Jean Le Rond d' Alembert came up with this betting system for bets which offer 50-50 or near 50-50 outcome, so is ideal for teh even money bets of roulette
. The system was based around the theory of "nature seeking equilibrium". Therefore if one outcome begins to dominate the results then its more likely in the future that the other opposite outcome will dominate in the future.
So for the game of roulette if an even money bet such as red has come up a number of times then you should start betting on black. As for the actual betting, the principle is that you add a single bet unit when you lose and decrease your bet by a single bet unit when you win.
So an example of the D' Alembert system would be if you were just betting $1 units and lost, your next bet would be $2. If you lost again, your following bet would be $3. If on the next betting round you won, your next bet would decrease by one unit and therefore be a $2 bet.
The problem with the system and equilibrium is that any bets you place will be in such a small quantity in relation to the long term equilibrium, which is something that could take millions of bets and still not be exact equilibrium. Its quite feasible for you to have long losing streaks. So its likely you will have lot of small winning sessions but, when you lose its likely to be a big loss.
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