# Donald & Natanson Roulette Strategies

The Donald Natanson strategy owes its name to its two authors, mathematicians Thomas Donald, who developed the original rules of the system and Lev Natanson, who later perfected the strategy in his book "Roulette" in 2001. Like many other roulette strategies, it is based on making the right bets. The Donald system makes wagers on simple winning odds, such as red/black, high/low or even/odd, starting with a base bet and increasing it in case of loss or decreasing it in case of win. This strategy to win at roulette works in the long term, but you must have a large capital to invest.

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## How the Donald Natanson Strategy Works

Thomas Donald conceived the initial version of this strategy and recommends that you need a bank with a size of at least 3,000 times the base bet. The strategy assumes that the number of gains is approximately equal to the number of losses over a fairly long game period.

You play the bets in roulette that have a payout of 1:1 (high/low, red/black or odd/even) and start with one base bet.

In the case of a loss, the size of the bet for the next roll must be increased by one base bet. In the case of gain, however, the next bet must be decreased by one base bet.

The last rule of the Thomas Donald system, which refers to the principle of changing the size of the current bet, has now been analyzed and perfected by Lev Natanson, a well-known Russian mathematician, author of many books on casino games and one of the developers of the Mariage software.

According to Natanson, the problem of the Donald strategy is that, after winning with one base bet, the player cannot continue decreasing the bet, in these cases his size for the next roll does not change.

So Lev Natanson proposed a solution for these situations. According to his perfected version of the strategy, after winning with one base bet, the player must continue to decrease the size of the bet, ie the size of the next bet will be equal to zero. In a real game situation this implies that the player must skip a round but still pay attention to the result.

Let's say that the player puts his chips on red. When he manages to win, and with a bet equivalent to one base bet (at the beginning of the game, for example), the amount of the next bet would be zero and the player would miss a round. If during this round the red wins, the rule to increase the bet in case of loss is applied and the size of the next bet for the red colour would be 0 + 1 = 1 base bet.

When the red wins on an omitted round, the size of the nonexistent bet must be decreased again by one base bet, so you will get a negative number.

Lev Natanson proposes that any bet with the "minus" symbol is a bet made on the opposite probability, in this case it would be the colour black. So, if the red wins the player continues to remove a base bet, if black wins, they add one base bet. If the amount to be bet is positive, they bet on the red, if the amount to be bet is negative, they bet on the black and if there is no amount to bet, they skip a round.

## Efficiency of the Betting System

The following comparison table shows the difference between the original system of Thomas Donald and its perfected version, the Donald-Natanson strategy:

 ROLL RESULT DONALD (ORIGINAL) DONALD - NATANSON (MODIFIED VERSION) BET BALANCE BET BALANCE 1 Red 1 +1 1 on red +1 2 Red 1 +2 0 +1 3 Red 1 +3 -1 on black 0 4 Red 1 +4 -2 on black -2 5 Black 1 +3 -3 on black +1 6 Black 2 +1 -2 on black +3 7 Zero 3 -2 -1 on black +2 8 Black 4 -6 -2 on black +4 9 Red 5 -1 -1 on black +3 10 Black 4 -5 -2 on black +5 11 Red 5 0 -1 on black +4 12 Black 4 -4 -2 on black +6 13 Red 5 1 -1 on black +5 14 Black 4 -3 -2 on black +7 15 Black 5 -8 -1 on black +8 16 Black 6 -14 0 +8 17 Black 7 -21 1 on red +7 18 Black 8 -29 2 on red +5 19 Zero 9 -38 3 on red +2 20 Red 10 -28 4 on red +6

According to Donald's rules, if the zero comes out the bet must always be increased, whereas in the Donald-Natanson system, the bet must be modulated, that is, the player must add one base bet to the amount of the current bet when it is positive, and subtract one base bet when it is negative. If the zero comes out a winner with a bet equivalent to zero, Natanson recommends increasing the bet, if the red has won more times than the black in the previous bets or, decrease it if the red has won less times.

On the other hand, according to the rules described in his modification, Lev Natanson showed that if during a number of runs equivalent to (2 * N), red and black have fallen N times, the size of the player's gain will be the maximum and it will be N base bets.

With this, for any correlation between red and black in the results, the order of their alternation does not influence in any way the size of the gain.

The characteristics of the Donald-Natanson system are reflected in the following table based on the final gain from the number of times the red wins in 36 rounds:

 Number of times red has won in 36 rounds 14 15 16 17 18 19 20 21 22 23 Final result of the game (in base bets) -22 -6 +6 +14 +18 +18 +14 +6 -6 -22

It is evident that the more equal the distribution of the red and black numbers in the results of the game, the higher the effectiveness of the system and, the higher the final prize.

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