What is the Martingale system?
A martingale is any of a class of betting strategies that originated from and were popular in 18th century France. The simplest of these strategies was designed for a game in which the gambler wins his stake if a coin comes up heads and loses it if the coin comes up tails. The strategy had the gambler double his bet after every loss, so that the first win would recover all previous losses plus win a profit equal to the original stake. The martingale strategy has been applied to roulette as well, as the probability of hitting either red or black is close to 50%.
Since a gambler with infinite wealth will, almost surely, eventually flip heads, the martingale betting strategy was seen as a sure thing by those who advocated it. Of course, none of the gamblers in fact possessed infinite wealth, and the exponential growth of the bets would eventually bankrupt "unlucky" gamblers who chose to use the martingale. It is therefore a good example of a Taleb distribution – the gambler usually wins a small net reward, thus appearing to have a sound strategy. However, the gambler's expected value does indeed remain zero because the small probability that he will suffer a catastrophic loss exactly balances with his expected gain. The likelihood of catastrophic loss may not even be very small. The bet size rises exponentially. This, combined with the fact that strings of consecutive losses actually occur more often than common intuition suggests, can bankrupt a gambler quickly.
Place a first bet of a minimum odd of 2.00.
If you win you double your money. If you lose, double your initial bet. You stop doubling when you win, in which case you make a profit equal to the initial bet. Thus, a series of six bets, you lose the first five and manage to make a profit on the initial bet if you catch the sixth.
The first bet with a stake of 1 AUD per share 2.00 - lost
The second bet stake 2 AUD(2x1 AUD) per share 2.00 - Lost
The third bet stake 4 AUD( 2X2 AUD) per share 2.00 - Lost
The fourth bet stake 8 AUD ( 2x4 AUD) per share 2.00 - Lost
Fifth-stakes bet 16 AUD ( 2x8 AUD) per share 2.00 - Lost
The sixth bet stake 32 AUD ( 2X16 AUD) per share 2.00 - won - 64 AUD
Your bets 1+2+ 4+ 8+ 16+32 = 63 AUD . 64-63 Win = 1 AUD - Win 1 AUD .
Problems arise in case of long strings of losing bets. Most times, the amount of the player's account is insufficient to cover the long string of losses or the maximum allowed by the bookmaker betting is reached.