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Even if the players' bankroll is unlimited, the real obstacle is the casino $500 limit.
The player will reach this limit between the 8th and 9th bet (the 9th bet should be $512).
However, the player can look at the game from the opposite side: All he needs is to change the casino edge in his favor.
At the 4th bet, the probability is 93% to win. At this stage of the game, the player already lost $15:
1 + 2 + 4 + 8 = $15
The player could, instead of playing at every roulette spin, wait until the results of the previous 4 spins are the same results in a row:
At this point, the probabilities to have 4 more spins (8 in total) with the same result is close to zero. The player will start to bet with the Martingale system with a very high probability to win within the first spins. Of course, no one can promise that the roulette will not continue with the same result up to 30 times, and even more, however, the player did improve his probability to win his $1:
|Spin #||Bet $||Probability to Lose|
If the player starts to bet at spin number 5, the probability to lose is 3.2 %, and if he continues to lose up to the 10th spin, the probability to continue to lose decreases to 0.1 % with a total of losses of $63.
At this point the player can either decide that this is his limit and stop playing, losing all those $63, or continue to double, up to the casino limit.
On one side, this system will decrease the player probability of losing drastically, however, the roulette won't be a game anymore. It is more like a broken machine that gives the player $1 every few spins. No more fun!
If the player starts to bet on the Red since the first spin, he is supposed, according to the Martingale system, to stick to this Red. With the Modified Martingale System, the player can wait until he finds 4 spins in which any one of the outside table results (Black/Red, High/Low, Even/Odd) is 4 times in a row and then start betting on this opposite row.
I like this Modified Martingale System. The player doesn't get an insurance, but his edge is much better.
Let's find out about the Grand Martingale System.