Why "Long time bet will lose"

Congzhong, the sixth courtyard of Peking University

ten month two No., the shooting of the Las Vegas Music Festival reminds us of the casino there and the old saying "Long time bet will lose".

Why, gamblers What about "long bet will lose"?

Let's talk about the rules of the casino:

Suppose that the game rule of the casino is that between you and the dealer, The probability of winning each other 50% 。

Look, is this the fairest rule of the game?!

It can be realized as follows: zero and one , random occurrence, each accounting for the overall probability 50% 。

set up: encounter zero Appear, the dealer wins; encounter one Appear, gambler wins ； Betting: The dealer and the gambler bet the same amount of money, that is, the gambler bet one The dealer also bet yuan one Yuan; Gamblers bet N The dealer will bet yuan N Yuan.

If a number appears one , all bets of the board belong to gamblers; If a number appears zero , all bets of the game money Return to the dealer.

Okay, set it up ， Now you can gamble.

Assume that gamblers have ten thousand Yuan, each time only Betting one Yuan, he You can bet ten thousand times. final The result is: the dealer and gambler win half and half, draw, and no one wins.

A trial question : Are gamblers willing to play like this ， Bet ten thousand times, and you won't win or lose ？

In fact, gambler Will change the amount of each bet, Sometimes bet one Yuan, sometimes bet fifty Yuan, sometimes bet one hundred Yuan; Every bet changes. If you gamble like this, the result will be how What about?

The smaller the amount of money you bet, the less money you lose or win, Overall capacity Play many times, The more you play, the more results you get It is close to the overall probability of half winning and half losing.

If you bet more, you will win more each time, Either Big win, or Large-scale transportation; However, due to the large amount of bets, Take them all one Ten thousand yuan, The number of bets will decrease, result Will deviate 50% The average probability of winning or losing.

After playing like this, only a few times will Play out Result: Either gamblers make a lot of money, or gamblers lose all their money Money, forced to leave the casino 。

crux Yes: When gamblers make a big profit, they often don't stop and leave until they have a chance to lose all their property. This is called "Long time bet will lose".

So, when gamblers make a lot of money, Correspondingly The dealer lost a lot 。 Zero sum game.

If gamblers can win all the dealers in one's hands The dealer was forced to stop all his money, Exit from the site, The dealer will become The party who "gambles for a long time and loses".

thus it can be seen, It is not the probability that determines the final win or loss, but the fact that who has more money , can persist to the end, persist until the other party loses all his money, and he has not lost all his money once 。

A big casino like Las Vegas, The money of the dealer is far away Far away More money than gamblers, This means that the dealer There is a chance to win all the money of the gambler.

On the contrary, if the gambler's money, Far more than the total amount of money of the dealer, if the money of the gambler It is tens of thousands of times of the total assets of the dealer, so the gambler will have the opportunity to win all the money of the dealer in his own hands and let the dealer go.

As a gambler, Who will have so many dealers money What about? If Really? If you have so much money, you can open your own casino Be a banker To win others' money , then it is not a gambler la 。

When the total assets of the gambler are far less than that of the banker, the only way to win is to go people ， firm active land leave Casino, never come back 。 If so, you will only have the chance to win in this life.

However, many gamblers refuse to leave after winning and continue to gamble , keep gambling If we go on, we will be forced to leave after losing all the money "Long bet will lose" sad ending.

Okay, now we can figure out why gamblers There are two reasons for "long bet will lose":

one 、 Gamblers themselves Is far less than the total assets of the dealer;

two 、 gambler Won't take the initiative to leave, continue Gamble on , until he lost all his property and was forced to leave. This is the human nature of gamblers greedy So it is.

October 5, 2017 Beijing