** There are a lot of craps ‘systems’ for sale which claim to give you a consistent, reliable income from the game. Now, if that was really possible, do you think the casinos would offer the game?** And, if a system really does work why does the ‘inventor’ have to sell it? Hell, s/he can just use their system at the casino and not worry about postage and handling and the other trappings of marketing by mail. Right? Are you with me on this? Dear reader, the game of craps cannot be beaten over a long period of time because the casino doesn’t pay ‘true’ odds on all the bets. If you and I flip a coin ( a 50-50 proposition), but I pay you 95 cents when you win and you pay me $1 when I win, who’s going to eventually end up with all the $$$? Sure, you might win for a while, but if we keep at it long enough, I’m going to clean you out. It’s the same at craps and no betting system, money management system or hedge system or any other legal way of playing the game will overcome the casino’s edge. But, if you keep the edge as small as possible, you might have some winning sessions. So, that’s the best way to play the game: keep the edge as small as possible. It’s actually fairly easy to do, once you understand the mathematics of craps.

**Craps Math is Simple**

**I****t’s all based on the fact that a pair of dice can produce only 36 combinations which range in total from 2 to 12. There’s only one way to make a 2 and one way to make a 12.** The other numbers have different ways in which they can be made, so their probabilities naturally differ. The most common number is 7; it can be made 6 ways, so everything else pretty much keys off that. An 11 or a 3 can be made in two ways, a 4 and a 10 three ways, 5 and 9 four ways and 6 or 8 five ways. Thus, the odds of rolling a 10 is 3 of 36, whereas rolling a 7 is 6 of 36, so the odds of hitting 10 before rolling a 7 are 2 to 1 against. Those are the ‘true’ odds. Now, the odds of throwing an 11 in any one given roll is 2 of 36 or 17 to 1. If a bet pays 15 to 1 for throwing an 11, are you being paid ‘true’ odds? I hope your answer is ‘no’. The difference between 17 to 1 versus 15 to 1 is the casino’s edge on that bet and it amounts to 11.11%. Should you make a bet where the casino has an 11% edge? I hope your answer is a resounding NO! Without getting overly involved with the math, that’s how the casino’s edge is figured on all possible craps bets. Some bets are okay and some are horrible, but the casino has an edge on all of them. That being the case, please read and commit to memory the following statement:

If you play craps long enough, you will lose all the money you care to bet at the game.

**I Understand, But Still Want to Play….**

**A****ll right, it’s your decision, but please listen to me when I tell you that you have to cut the house edge as much as possible in order to give yourself a chance at having a winning session. There are two ways to cut the edge. **The first is obvious: make bets with a small house edge; I call that the ‘intrinsic’ edge. The second, which most authors ignore, is what I call the ‘grind factor’. If you play any game where the casino has an edge, you’re much better off placing one large bet than you would be if you placed a series of small bets. Let me give you an example. A pass line bet has a casino edge of about 1.4%. So, if you bet $100, the mathematical ‘expectation’ is get a return of $98.60. With me on this? Of course, you either win $100 or lose $100, but if you were to do this for a number of trials, it would work out, in the long run, that the casino made $1.40 on each bet. Now, you go into a casino with ‘X’ dollars to risk. If that amount is $100 and you bet it all on the line and walk away, win or lose, your total mathematical expectation for that trip is -$1.40. But what if you walk in with the same $100 and bet $5 at a time? Your expectation on a $5 bet is 1.4% X $5 = 7 cents. Bet the line 20 times and you’ve reached the -$1.40 expectation of a single $100 bet, but at just $5 a pop, you’ll likely bet the $5 more than 20 times. Now the casino is ‘grinding’ you. Bet $5 sixty times and your total ‘action’ is $300, so your expectation is 1.4% X $300 = $5.20. Yes, I know. If you bet the $100 three times, the expectation would also be -$5.20. But remember, you walked away after winning or losing the $100. You might still win or lose the $100 by betting $5 at a time, but you’re paying a much higher price for the privilege. And that will come back to haunt you if you are a regular player of the game. If you bet the line 60 times and win $100, your expectation is to lose 1.4% X $300 = $5.20, so you are $105.20 above expectation. The next time you play, you may win again and you’ll be even more above expectation. But one fine day, the ‘odds gods’ will have their way and you’ll get back to the mathematical expectation. No matter how much you win, the math must be satisfied and you’ll begin losing. Those of you who currently play the game know exactly what I mean. You have some winning sessions and then one day you can’t win to save your butt. That’s just the realization of the negative expectation you’ve built up. I have similar experiences in video poker play, though it’s opposite, since I’m playing with a positive expectation (not positive thinking, but positive mathematics – I have the edge in that game). I’ll lose, session after session, and it sometimes becomes a chore just to go and play. But knowing I have an edge keeps me motivated, so I hang in there and then one fine day the $$$ start rolling in. My positive mathematical expectation is being realized.

