Another Foolproof Roulette System Bites the Dust

Twice last week, I was buttonholed by bettors bragging about foolproof roulette systems they'd devised. Once in person. Once via e-mail on the Internet. By coincidence, both players had struck upon essentially the same ostensible secret of success.

Details differed, but here's the nub. 1) Wait for five successive hits anywhere in the left-hand column of the layout or on 0 or 00. 2) Bet $500 each on the middle and right-hand columns because they're "due." 3) If the bet wins, quit with $500 profit. 4) If the bet loses - another hit in the left-hand column or 0 or 00 - the other two columns are "past due" so bet on them again.

Both players told me they figured the systems put the odds in their favor. Both claimed they'd been playing and were ahead. Both said the casinos were giving them freebies galore because the dumb dealers and pit bosses didn't realize what was happening. And, both asked my opinion.

First, "waiting" for some sequence of events to indicate that a result is "due" is irrelevant. Roulette is a game of independent trials. On each spin of the wheel, the ball can land in any of 38 grooves with equal probability. Previous results don't matter.

Second, betting $500 each on two columns has 63.16 percent chance of winning and 36.84 percent chance of losing; that's odds of 1.71-to-1 for the player. Don't mistake this for a positive expectation, though. The problem is that a loss is a $1,000 setback while a win is worth $500; that's 2-to-1 against the player.

Effects of the disparity between 1.71-to-1 "for" and 2-to-1 "against" become clear considering the results of multiple bets.

In two spins, this system gives players 39.89 percent chance of winning twice and earning $1,000, 46.53 percent chance of winning once and losing once for a net loss of $500, and 13.58 percent chance of losing twice at a total cost of $2,000. There's not only more chance of being behind than ahead, but the maximum possible profit is still just half the greatest conceivable loss.

Additional play makes the situation increasingly bleak. Consider five bets. Probability of profit is 10.05 percent for $2,500 and 29.31 percent for $1,000; likelihood of loss is 34.20 percent for $500, 19.94 percent for $2,000, 5.81 percent for $3,500, and 0.69 percent for $5,000. After 100 bets, the chance is only 23.27 percent of being ahead at all, compared with 76.73 percent of being behind. And after 1,000 bets, the chance of earning any profit is a mere 1.07 percent, contrasted with 98.93 percent of suffering a loss. Statistically, these last figures imply that for every hundred players betting this system a thousand times, one would be sure it was foolproof and the other 99 would be licking their wounds.

Last, there's the question why the casino bosses hand out meals, rooms, transportation, and tasteless merchandise to solid citizens using this system. It's because the 1.71-to-1 and 2-to-1 odds give the house a high 5.263 percent edge. So, when a player puts $1,000 total on two columns - win or lose - the casino chalks up a theoretical gross profit of $52.63. Averaged over many players, the laws of probability say this figure should accurately predict actual return - as, indeed, it does.

Casinos typically allocate 20 percent of the theoretical gross take on games to "incentives." Bet the two columns for $500 each 10 times during a day. The casino calculates a $526.30 hold on the $10,000 action. At 20 percent, this gets you about $100 in "comps," which actually cost the joint roughly $50 in "hard money," leaving a fat $475 on the earnings ledger.

Oh yes. When players explain their systems and ask what I think, what should I say? If it's not what they want to hear, they'll argue with me. If I prevaricate or act impressed but don't really respond, I'll feel dishonest with myself. So, when feasible, I try to follow the philosophy of the immortal Sumner A Ingmark:

If asked an opinion, please exercise tact,
You'll ruin a friendship by stating a fact.