# The Martingale System

Doubling your bet when you lose

- Also known as: Double-Up Progression
- Type: Negative Progression

The *martingale system* is the most popular and most fearsome of all betting systems, mostly due to it's simplicity and rapidly increasing bet sizes.

However, just like every other betting system, it is flawed, and will not help you to win money in the long run from roulette.

## How does the martingale system work?

The basic idea behind the martingale system is that you **double your bet after every loss** in an attempt to recoup your losses (and win one bet).

If you win, you return back to your initial betting unit.

The basic idea is that you keep doubling your bet size when you lose so that you will eventually recoup the losses from your previous losing streak and always come out on top:

So for example, if you bet $1 and lose, you double your bet to $2 on your next go. If you lose again, you double it again to $4. If that *wins*, you have won $4 and have recouped your $3 loss with a profit of $1 on top (which is the original amount you were trying to win at the start).

You then go back to betting $1, and the system starts over again.

## Martingale system simulator

### Algorithm / Code

Here's some working Ruby code that shows how the martingale system works from a programming perspective.

```
# Settings
unit = 1
balance = 100
spins = 500
# Set the initial bet size
bet = unit
# Repeat for a given number of spins
spins.times do |i|
# Spin the roulette wheel
result = rand(0..36)
# Check if the result is a win
win = (result >= 19) # using the high numbers as the even-money wager
# Print bet size and result
print "Spin #{i}: bet=#{bet} #{win ? "(win)" : "(lose)"}, "
if win
# Update balance
balance = balance + bet
# Reset bet to initial size
bet = unit
else
# Update balance
balance = balance - bet
# Double the size of the bet
bet = bet * 2
end
# Print new balance
print "balance=#{balance}\n"
end
```

## Why is the martingale system flawed?

At first this system seems reasonable, and you might be thinking "fair enough". However, this particular system depends on two critical factors for its success:

**There must be no table limit.**If there is a limit on the table you*will eventually hit it*after an extended losing streak, and you will not be able to bet enough to recoup your losses.**You need an infinite bankroll.**If you do not have an unlimited amount of money to gamble with, at some point you will go on a losing streak longer than you though possible and you will lose everything.

In short, bad luck can keep going for longer than you can keep solvent, and the betting limits imposed by the casino prevent you from continuing with the martingale system.

### Examples

#### 1. You have a bankroll of $75

Let's say you are playing roulette with $75, and you are betting $5 at a time. Using the martingale system, you can only afford to encounter 4 losing spins before you lose your money, as you will have bet $5 + $10 + $20 + $40, which equals a total of $75.

Therefore after the 4th spin, you are left with no money to bet with to try and recoup your losses and win money.

#### 2. The table limit is $200 per bet

Let's say you are Bill Gates and you are drunk. You have an (almost) infinite amount of money to play with, and again decide to bet $5 each time, but the table has a **maximum bet of $200**.

This time it will take 5 losing spins ($5 + $10 + $20 + $40 + $80 + $160) before you are unable to bet a large enough amount ($320) to try and recoup your losses and come out a winner. All you can do now is repeatedly bet the table maximum of $200 and hope to get lucky, but now you are no longer using the martingale system.

At this point you might as well have just bet the same amount on each spin, because the casino has prevented you from continuing with the martingale system (and there is nothing you can do about it), and now you're just losing money directly to the house edge.

Note: Whilst a large number of losing spins is not going to be common, the fact of the matter is that it is going to happen eventually if you play for long enough.

## How often do losing streaks happen?

Long losing streaks are **more common than you think**.

Here's a table showing the probability of losing streaks of increasing length when betting on red/black in roulette. It also shows the amount you could lose when using the martingale system from a starting bet of $1:

Losing spins in a row | Total Loss | Probability | Frequency |
---|---|---|---|

1 | $1 | 51.4% | 1 in 2 |

2 | $3 | 26.4% | 1 in 4 |

3 | $7 | 13.5% | 1 in 7 |

4 | $15 | 7.0% | 1 in 14 |

5 | $31 | 3.6% | 1 in 28 |

6 | $63 | 1.8% | 1 in 54 |

7 | $127 | 0.94% | 1 in 106 |

8 | $255 | 0.48% | 1 in 207 |

9 | $511 | 0.25% | 1 in 403 |

10 | $1,023 | 0.13% | 1 in 784 |

11 | $2,047 | 0.065% | 1 in 1,527 |

12 | $4,095 | 0.033% | 1 in 2,974 |

13 | $8,191 | 0.017% | 1 in 5,792 |

14 | $16,383 | 0.0089% | 1 in 11,279 |

15 | $32,767 | 0.0046% | 1 in 21,965 |

So roughly 1 in every 22,000 repetitions of the martingale system you'll be **down $32,767**, and facing the prospect of having to make a $32,772 bet to continue (assuming the casino allowed bets of that size).

Now, I know 1 in 22,000 seems like long odds, but if you're repeatedly trying the system over and over again during your session they're actually much shorter than you think. If you restart the system ten times during one session, your chances of seeing this kind of catastrophic loss are closer to **1 in 2,200**.

It's easy to think "it will never happen to me", but that's just inexperience talking. If you've ever gambled before you know about the wild nature of probability, and you'll also know how brutal it can be when you least expect it.

Warning: The amount you're betting from one losing spin to the next increases *exponentially*, and whilst losing 10 or more spins in a row is unlikely, it's hardly out of the realms of possibility.

## Conclusion

You can use the martingale in almost any form of betting or gambling. You could use the system when playing blackjack, craps, coin tossing, anything. Some gamblers even use the martingale system on slot machines. However, it doesn't matter which game you use it on, because you're always going to lose.

The worst thing about the martingale system is that things can get *very* expensive *very* quickly.

Before you know it you could be laying down a substantial amount of money on the table. This is another reason why I wouldn't recommend implementing the martingale system (if the fact that it doesn't work wasn't reason enough).

If you want to bet for small stakes to see how the martingale system works, then be my guest. You might have some fun with the system, but make sure that you are betting *small* so that you can keep a lid on the amount of money you are betting with as things start to escalate.

Just be sure to not try to use the system as a way to make money. The results can be devastating.