Nowadays the old system of Tomas Donald has been subject to critical review by the serious mathematician Lev Natanson. His thoughts are as follows:

“I always bet on a red. Suppose, the initial bet is $1. If a black has come out, I increase a bet by one unit, and if a red has come out, I decrease a bet by one unit. But what should I do, if I have bet on a red and won? According to Thomas Donald the bet should remain invariable, as there are no zeros or negative bets. ” And then the mathematician decided to change this system a little: after bet on a red and a winning, the bet should be decreased by one unit. And if you bet only $1, the next bet should be equal to zero. It is clear what zero bet is i.e. you just skip the successive spin.

And then you observe which colors have come out. Suppose, the red has won again. If so, you decrease a bet by one unit again and the next bet (according to the system) is equal to -1. And what does the negative bet on a red mean? It means the next bet on a black. And whatever happens in the sequel, adhere to the only rule: if a black has come out, it is recommended to increase a bet, if a red has come out, you should decrease a bet. For example, after first three spins a red always drops: after the first spin we won $1, then we bet on a zero and later - $1 (bet on a black). Before the fourth spin we should make a bet of - $2 i.e. we make a bet of $2 on a black.

It can be proved that if a black and a red drop per N times out of 2 N spins, the winning will amount to N initial bets. Hereby the sequence, where a red and a black take turns, doesn’t influence on the size of winnings.