There are no free comps

It was a busy night in Las Vegas, at the end of a busy day. I hadn't eaten since breakfast, all the restaurants were crowded, and I found myself dining at the counter of a casino coffee shop.

From my stool, I couldn't help but overhear the conversation to my left. A man and a woman, late 20s or early 30s, were going over their plan of attack for the roulette wheel.

"That's all we have to do," he told her. "I'll bet red, you bet black. Wins balance losses. We'll get our comps for free."

I stayed focused on my roast turkey and dressing, but apparently my smile was obvious.

"Do you see a problem with that plan?" he asked.

Your wins and losses won't always balance, I told him. Whenever a 0 or 00 turns up, both red and black lose.

"Yeah, but what are the odds of a 0?"

The same as any other number, I said, shaking my head and smiling.

"Well," he said, "it's still better just losing on the zeroes than losing on red AND the zeroes."

I didn't want to make a big issue of it, so I just I wished them luck and went back to my dinner. But actually, they weren't getting any better deal by confining their losses to the zeroes than by both betting red or both betting black. In fact, the house edge is exactly the same at 5.26%. Either way, they'll spot the house an average of $5.26 for each $100 wagered.

Let's say the two of them were each betting $5 on red, for $10 at risk on each spin of the wheel. In a perfect sequence of 38 spins in which each number — 1 through 36, along with 0 and 00 — occurred once, they would risk a total of $380.

On the 18 red numbers, they'd collect $180 in winnings plus keep their $180 in wagers. So at the end of the sequence, they'd have $360, and the house would have have $20 of the original $380.

Now let's say one wagers $5 on red and the other wagers $5 on black. On 36 of the 38 numbers, the red and black wagers would cancel out. One bet would win, the other would lose.

That leaves two more numbers, 0 and 00. On those, both red and black lose, meaning the couple loses $10 on 0 and $10 more on 00.

That's a total of $20 in losses. At the end of our 38-spin sample, the couple has $360 of its original $380 in wagers, and the house has $20, the same as if they'd bet opposite sides.

To express the house edge in percent, divide that $20 the house keeps by the $380 in wagers. That comes to a shade more than 0.0526. To convert to percent, multiply by 100. That's a house edge of 5.26%, regardless of whether the couple combines to bet $10 a spin on either red or black, or breaks it down into $5 on red and $5 on black. Same house edge, same cost for their comps.

I didn't run into the couple again, so I don't know how they did. I hope they had a run of luck and got their comps at low cost. Nearly every system works sometimes, but none work all the time. The odd are the odds, and you can't count on opposite bets to take you to the lunch counter for free.

** * ** * **

The couple I overheard at the counter had roulette on their minds, but from time to time I get e-mails from craps players plotting a similar attack. They'll ask what happens if one player bets on the pass line, and the other bets on don't pass. Will the bets cancel each other out, meaning they neither make nor lose money, but get their comps for free?

Just as in roulette, there's a pitfall. When the come-out roll is a 12, pass line bets lose, but don't pass bets don't win. They push, and the you just get your money back with no winnings.

If you bet $5 on pass and I bet $5 on don't pass, on 35 of 36 possible come-out rolls our bets will cancel out. But on one of 36, the 12, your pass bet will lose and my don't pass bet will push. That gives us a net $5 in losses from our $360 in wagers per 36 come-outs. Divide 5 by 360, the multiply by 100 to convert to percent, and you have a house edge of 1.39%. That's the average of the 1.41% house edge on the pass line and the 1.36% house edge on don't pass.

Don't get the comps for free on this system, either. You just spot the house the same edge it gets on pass and don't pass bets from different bettors all day long.