Gambling Systems – The D’Alembert System

The D’Alembert is a system invented in 18th century France by Jean le Rond d’Alembert, a French mathematician, physicist, and philosopher. It is based on a theory of “Natural Equilibrium”. The system reasons that after a win, you are subsequently more likely to lose and that after a loss, you are subsequently more likely to win.

How it works

After a win, the system reasons that you are more likely to get beaten next go, so you subtract 1 chip from your next bet. Conversely, after a loss you are more likely to win, so you add one chip to your next bet. You do not double your money like in the Martingale system – instead you progressively either increase or decrease your bets. This ensures you are not vulnerable to sudden substantial increases in your bet and the elimination of your entire bankroll.

Let’s take an example.

You place a $5 bet and lose (-$5 gain). You add another unit and you place $6 and lose again (-$11 gain), you add another single unit and place $7 and you win ($-4 gain), then you decrease by a single unit and place $6 and win ( $2 gain) and so on.

Where’s the flaw?

This system relies upon the oldest misconception in the book, often known as Gambler’s Fallacy. The fallacy is that the results of a previous bet have some influence upon the next. But the Roulette table or the Poker deck or whatever gambling location has no memory of previous results. Even if red hits eight times in a row, the next spin is still even money. Another example of the fallacy is a coin flip: suppose that we have just thrown four heads in a row. A believer in the gambler’s fallacy might say, “If the next coin flipped were to come up heads, it would generate a run of five successive heads. The probability of a run of five successive heads is (0.5 x 0.5 x 0.5 x 0.5 x 0.5), or 1 / 32; therefore, the next coin flipped only has a 1 in 32 chance of coming up heads.” However, 1 in 32 in the chance of 5 heads in a row if you place the bet BEFORE any of the throws. If you place the bet after 4 of the throws have already happened then the probability is (1 x 1 x 1 x 1 x 0.5). The first 4 have already happened, and so their probability is 1. This means the next flip has an even money chance, just like any other.

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