If you keep doubling your stake once you lose, will you win the gamble eventually?
Well, that sounds like an exciting question. Every people go to Casino for a chance of gaining huge profit or success with the little amount of money. However, in most cases, people get a result of the loss. To avoid the risk, people have considered so many ways to guarantee a win. Among of these ideas, doubling your stake every time you lose seems to be quite reliable.
Suppose we have a simple gambling game with expected value of 0, or the expected value is just equal to your input. Let’s set a scenario, where you use 1 dollar as the stake. If you win, you get 1 extra dollar, and if you lose, you will lose your stake. Also, here we assume you will double your stake if you lose, and the game ends when you win.
Table showing the game
To better show this, here is a table showing some possibilities:
From this table, we can easily observe that the actual profit is only 1 if you win, but the loss will be larger and larger as the stake doubles. Indeed, you will win the gamble and get all your cost back by doubling your stake. Although the risk is small here, the input and return do not really match in this case.
When people want higher returns, they go to casinos. Winning the jackpot is always a great incentive for gamblers. However, the casinos are not set to benefit gamblers, but for earning money. To make sure they are not running a deficit, casinos will never provide you a chance to play a fair game. In this case, the probability of winning is too small. Moreover, if you keep doubling your stake, your number of stake will follow 2^n, where n is the number of trials. As we all know, this function grows rapidly.
The value of 2^n Source: http://image.slidesharecdn.com
From the table we can see, 2^10 is about a thousand, but 2^20 is around 1 million! If the probability of winning is 1/20, which is actually large in casinos, then you need at least a million to guarantee that you are not making a loss.
Here is a video using this strategy in a gambling scenario:
https://www.youtube.com/watch?v=Kwjk99DdYMk
The “Martingale” in the video is the fancy term for doubling your stake, and it’s widely used in the research of Statistics as well as Mathematics. In these subjects, researchers’ studies are based on computing variables such as expected value. When they consider the case of casinos or gambling in real life, the expected value can even be negative, which means 1 additional dollar will cause you to lose several cents or even more.
Obviously, doubling the stake is not a good idea. There is no strategy for easy winning, and hard-working is the only secret behind success.
