The Martingale system is the most well known system in roulette. Its a progressive
system that uses Money Management to try to overcome losing streaks and the house edge:
It is generally applied to the 'even' bets such as Red/Black, Even/Odd, Low/High. Where you have 18/37 = 48.6% chance on an individual win.
The principle is to bet $1 on Red or Black, and then when you lose double your bet untill you win.
So you will be betting $1, when lose $2, when lose again $4, lose again $8, ...

The philosophy behind this system is that you win back ALL your losses on the last win. So in the example above,
when you lost 3x, you lost $1+$2+$4= $7. Now you are betting $8 and when you win you have regained all your losses
and even increases your bankroll with $1.
(not all tables allow $1 bets on Red/Black, but then take the minimum table limit).

` It maye be the olderst roulette system, and its even explained on wiki. The system sounds intuitively very attracktive.
However many mathematicians have rushed to prove that 'in theory the system does not work'. As on the long
run you may lose so many times that you are going bankrupt.
In our case though we don't use 'infinate mathematics' but a simple simulation of 18 spins to see if this system
can work. Our bankroll is limited to $100, so already we can see that with doubling up our bet, the maximum amount of losses we can have
in a row is 5, as after that we go bankrupt ( bet $1 on 1st lose bet $2, on 2nd lose bet $4, on 3rd lose bet $8,
on 4th lose bet $16, on 5th lose bet $32, and now we have a bankroll of only $37 left. We can not double to bet $64 and recover
all our losses).

The question now is what is the chance to have 6 losses in a row when betting Red: its 1.8%. (its the
chance of hitting Black or Zero 6x in a row: 19/37 *19/37 *19/37 *19/37 *19/37 *19/37 = 1.8% )

This sounds low, but if you play roulette you have probably seen 6 Reds or Blacks in a row. So it does happen.
(read our Statistics section to get more feel for the %).

The disadvantage of progression systems is that it can make you bankrupt fast. When playing 6 spins in a row there is a 1.8%
chance that you lose all your money. However when you play more than 6 spins, the chance of getting 6 loses in a row
slowly increases, and also the chance of having 7 loses, 8 loses, ..., in a row starts to emerge.

Below the chance graph is shown for using the Martingale system on Red/Black bets after 18 roulette spins.

When starting with a bankroll of $100 and start betting $1 after each win, and double the bet after each lose.

You can win 18 times and end up at $118, or lose 7 or more times and end at $0.
However interestingly most likely you end somewhere in between $100 and $118.

After 18 spins there is 80% chance that you end up with more than $100 ! This is more chance than with any of the flat betting methods.
Clearly with this strategy it is best to stop after a win. That is shown on the next page.

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