September 17, 2021

# Martingale Strategy Explained

A martingale strategy is a betting method designed for games where the gambler wins a 50/50 bet like a coin flip wins landing on heads and loses on tails. This strategy betting structure has the gambler double their bet if they lose so the first win would recover all previous losses and get back to even. The martingale betting strategy has also been applied and used on the roulette wheel as it also has a near 50% winning percentage with red or black excluding green zeros.

While this strategy can get a gambler back to even early on in a betting sequence it also presents the risk of ruin for a large sequence of losses on bets. As the gambler doesn’t have infinite money and there are table limits in casinos, during a losing streak once the bet size has compounded to more money than the gambler has or the casino doesn’t allow the bet size due to table limits the gambler is financially ruined as they can no longer bet large enough to win all losses back.

Large consecutive losses occur more than is expected even with a 50% win rate with bets.

Here are the odds of eventually having consecutive losses in a 50 trade period with a 50% win rate:

1 loss: 100%

2 losses in a row: 100%

3 losses in a row: 100%

4 losses in a row: 95%

5 losses in a row: 77%

6 losses in a row: 51%

7 losses in a row: 29%

8 losses in a row: 16%

9 losses in a row: 8%

10 losses in a row: 4%

11 losses in a row: 2%

The amount of consecutive trades a martingale strategy can take before ruin depends on the initial bet size.

Here is the compounding of growth in doubling down during losing streaks starting with a \$100 bet:

1. \$100
2. \$200
3. \$400
4. \$800
5. \$1,600
6. \$3,200
7. \$6,400
8. \$12,800
9. \$25,600
10. \$51,200
11. \$102,400

The above dangers of compounding losing size shows the impossibility of the Martingale strategy winning over the long term as the first long losing streak is the last. Due to the table limits of casino bet sizes and the limit in capital a gambler eventually runs out of time or money using this betting strategy during losing streaks. They only way to win using this method is to have an early winning streak and walk away while you are ahead.

The anti-martingale (or reverse Martingale) strategy instead of doubling down on losses, increases bets after wins and reduces bets after a loss. An anti-martingale bet sizing method halves a bet after each loss and doubles after each win. This is the opposite strategy from the Martingale system where a losing bet is doubled down on but a winning bet is halved. The anti-Martingale strategy is a method for compounding consecutive wins and minimizing consecutive losses and is a much better strategy than the original Martingale Strategy.

The most important factor to consider before taking on any betting system is the risk of ruin.