**The Psychology of Gambling**

**I**** don’t think any casino patrons are more superstitious than craps players, and I’m including slot players in that assessment.** I have friends who are craps players and they can rationalize any losing streak through every reason imaginable, except mathematical expectation. They tell me about how the shooters couldn’t hit the end of the table with both dice, or how someone’s hand hit the dice in the air, etc., etc., ad nauseum. But if they kept detailed records of every bet they made, they’d discover that their result was just what the expectation told them it would be. But nobody does that, so it’s easier to blame ‘outside’ factors. And that same sort of thinking has most of you thinking I’m nuts for recommending that you make one bet with your entire bankroll and walk, win or lose. But that’s the way to get around the ‘grind factor’ though I will admit it’s not a lot of fun playing that way. So let’s find a compromise here. What we need are bets which are big enough to keep the grind factor to a minimum, yet small enough to provide some playing time. We can do that with the odds bet.

**Free Odds**

**Y****ou won’t find this bet marked on a craps table, simply because the casino would prefer you not make it.** They’ll let you make it, but won’t offer a lot of help at it; you do it anyway. The odds bet can be made if you have placed a pass or don’t pass bet. Let’s stick with pass line betting, but remember it also applies to don’t pass bets as well, though with some modification.

**A****ny pass line bet has a 1.4% house edge built into it. Once a point is established (4,5,6,8,9 or 10), you may place an additional bet behind your line bet and, if the point is rolled again, you are paid even money (1 to 1) on the pass line bet and at true odds for the odds bet.** Let’s say you had $20 on the line and the point rolled is a 10. If you place an odds bet of $20 behind the line and a 10 is rolled before a 7, you’ll be paid $20 for the line bet and $40 for the odds bet, because the odds of a 10 before a 7 is 2 to 1 against. Got that? Good. The $20 on the line has a 1.4% house edge, so its expectation is -$.28. The odds bet has 0 expectation., because it’s paid at true odds; you’ll win as much as you lose. So why make it at all, you ask? Let me ‘splain it to you.

**Craps, The GameMaster’s Way**

**M****y way is simple. You first pick the casino, because you want to play at one that offers multiple odds**. You’ve seen the ads “10X Odds”, etc. Ten times will do nicely, but I realize not all of you have such choices. This will work with single odds, but multiple is better. Anyway, let’s assume that 10X odds are available for my example. The best way to play is to find a $5 table, put $5 on the pass line and put an appropriate amount (according to your bankroll) behind the line. Let’s say you have $100 to risk, then put $20 behind the line. With that, you’ve cut your expectation to -7 cents and yet you’re betting big enough to cut down on the grind factor. If the point is 2 or 10, you’ll make $45 if it hits; if it’s 5 or 9, you’ll make $35 and you’ll collect $29 if the point’s 6 or 8.

**T****he biggest obstacle to overcome with my way of playing is that you’ll lose the $100 fairly quickly if a point isn’t made. Another problem is deciding when to stop.**Only you can answer that part of the equation, but I like to ‘lock up’ winnings by putting chips in my pocket and walking if what I have on the rail is lost. But by restricting your bets to $5 on the line, you can easily keep track of your expectation. Each bet represents 7 cents to the casino, whether it wins or loses. Don’t forget that along the way you’ll win some 7s and 11s and lose to some craps (2,3 or 12); each has a 7 cents negative expectation. That might be a way to determine a quitting point; when the expectation hits a number like $3.50 (50 decisions) or something similar, walk. And write down the number every time, so that when total’s at -$100 and you get blown out, you’ll understand why.

**H****ow should you play if you have more than $100 to risk? First, don’t start betting more on the line, save the increases for the odds bet.** ALWAYS bet the minimum on the line. If you want to get more $$$ into action, use the come/don’t come line. It’s like an extra pass/don’t pass line with the exact same expectation. But by placing $5 on the line and $5 on a come bet, your expectation is now -14 cents and each additional come bet increases that by 7 cents, but it does cut down on the grind factor so it has its advantages.

**B****ut remember, it’s all about expectation. I know some of you are itching to write me and offer advice on other bets to ‘hedge’ your come bets or other strategies. **Don’t. Every bet in craps has a negative expectation and all those other bets simply increase it, some at an exponential rate. I don’t make them and you shouldn’t either.

As always, I wish you luck.