Martingale on draws mathematical strategy

As we have seen in a previous article, martingale has two essential parameters, which make it more or less risky: If the successive odds are too low, the stakes to wager increase too quickly, and make the martingale (very) risky.
If the probability of winning is too low, there too the martingale risks dragging on before finishing and winning and, even if the winnings will increase more slowly, you will have to be (very) patient and risk losing a lot of times.

The classic, or doubling up, martingale with odds of 2 and a winning probability of 50% is quite risky: stakes explode quickly, and a fairly long series of successive losses is likely (for example, there is a probability of around 2% of having a series of more than 6 successive losses, and therefore of having to invest more than 100 times your initial stake. On this page, one can find the complete mathematical details of the corresponding probability calculations ).

Odds of 3 is reasonable, a good compromise. This odds is very often found on draws, and are often even overestimated because they attract fewer bettors (the vast majority of whom prefer to bet on the victory of their favorite team).
There is thus grounds for setting up an interesting martingale.

Is this really mathematically reasonable ?

First point is that odds of match ending in a draw are often overestimated (mainly because not much punters are betting on them) but this point is not clearly a mathematical one.
Statistics can here be more helpfull, estimating the likelihood of a soccer ending in a draw. The percentage of matches that end in a draw can of course vary, for example from one country to another. In the Premier League for example, recent statistics suggest that 26% of all matches are draws, compared to 27% in the Bundesliga and 23% in La Liga. The percentage can then be (very) roughly approximate around 20 to 30%, that is roughly one matched in four.
Here is some statistics every motivated bettor can calculate by his own, using for example past year figures.
This shows therefore that the Martingale betting system focusing on draws, as a soccer betting strategy, is, mathematically speaking, a reasonable strategy which will end after at most a few rounds.

Mathematical calculations and details of the Martingale on draws

We therefore assume that the odds of each draw are 3.
We bet at the very beginning 5 euros for example and let's say that, for example also, we set ourselves the objective of winning 10 euros (net profit, of course).
So we bet 5 euros at the very beginning.
With odds of 3, if we win we earn 15 euros, therefore 10 euros net profit, and the martingale ends immediately and successfully and a super return of 200%.
Otherwise, we now bet 7.5 euros.
If we win, we earn 7.5×3 = 22.5 euros, minus our wagers 5+7.5 = 12.5 euros, so we obtain a net profit of 10 euros, and now a ROI of 10/12.5 = 80%
If we lose, we are now betting 11.25 euros on next match draw.
If we win, we earn 11.25×3 = 33.75 euros, minus our wagers 5+7.5+11.25 = 23.75 euros, so still a net profit of 10 euros with a ROI of 10/23.75 = 42%
and we continue like this…

Successive loss Probilities

The probability of losing the 1st game is 2 chances in 3 (1 chance in 3, or 33%, chance of winning).
The probability of losing the 1st and 2nd games is 44%.
The probability of losing the first three games is 29%...

Successive loss Probilities

To win 10 euros, with constant odds of 3, you must successively bet the following amounts, with a probability of loss (loss of all previous successive rounds):
Round №MiseProbability of lossROI

Bet calculator

A martingale can quickly prove impossible to follow, because of the increase in stakes, from one round to the next, and which can be dizzying. Complete mathematical details can be found for example on this page and where we see (after sophisticated mathematical calculations of probabilities) that the amount to invest to respect our martingale and finally win can quickly become astronomical if we lose a few rounds more.
It is therefore very important to have from the beginning a full view of what awaits us in order to be able to anticipate, because if the martingale allows us to win the desired net stake without fail, it should in no case be truncated before having won a game because then the total stake invested would simply be lost. In particular, you must be able to predict the future wagers that will be necessary to make so as not to be forced to stop the martingale due to bankruptcy.

Use the martingale calculator

Other readings on martingale strategy: