gamblers use the following scale to evaluate their cards. The value of Jacks, Queens, and Kings is equal to 10 points. An Ace could be assigned 1 point or 11 points. The value of the rest cards corresponds with the numerical value. Eights had 8 points; nines had 9, and so on. The gambler who had the most points from the bottom of the pile was deemed a winner. After assessing the cards, every gambler, including a croupier, had the right to take from a packet or, to simplify, take a widow, any number of cards. If the number of points after a widow exceeds 21 points, the gambler must quit a game.

Stakes were subject to special rules. In the beginning, there were upper and lower limits. Every gambler was allowed to choose a stake within these bounds depending on his evaluation. If the casino visitor had a “better” number of points than the croupier, the gambler gained his stake. If a gambler or croupier has the same number of issues, the game ends in peace. The result is “harmless” for both the gamblers and the casino.

We should also note that a croupier does not have to open his cards if more than 21 points are on the cards. After all the gamblers have opened their card, a croupier is not required to open his cards. Therefore, casino gamblers can’t determine the number of points of the croupier to help them plan their next game strategy (whether they want to gamble or not) and build their game strategy. It provides a lot of advantages to croupiers. This is something that all gamblers know and keep playing. It is impossible to stop someone who doesn’t take risks and does not win.