Gambler ruin or the casino always wins

Gambler's ruin is a term of gambling terminology as well as the gambler's conceit and the gambler's fallacy. This term is applied for signifying few related conceptions of the theory of probability.

The probability

Probability is a means to express the belief that some event will happen or has already happened.

Statistical ideas

Speaking about the gambler's ruin it is necessary to mention three main statistical ideas of roulette betting which are interconnected.

  1. When the player does not reduce the bet after the loss and just raises it to a fixed part - he will finally lose (despite of the positive expected value).
  2. The player who has limited bankroll and who plays a fair game will lose as against the gambler with unlimited bankroll.
  3. The player who gambles with a negative expected value will finally lose. And it does not matter which system of roulette betting was applied by the gambler.

Huygens' theorem

Actually, the gambler's ruin is another name for the Huygens' theorem. Christian Huygens is a prominent mathematician and physicist of the 17th century. His theorem demonstrates how it is possible to calculate the probability that the gambler will win a series of bets until the other player's stake is lost. It is on condition that the initial stakes and the probability of winning are known.

Classical example of gambler's ruin

It is considered that the casino player always has a limited bankroll, whereas the casino possesses a measureless amount of money. The idea of the gambler's ruin is that the player will never win all the casino money. Whilst the casino has all the opportunities to take all the player's money. The advantage is the important thing and the casino has it. So, after a range of small wins the gambler can lose more than he won.

The gambler's psychology

It is naturally that every gambler always wants to win. And when he has not a lot of money left, he tries to show the desire to win and to try again. The player will rather prefer this variant to going home with a little amount of money left. This is the gambler's ruin - the casino keeps winning.


Michael Shackleford is a well-known person in the world of gambling. He is an owner of gaming consultancy business and adjunct professor of Casino Math course.

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