The odds bet in craps

Ron is a novice craps player, or he will be the first time he plays.

"I've read your book, and one by Henry Tamburin and another by Frank Scoblete," he told me on the phone. "You all make it sound so easy, but every time I go to a table, I chicken out."

I laughed. That sounds like dozens, if not hundreds, of casino players I've spoken with over the years. My wife and I have walked through bets and procedures with a pair of dice at home. But she's never tried it in a casino. She'd rather head toward video poker, or the video slots.

"Oh, I'm going to give it a try," Ron said. "It sounds like fun, and the odds are pretty good. But I think I'm going to wait until I go to Las Vegas, where I can go to some little joint and play a $1 or $2 table. I don't want to be betting $10 a pop the first time I try.

"I have a question for you, though. The best bet is to play the pass line and back it up with true odds, right?"

Betting don't pass and laying the odds is a little better, but if you want to bet with the shooter, then yes, pass plus odds has the lowest house edge.

"And the more odds allowed, the better, right?"

Right. The pass line bet by itself has a house edge of 1.41 percent. The free odds — a second wager you can make after the shooter has established a point — pays at true odds and therefore has no house edge. If the house allows only single odds — the free odds bet must be the same size as the pass bet — the house edge on the pass-odds combination drops to 0.8%.

The more free odds allowed, the lower the house edge on the combination drops. At double odds, where your free odds can be twice the size of your pass wager, the house edge on the combination drops to 0.6%. It's down to 0.3 percent at 5x odds, 0.2% at 10x odds, and a minuscule 0.02% at 100x odds, where your free odds wager is 100 times your pass bet.

"OK, that's what I thought," Ron said. "Not the exact numbers, but the trend. The house edge shrinks as more odds are allowed."

Right.

"So is there ever a point at which the house edge disappears altogether? If the casino allowed you to put up a million times odds, would you be getting an even chance or better?"

No, I'm afraid not. The house always has an edge, infinitesimal as it may become, on the pass-odds combination.

"Why? The house edge keeps getting smaller and smaller. Doesn't it have to zero out at some point?

Think of the pass line and the free odds as separate bets — which they are, really, although the odds are offered only if you bet pass or come, and the chance to lay the odds only if you bet don't pass or don't come.

One wager is the pass line. The odds on that wager are always 1.41%. The other wager is the free odds, with no house edge.

If you bet $5 on the pass line, and $5 in free odds, then you're facing a 1.41% house edge on $5, and no edge at all on $5. Bet $5 on pass and $10 in odds, then you're still facing a 1.41 percent edge on $5, but the overall house edge on the combination has diminished because a larger percentage of your total bet is on the free odds.

Same deal with 100x odds. The house edge is smaller still, because $500 of your $505 total bet faces no house edge — but there's still that 1.41% edge on the other $5. At a million times odds with a $5 base bet, you'd have $5 million on the table facing no house edge, but the $5 on the pass line would STILL be facing a 1.41% edge.

The house edge on the combination declines as the percentage of your wager that is in free odds increases. But the house edge on the original pass bet never goes away.

"I think I see that," Ron said. "So what's your strategy? The house edge does decline as you bet more free odds, so do you always bet maximum odds? If you're at a $5 table that allows 100x odds, do you always bet $500 in odds?"

That's far too rich for my blood.

"Mine too. So what do you do?"

Bet the table minimum on the pass line. Save the rest of your normal-sized wager for the free odds. If your bankroll grows and you want to increase your wager, do it by increasing your free odds. Do not increase the size of your pass bet until you've maxed out on odds.

There's no sense in increasing the portion of your wager that does buck a house edge while a no-edge option remains.

"Thanks," Ron said. "I'll give that a go — when I can find a cheap table."