So the chances in craps are (on a fair dice roll):

- Win in first roll: 6+2 = 8 in 36 times
- Lose in first roll: 1+2+1 = 4 in 36 times
- Continue from first roll: 36-8-4 = 24 in 36 times

Regardless of target, you loose 6 in 36 times on any other roll

If target = 4 or 10:
- Win 3 in 36 times

If target = 5 or 9:
- Win 4 in 36 times

If target = 6 or 8:
- Win 5 in 36 times

The roller is at an advantage in the first roll, but at a disadvantage in any other roll.

I'll never understand why people gamble.

My favourite saying: "lottery tickets are a tax on stupid people".

Continuing where MigB left off:

The target will become:

• 4 or 10: 6 in 36 times
• 5 or 9: 8 in 36 times
• 6 or 8: 10 in 36 times

After the first roll, any result that isn't a win or a loss causes a new roll with the same odds, so the chances that the whole series of rolls ends in a win are:

• If target = 4 or 10: 3/(3+6) = 1/3
• If target = 5 or 9: 4/(4+6) = 2/5
• If target = 6 or 8: 5/(5+6) = 5/11

The chances for a player who bets that the roller is nifty are:

• loss: 4/36 (first roll) + 2/3·6/36 (target = 4 or 10) + 3/5·8/36 (target = 5 or 9) + 6/11·10/36 (target = 6 or 8) = 0,5070707...
• win: 8/36 (first roll) + 1/3·6/36 (target = 4 or 10) + 2/5·8/36 (target = 5 or 9) + 5/11·10/36 (target = 6 or 8) = 0,4929292...

That is, the roller is at a very slight disadvantage in the series of rolls as a whole. (And Gwynn calls that a simple game?)

Gwynn didn't say, but I assume that players who bet wrong lose the whole bet, so in each bet the same amount is either won or lost. Thus it seems that a player can win very slowly in the long run by consistently betting that the roller is crappy. A casino wouldn't allow a gambler to win in the long run, so something must be missing from the explanation.

The missing piece is the half fizzbin...

In all seriousness, though, I suspect the casino payoff have to do with limitations on what the roller can and cannot do. Like in poker, where the first hand must enter the game, and cannot fold for free if he gets a crappy hand.
So is the roller allowed to bet against herself?

Because its a chance to win big money without working. Peeps are willing to take a chance for that.

You can be the shooter and bet Don't Pass. MOST folks who seriously play the Don't Pass line will pass the dice instead of shooting against themselves as it's bad table etiquette. You're actually betting that you crap out on the first roll or 7-out after the point is made. Since you're playing, in essence, as the house you're betting on the house advantage.

If you place a bet on the passline and a point is made you can place your odds as an additional bet behind the passline. if the point is a 6, you place the odds behind in multiples of $6 (math odds work out better on the payout for $6 rather than $5). If the point is then made the passline gets paid 1:1 but the odds are as if you've placed a standard bet on the number itself so a $6 bet makes you $7 back.

Placing bets on the Don't Pass line inverts this. Once the point is set if a 7 comes up before that point is made the don't pass line gets paid 1:1 on the bet. You can also place odds on a don't pass bet, Say the point's a 6, like above, a Don't pass odds bet would be $7 on the line. However the payout is inverted, a $7 odds on a don't pass pays $6.

Craps is a SLOW gain game. There's no jackpot to hit. It's a game where you gain money slowly over multiple bets, but to cover the combinations you have to put a lot of money on the table to start. If a shooter sets a point, a typical player will put odds on the line, and a few number bets. The way i play ($5 min bet table) i'd have about $28 dollars out after a point gets set (Passline, odds, 2 numbers with single bets). If the shooter craps out on his second roll I lose that $28. To make those bets back the shooter would have to hit my numbers at least once FOR EACH BET i put on the table before he craps out again.

Craps is one of the worst games for a casino in terms of margin against an experienced player. They just keep it around because it's such an old and popular game that people complain if they don't find it.

Of course there's always beginners to win from as well. Craps makes big profits off people who don't know what they are doing.