The main thing about these bets is the real payoff. We mentioned calculating this in “What’re the Odds,” but now we’re going to go through it step-by-step just to make sure you’re on the same page. Basically, all you do is subtract the number of units lost from the number of units won, keeping the units you bet on the winning proposition on the right side of the dash. So looking at the simplest of these, Voisins du Zero, you have to bet one unit on each of the five “neighbors,” including the middle number. Now let’s say the middle number wins. You lose the units you bet on the other neighbors (four units total) and win 35 units on the middle number. Because you’re sustaining a loss, you’re actually only winning 31 units for every one unit you bet. So the real payoff for this bet is 31:1. This is much better than a “quad” or “carre” bet in which, if you placed five units on it, would only pay 8-1 with real odds of 33:4. But it doesn’t come close to the American contiguous; whose real odds are 11:8 for a coverage area of two uninterrupted sequences of eight pockets.
If you really want to work it out, the question of which contiguous is better becomes much more involved. But, contrary to what you might think, determining this is more a matter of exposure than probability. Most people mistakenly believe you can find out how far ahead you’ll get by treating an outcome’s probability as a portion of 100 bets. They reason that if they have a 50-percent chance of winning on a coin toss and there are 100 tosses they should win 50 times. However, the probability that any set of 100 tosses would have exactly 50 heads and exactly 50 tails is only 8 percent. Why? Because, when we’re talking percentages for an occurrence, we’re only looking at the likelihood that it will happen on one trial. The other trials—assuming they’re all made with the same equally balanced coin and that coin doesn’t incur any physical wear from being flipped—are totally separate events and are unrelated to the first event.
Over time, it’s true, the number of times an outcome occurs will eventually average out to something close to its percentage probability. But that “over time” is actually a long, long time—perhaps billions and billions of flips (or spins). The best route with any game of chance, then, is to always play a single bet with the greatest coverage. This will give you a greater probability of winning on each spin, which in the end, is the best you can hope for.
Really, whichever type of contiguous bet you choose, you’ll still be in the hole because of that infernal vig. Over time, if you play either of them by themselves and don’t change the amount you bet, you will incrementally lose a small about of your bankroll on each bet. You can test this yourself by using a short mathematical formula for determining the “expected value” of a wager. All you do is multiply the amount of you’d lose on a bet by your probability of losing and add the real payoff times the probability of winning.
For the French neighbors bet, this would look something like this:
$4.07 – $4.32= -$.25
And for the American contiguous:
(-$4 x 26/38) + (-$1 x 33/38) + ($4 x 12/38) + ($2 x 5/38)=?
(-$2.74) + (-$.87) + ($1.26) + ($.26)=?
$1.26 + $.26 – $2.74 – $.87=?
$1.52 – $3.61= -$2.09