Martingale Betting System
Martingale probability theory
Martingale betting systems, that are also known as doubling-up or progression systems, are the most popular with casino players. The basic principle of this system was invented about 300 years ago and was extremely popular in 18th century in France. The classic Martingale betting system is based on martingale probability theory introduced by French mathematician Paul Pierre Lévy. The system is still used by roulette players for repeating even-money outside bets.
Classic Martingale System
The idea of classic Martingale system is to double up the next bet after each loss and to reduce it to the initial amount after each win. Eventually the win covers all the net losses of the previous bets.
For example, if you bet 5 units and lose the bet, the next bet is doubled up to 10 units. Then if you lose your 10-unit bet, you must bet 20 units on the next spin of the roulette wheel. After next loss the bet is increased to 40 units. At last you win the bet which means that the next roulette bet is reduced to the starting amount and you bet 5 units again. As a result, you have a gain of 5 units: 40 - (5+10+20)=5.
NOTE: The main problem about Martingale betting system is that the player can reach the table betting limit very quickly as a result of constant losses. Unfortunately, the long losing streaks are not rare in roulette games, and that is why you can exceed the maximum betting limit in a few games.
Most roulette tables have the limit of $500. As a result of seven losses in a row you reach the betting limit with the initial bet of, for example, $5.
| Bet | 1st | 2nd | 3rd | 4th | 5th | 6th | 7th | 8th |
|---|---|---|---|---|---|---|---|---|
| Size | $5 | $10 | $20 | $40 | $80 | $160 | $320 | $640 |
In order not to lose big money and avoid busting the maximum allowed bet, you are recommended to start betting cycle with small amounts, at least with $1 bet.
Grand Martingale System
Grand or also Great Martingale is the variation of classic Martingale system which involves even greater growth of bets. So, after each loss the player must double the bet and add one more unit to the doubled amount. As a result, the sequence of bets will be like this (if you start betting with 5 units):
If there is a series of constant losses, the player can reach the table limit quicker than when using classic system. That is why Grand Martingale is good for roulette tables with at least $1,000 limit. This is how the bet can grow and bust as a result of losing streak:
| Bet | 1st | 2nd | 3rd | 4th | 5th | 6th | 7th | 8th | 9th |
|---|---|---|---|---|---|---|---|---|---|
| Size | $5 | $11 | $23 | $47 | $95 | $191 | $383 | $767 | $1,535 |
If the series of losses is finally broken by win, the net gain is always initial bet plus one unit, but not only the initial bet like when applying classic Martingale. Of course, it is possible to use another variations of this system, for example, add 2 or more units to the doubled bet amount after each loss. But such roulette strategy involves much risk.
Reverse Martingale System
If you prefer to take advantage of winning streaks rather than losses, you can use Reverse Martingale system. It means, that you double the next roulette bet after each win rather than loss and go back to the initial bet when you lose. This is the formula of Reverse Martingale (if you start betting with 5-unit bet):
It is considered to be less risky than traditional Martingale betting system. However, the first loss after a sequence of successive wins will wipe out the potential gain from the whole streak.