Martingale Betting System
The Martingale Betting System was not conceived by a person named Martingale. Instead, it refers to a class of betting systems popular in France in the 18th century.
The simplest of these systems was designed for a game in which the bettor wins his stake if a coin comes up heads and loses it if the coin comes up tails. The system required the bettor to double his bet after every loss, so that the first win would recover all previous losses plus win a profit equal to the original bet.
Today, the Martingale Betting System is applied mostly to casino games like Blackjack or Craps. The system is still the same - the player is required to double his bet after a loss and is required to drop back to the minimum bet after a win.
For example, you start at $2 in a Blackjack table and lose in four straight hands. Then, on the fifth hand, you win! For simplicity, let's just say that all the bets were even money.
You would have lost $2+$4+$8+$16 = $30 on the four losing hands and won $32 on the fifth hand.
The losses were covered ($30) and you had a profit of $2 (equal to the original bet).
In the old days, the Martingale Betting System was believed as a sure thing by those who practiced it. After all, a bettor with infinite bankroll will eventually win despite straight losses.
Of course, no bettor possessed infinite wealth, and the exponential growth of the bets would eventually bankrupt those who choose to use the Martingale.
It is widely believed that casinos instituted betting limits specifically to stop Martingale players, but in reality the assumptions behind the strategy are unsound.
Players using the Martingale system do not have any long term mathematical advantage over any other betting system or even randomly placed bets.