Written by / First Psychology Writers
Editor / Tommy
It's common to hear people who are keen gamblers say:
Those who don't know much about gambling may mistakenly think that this is because the gambler himself is smart and always wins;
But the person who really knows the secrets of gambling knows that this is not possible, because he knows that gamblers lose far more than they win.
In fact, what most people don't understand is that behind all gambling is a strict set of mathematical rules, and the excitement of gamblers eventually losing money is inevitable.
These rules include the "Gambler's Loser's Law" and the "Kelly Formula" that gamblers can never overcome.
1. The law that gamblers must lose
This law uses a mathematical formula to explain the percentage of gamblers who win and lose.
Suppose the gambler's initial bankroll is n, and the result of each gamble is a win or a loss, i.e. the bankroll will become n+1 or n-1. The odds of a gambler winning or losing a game are 0.5 each.
Under such assumptions, we will deduce the probability of the gambler's funds going to zero.
Further assuming that starting from the bankroll n, the probability that the gambler's continuous gambling funds become 0 is T(n), and the overall probability is 1,
We get:
T(0) = 1 T(n)=0.5T(n-1)+0.5T(n+1) T(n) = (T(n-1) + T(n+1))/2, 对于n > 0 这个式子表明资金n有一半的机会变为n-1，一半的机会变为n+1。
接着推导得到T(n+1) = 2T(n) - T(n-1)。
设T(1)的值为a，其中0 < a <= 1 根据T(n+1) = 2T(n) - T(n-1) T(1) = a T(2) = 2a - 1 T(3) = 3a - 2 T(4) = 4a - 3 ... T(n) = na - n + 1.
We know that for any n, T(n) >= 0.
When n(a-1) + 1, a is close to 1, so we prove that T(1) is approximately equal to 1, and the same process can be derived from T(2), T(3), ...... and so on are all equal to about 1.
This result is somewhat counter-intuitive:
No matter how much money you have, as long as you continue to gamble with a 50% probability, the end result will be "long bet will lose", and you will eventually lose everything.
Therefore, through this mathematical calculation, it can be seen that no matter how clever the gambler is, he will not be able to defeat the laws of mathematics in the end.
Sadly, despite the facts, it is very difficult for anyone to convince a stubborn and obsessive gambler to stop gambling because it is somehow a flaw in their character.
In the eyes of rational people, gambling should be given up and the so-called luck should be stopped.
Because, the established laws of mathematics have made it clear that gambling only makes people lose more and more, not win more;
Moreover, casinos usually use the theoretical formulas of mathematicians such as Gauss, Kelly, Bernoulli, etc.
Gamblers rely on luck, while casinos rely on mathematics.
2. The Kelly Formula on the Casino
The famous Kelly Formula is based on the same principle.
[Kelly's formula f* = (bp - q) / b] (In fact, Kelly, the creator of the formula, was not a veteran gambler or mathematician, but a physicist, and his research field was the relatively new television signal transmission protocol at that time. ）
An in-depth analysis of the gambling scene shows that when the probability of winning or losing between gamblers and casinos seems to be equal, individual gamblers are still at a disadvantage.
This is not only related to the aforementioned "gambler's law of loss", but also involves the "infinite wealth theory", the core of which is:
In the case of equal chances of winning and losing, the one with more capital on both sides has a greater chance of winning.
For example:
If both gambling players have $5 each, it seems that both sides have a 50% chance of winning or losing, according to the rules until they lose everything.
However, let's say you have $5 and I have $10 in a game, and the rule is still until you run out;
In this case, your chances of winning are actually only 33.3%, and the chances of losing are as high as 66.7% (because of the difference in bets, you don't even know your opponent's bankroll and level of preparation).
Therefore, if we really plan to try our luck at the casino, then at least be prepared psychologically:
Once you enter the casino, you are at a disadvantage
Unless a 100% win rate is guaranteed, a bet should not be placed
What is visible is probability, and what is not visible is the trap of mathematics.
The only strategy to win is:
Do not engage in gambling.
This is because, as mentioned earlier, the mathematical theorem "gambler loses out" is in front of you to ensure that you win more and lose less, and the "law of large numbers" proposed by the mathematician Bernoulli, which is often used in casinos, determines that the game is an unequal game from the start.
In addition, casinos usually set a maximum betting limit.
The reason for setting this rule is not that the boss seems to be kind enough to protect gamblers from bankruptcy, but that the casino has set up a protective measure to protect its own funds, and the logic behind this is the "law of unlimited wealth".
Assuming that the richest man in the world takes out much more than the casino's own funds several times to participate in gambling, according to the law of large numbers and the probability of winning or losing, the casino will completely lose the initiative and may lose all profits.
Therefore, casinos usually set a maximum betting limit in advance according to their own financial and financial capabilities to resist the risk of capital backlash brought by the "infinite wealth theorem".
To sum up, combined with the knowledge of mathematics and probability, we can clearly see that any individual who is involved in gambling can only lose in the end, because gamblers can never defeat the rules of mathematics and the laws of probability. In a casino, the only effective way to win is not to gamble.
3. Cultivate a "gambling mindset" to face life's challenges
Life outside the table is equally uncertain.
In fact, everyone's life can be compared to a big roulette game. We have no way of knowing how many opportunities the next roll of the dice will bring.
But the truth is that everyone bets on the table of life and must try their best to win in a limited time and space.
However, the victory or defeat of the real battlefield of life is not determined by personal passion and hard work alone.
Most people are like temporary participants at the table - passively accepting the hole cards from society, playing according to the preset rules, and following the game;
In this environment, where there is a high probability of losing to the rule-makers, there are occasional gains.
But in a continuous, irreversible trend of failure, they will eventually leave the table and end their lives.
Therefore, more and more people are realizing that it is better to play with the rules on the basis of understanding the rules than to follow them honestly, so as to maximize their personal interests.
- Take risks when you're stable
- Quickly and decisively stop losses when faced with possible losses
- Always act in an altruistic mindset
- Think before you act and make a one-step plan for ten years
-Stick with something
Strictly speaking, these ideas and strategies are not entirely bets, and some even reflect the pursuit of development in conservatism.
But in any case, it is better to move forward with a plan than to move forward blindly and ignorantly.
Because, at some critical moment in life, we have to gamble once, and when faced with a situation where we have to gamble, I hope that each of us can be prepared and bet wisely.
The End -
The First Psychological Writing Group | A group of young people who like to look up at the stars
Key words in this article: gambling thinking, psychology
The picture comes from the Internet, please contact for infringement
WeChat public account: First Psychology