A Martingale is any of a class of stake strategies that originated from and were popular in 18th century France. The word most likely has its origin in the vocabulary of gamblers describing a winning system. In fact, at the time it was not unusual for gamblers claiming to have a sure winning strategy or Martingale. 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% as it is on the other even chance bet options.

The martingale betting strategy is basically a sure thing. The reasons why its value is limited are on the one hand that the gambler requires a huge bankroll to overcome long losing streaks and on the other hand that casinos have table limits to limit the maximal possible bet amounts. 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. 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 in the long run. In a casino, the expected value is negative, due to the house's edge.

Example of a Martingale progression for a losing streak of 13 consecutive losses:

1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048, 4096, 8192

01) Bet: $ 1 on 1 spot. Profit on a Win: $ 1. Bankroll Needed: $1

02) Bet: $ 2 on 1 spot. Profit on a Win: $ 1. Bankroll Needed: $3

03) Bet: $ 4 on 1 spot. Profit on a Win: $ 1. Bankroll Needed: $7

04) Bet: $ 8 on 1 spot. Profit on a Win: $ 1. Bankroll Needed: $15

05) Bet: $ 16 on 1 spot. Profit on a Win: $ 1. Bankroll Needed: $31

06) Bet: $ 32 on 1 spot. Profit on a Win: $ 1. Bankroll Needed: $63

07) Bet: $ 64 on 1 spot. Profit on a Win: $ 1. Bankroll Needed: $127

08) Bet: $ 128 on 1 spot. Profit on a Win: $ 1. Bankroll Needed: $255

09) Bet: $ 256 on 1 spot. Profit on a Win: $ 1. Bankroll Needed: $511

10) Bet: $ 512 on 1 spot. Profit on a Win: $ 1. Bankroll Needed: $1023

11) Bet: $ 1024 on 1 spot. Profit on a Win: $ 1. Bankroll Needed: $2047

12) Bet: $ 2048 on 1 spot. Profit on a Win: $ 1. Bankroll Needed: $4095

13) Bet: $ 4096 on 1 spot. Profit on a Win: $ 1. Bankroll Needed: $8191

14) Bet: $ 8192 on 1 spot. Profit on a Win: $ 1. Bankroll Needed: $16383

TheGrand or Great Martingale system makes the player bet even more.If the player loses a hand he has to double his bet and add one more unit to that amount. The sequence is:

1, 3, 7, 15, 31, 63, 127, 255, ...

If you are on a bad streak you will reach the table limit quicker than when you are playing the classic Martingale strategy.
If you finally win, the net gain is the initial bet and one unit. You can use this system with little changes; for example, add 2,3 or more units instead of 1 to your doubled bet amount after a loss. But using such a strategy you can lose a lot of money.

This is also known as the Reverse Martingale, the Paroli or the Parlay betting strategy. In a classic Martingale betting style, gamblers increase bets after each loss in hopes that an eventual win will recover all previous losses. The Anti-Martingale approach instead increases bets after wins, while reducing them after a loss. The perception is that the gambler will benefit from a winning streak, while reducing losses while having a losing streak. The Anti-Martingale strategy fails to make any money in the long run too. But like the Martingale it can be use in the short run of a session if the gambler understands what he is doing and is aware of the risks involved. The Martingale is perfect for players who are willing to take the risk of losing a large amount of money on some occasions in exchange for frequent small wins. If you use the Martingale in a casino, chances are that you'll end most nights with small wins. A very nice tool to calculate Martingale type progressions for all roulette chances you can find at loothog.com.

For demonstration purpose we have tested a simple roulette system. The rules are just to bet High and Low even chances following the previous spin result using the Martingale. As you can see in the charts most of the time the bet amounts stay relatively moderate but at times they increase up to a maximum of 16384 units in the RNG and 65536 units in the Live Dealer test run. The longest observed losing streaks are 14 spins 16 spins long respectively.