Martingale Analysis

We are not going to go into too much mathematical detail, here, but it is interesting to take a look at the maths (or math depending on where you're from) behind the Martingale System and ask the question: "What makes it tick"? When we say maths, what we really mean is the numbers, the odds.

Specifically for roulette players, we going to explore the following question: "What are the odds of playing the martingale strategy on say even payout bets in roulette, and continue winning to double your money?

Since a Martingale betting profile goes something like this:
1,2,4,8,16,32, and we are assuming that you are going to want to bet more than 1, so let's say we start at 4 and go:
4,8,16,32,64,128 and we assume the table limit is 200.

So the question becomes:
What are the odds of  losing 6 roulette spins in a row assuming we are betting red/black or even/odd. Is it low? Is this a viable startegy?

Well, actually, your odds of a 6 loss streak are greater than you might think.
The odds of losing one spin at roulette are 52.6%. If you only play 6 spins, the odds of losing 6 times in a row are 2.1%, pretty good, in other words. BUT. Hang on. If you want to double your bankroll, you are going to have to play more than 6 times. The more spins you play, the bigger the odds of losing 6 times in a row.

If you play 73 spins, there is over a 50% chance that you will lose 6 spins in a row.
Then, after 150 spins, the odds go up to over 77%, and if you sit at the table for 250 spins, your odds of getting burnt 6 times in a row are over  90%.

Example
Let's say we want to bet $8 a go- this gives a run of 6 and keeps us within the table limits (if the outside bet limit is $256), so 8,16,32,64,128,256

Now let's set a bankroll of $160, so we are only using 5% of our initial capital on the first bet. To double our money in the unlikely even of winning every single bet, we need to play 20 spins. If we win every time on the 6th bet (pretty hair-raising!), we'd need 120 spins (your odds of losing more than 6 times in a row are now over 50%).
In reality, the number of spins you will need to play will sit somewhere between 20 and 120.

You can start to see the pros and cons here of the Martingale. Obviously, you are going to be able to handle longer sequences of losses if you start low (say 1), but then it's going to mean that you need to sit in for more spins to hit your profit target, so your chances of hitting 6 losses in a row are higher.

You can optimise by 
(1) Starting with a low first bet
(2) Minimising the time you spend at the table.

Unfortunately, these are opposites in roulette!
From a casino's point of view, the odds are good that a player bust out before he is able to double his money.

In summary

  • Bet low to begin with
  • Try and keep your session as short as possible
  • Play on tables with a high limit, but set your own maximum Martingale. Remember, betting $256 to win back a $1 bet seems kind of crazy when you look at it in isolation- it's still a 50/50 bet (less actually because of the 0 pocket), and the wheel has no memory.