The oldest roulette systems

The D’Alembert

Ringing in as the second oldest roulette system, the “D’Alembert” does a lot to correct for the Martingale’s shortcomings. Unlike its forerunner, you don’t need deep pockets to play it and will probably never hit a table limit with it. This is because it is a “series betting system.” That is, it isn’t a true progressive like the Martingale (which calls for only increased bets) and instead requires you to both lower your bet by one unit when you win and raise your bet by one unit when you lose.

The problem is that, although the D’Alembert is named for a famous French mathematician, the theory behind it (that the more often an unselected outcome happens, the more likely a selected outcome becomes) is plain-out hogwash. A number or color is never “hot” or “due,” and if you let yourself think so, you’re bound to wind up in a reality-T.V. version of that movie “Lost in America.” For this reason, we’ve decided not to describe the D’Alembert and strongly advise you against using it. If you do decide to try it for experiment’s sake, however, simply treat it as a Martingale with your initial bet set at twice the table minimum; if you win, decrease your bet by half, and if you lose double it. Otherwise use all the corrective strategies we explained for the Martingale.

The “Three-To-Two”

The Three-To-Two is kind of like the James Bond of roulette systems: it has gone by many names and everyone who realizes it’s there mistakenly thinks he’s a super-genius. Basically, it requires you to bet on the Black and the third column or Red and the second column at a ratio of 3 to 2 (hence its proper name). That is, for every three units you place on the color, you have to place two units on its corresponding column.

At first glance, the Three-To-Two looks promising because, technically, it covers about 70 percent of the wheel. But the truth is, its expected value shows that it’s still a negative-sum bet (i.e. you will lose a small amount of money to the house every spin). Consider: Every time you win on only a color bet (about 38 percent of the time on an American wheel), you will lose your whole column bet, making your real payoff about 1-3. Likewise, if you win on only the column bet (21 percent of the time), you will lose all your color bet, and your real payoff will be 1-2. On the rare occasion that you win both (about 11 percent of the time), yes, you will win a much larger amount, but even this is only a 7-5 payoff. To put it in terms of sheer numbers though, here’s the expected value for a Three-To-Two when it’s played with unvaried bet amounts on an American wheel with a $10 minimum:

(-$25 x 12/38) + ($5 x 14/38) + ($5 x 8/38) + ($35 x 4/38)=?
(-$7.89) + ($1.84) + ($1.05) + ($3.68)=?
$6.57-$7.89= -$1.32

So you see, the Three-To-Two isn’t half as ingenious as the casinos and their lackeys (i.e., non-GP gambling-news sites) would have you believe. We would, however, like to point out that it’s not entirely impossible to use because, like the Martingale, it can be tweaked to some extent. Foremost of these corrections is that, if you’re going to use it, you must play it on a French Wheel that offers En Prison, and you must always take the held-over option. This will up your probability of winning overall and sometimes give you 3/5 of your original wager back when a zero hits. Plugging the Single-Zero numbers into the expected-value equation, we find the loss rate per spin is a little more in our favor:

(-$25 x 10.4995/37)* + (-$10 x .5005/37) + ($5 x 22/37) + ($35 x 4/37)=?
(-$7.09) + (-$.14) + ($2.97) + ($3.78)=?
$6.75 – $7.23= -$.48


Note: .4995/37 is the equivalent to the 1.35-percent house advantage expressed as a fraction; because En Prison only partially protects you from losing your total bet, the possible loss for this fractional value is still $25; the “-$10” represents the amount lost on the column if you win your imprisoned bet back.

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