What is the principle of probability that you must win after a long bet?

The principle of probability theory is the "law of large numbers".

At the beginning of the 18th century, the French mathematician Jacob Bernoulli proved the law of large numbers from a mathematical point of view, which was called Bernoulli's law of large numbers by later generations. The law of large numbers tells us that under the appearance of a large number of repetitive random events, there is often a certain law of necessity, that is, chance contains some kind of necessity under the condition of infinite repetition.

The outcome of a gamble is random, and in general, the win rate in the casino is not very high, like 21, with only about 51% of the win.

So, just one or two gambles, or even a dozen in a row, you have the possibility of winning in a row, but as the number of gambles increases, the inevitability begins to manifest itself like a miracle.

Divide the number of times you win by the total number of times this number will get closer and closer to a fixed number, which is the law of large numbers. Take 21 as an example, the more you bet, the closer the win rate will get to 51%. Don't underestimate this little extra 1% win rate, it is this win rate that makes the casino make a lot of money.

Yes, it is the "law of large numbers" that guarantees the job of the casino owner, and as long as there are people gambling, the casino can win forever.

Gambling for a long time is the "casino theorem" in the principle of probability. It points out that no matter how the casino deals cards or rolls the dice, and no matter how the player places his bets, the casino will always make a profit and the player will always lose money in the long run. This is because the odds in the casino are always slightly lower than the actual probability of winning, so players need to win more games than the odds to make a profit, which is highly unlikely for a long time.

Therefore, the idea that you must win after a long gamble is wrong, and it is a game that will be affected by time and luck, resulting in profit and loss.

A mathematical theorem or formula is cold, but it works. For investment and life, there is a gambler's must lose theorem, which explains why gambling for a long time is bound to lose money from a mathematical and probability perspective. For example, goals, money management.

Suppose the gambler's initial bankroll is n, and each time he loses or wins, the bankroll becomes n+1 and n-1 respectively. The probability of losing or winning is, find all the time.

What is the probability that your bankroll will become 0 after betting? Suppose the probability of starting from n and continuing to become 0 is t(n).

Then we have:

t(0) =1

t(n)=;

t(n) = t(n-1) +t(n+1) )2, for n > 0

This second equation is equivalent to the number n with half the chance to become n-1 and half the chance to become n+1.

Then the transformation is equivalent to t(n+1) =2t(n)-t(n-1).

Let t(1) be a, then obviously 0< a<=1. Use t(n+1) = 2t(n)-t(n-1).

t(1) =a

t(2) =2a - 1

t(3) =2(2a-1) -a = 3a - 2

t(4) =4a - 3

t(n) =na - n + 1.

We know that t(n) >0 is true for any n.

In the case of n(a-1)+1, a is close to 1,

So we prove that t(1) is approximately equal to 1The same process can be obtained that t(2) is approximately equal to 1,All the way down, t(n) is about equal to 1

In this way, we come to a somewhat counterintuitive conclusion: no matter how much money you have, you use a 50% probability.

If you gamble, "you will lose if you gamble for a long time". Some gamblers will bet more at a time, not 1 unit at a time, but we don't.

It's hard to agree, this will only change the way you lose, as long as it is a 50% probability, you will always lose it in the end.

I have always been very poor at mathematics and can't understand these formulas. But I also see the contract market as a casino, that.

There are a few points to be wary of.

The most important thing is that as long as you are in the market, the probability of your death is 100%. That requires respect for this law and reverence.

1 The more greedy you are, the greater the probability of the principal returning to zero, 2 It is easy to win a small amount with a big one, and it is difficult to win a big one with a small one. Suppose the probability is 50%, your principal is 100,000, and you want to earn 10,000 with your probability.

10-1 10 = 90%, the probability of losing all is 10% The probability of 100,000 earning 1 million is 99%.

3. The above is still the case that the gambling game is fair, but the market is not fair, and the information and funds are unfair, resulting in the loss of most people in the market.

It's a common gambler's fallacy that you can't win after a long gamble. Gambling games are usually designed with a fixed payout ratio and mathematical expectations, which means that the gambler's expected return is negative in the long run, i.e. losing money. This is because gambling establishments usually set a certain profit rate or commission ratio in order to make profits, and gamblers are often affected by psychological factors such as greed, impulsiveness, and gambler's fallacy during the gambling process, which leads to losses.

The principle of probability tells us that the outcome of each gamble is independent, and that the outcome of a previous gamble will not have an impact on the outcome of the next one. Gamblers are faced with separate bets and fixed odds each time they place a bet, so they cannot increase their probability of winning by increasing the amount of bets or increasing the number of bets. In the long run, gamblers are more and more likely to lose, so they should not be considered to win after a long gamble.

Therefore, gambling is an unreliable way to make money, and for the sake of self-interest and financial security, people should treat gambling rationally and adhere to reasonable risk control strategies.

Although gambling has a bad reputation, it is the cause of probability research. That is, probability occurs due to gambling.

The principle of gambling is that the occurrence of one situation A and the occurrence of another situation B have the same chance, and it is either/or, if there are two people in A who think that a situation will occur, B thinks that B will occur, and there is a dispute, then the two agreements: after the situation occurs, see the result, who is right will get the other party's material reward, so that the so-called "gambling" occurs, in which the material as a reward is "gambling money", so, From this most primitive and fair gambling, it can be seen that the probability of gambling is that the winning rate of all parties involved in the gambling is equal, which is also the formula of probability, otherwise no one will participate in this gambling game, and there will be no gambling.

As the saying goes, nine out of ten bets are lost, and that's the probability.