Introduction

• Using the above described strategy, a gambler with infinite wealth will eventually land on heads. As a result, the Martingale betting strategy is considered a sure win for those who practice it. However, since none of the participants have the ability to keep betting forever, many inevitably lose.
  
  

The Facts

• The Martingale strategy is not used in modern casinos due the fact that there are table betting limits. While the strategy itself is not a threat to the casinos, the table betting limits are used to limit the casino's short term variance, according to AbsoluteAstronomy.com. Variance is a statistics term that is defined as the expected square deviation of a variable (or distribution) from its expected value. It measures the spread of a particular distribution.
  
  

Considerations

• It is possible to have variance from the expected negative return (by avoiding a losing streak) in any betting system. As a result, even when an individual loses the majority of his bets, he can still recover if he were to win once (regardless of the previous losses), using the Martingale strategy.
  
  

Analysis

• The Martingale betting system can be applied to the roulette table. In particular, the problem investigates the probability of losing six spins of the roulette in a row, assuming that the bets are odd/even or black/red, according to AbsoluteAstronomy.com. A lot of people think that the likelihood of losing six spins in a row are slim and that, with patience and enough monetary reserves, they can win and even increase their bankroll by 100 for each round.
  
  

Results

• The odds in the roulette problem discussed above are, in fact, not in the gambler's favor. The odds of losing are 20/38 or 52.56 percent. If an individual spins the roulette six times, the odds of losing become q to the sixth power or 2.13 percent. However, if the person continues to play more spins, the odds of losing six times in a row begin to increase. For example, there is a 50.3 percent chance that a person will lose six times in a row when he spins 68 times. There is a 80.6 percent chance of losing six times in a row if there are 150 spins and 95.3 percent chance of losing six times in a row if there are 250 spins.