This is the 1st in a series of craps posts aimed at players who want to start winning more often. I’m including everything you need to know about craps to get the best odds of success. Most of the information in the posts in this series is not aimed at beginners. You should probably already understand the basics of craps before digging too deep into this series. The idea is not to provide how to play craps posts but to provide new information and ideas that might take your existing craps game to the next level.

## Craps Is a Negative Expectation Game

Yes, craps is a “negative expectation” game. But what does that mean, exactly? Gamblers and mathematicians like to talk about bets in terms of their “expected value.” The expected value of a bet is a simple formula, too:

(The amount you stand to win X the probability of winning) – (The amount you stand lose X the probability of losing) = Expected value of a bet

Here’s an example:

You bet \$2 on a coin flip, but if you win, you only get \$1. You have a 50% chance of winning \$1, which amounts to 50 cents in expected value. But you also have a 50% chance of losing \$2, which amounts to -\$1 in expected value. Subtract one from the other, and you get an expected value of -\$0.50.

It should be obvious that if you flip a coin repeatedly long enough under those terms, you might get lucky in the short run, but you’ll go broke in short order in the long run. (“In the long run” just means “eventually.”) All casino games design their odds of winnings and payouts to provide you with a negative expectation, by the way. That’s how the casinos stay in business.

In some games, the expectation is the same no matter what. In other games, like craps, you can choose from an entire all-you-can-bet buffet of wagers. Some of these wagers have a bigger negative expectation than others. One of the subjects I’ll cover in this series of posts is which bets are better and which bets are worse.

## Why I Love Craps and Why You Should, Too

Blackjack has its fans, and I understand why.  But craps is my game, and if you have the right personality, it’s probably your game, too. It’s fun, scary, exciting, suspenseful, and the most entertaining game in any casino which offers it. One of the reasons it’s so great is this buffet of bets I just talked about, by the way.

At most craps tables, you’ll find a huge crowd of players yelling, stuttering, and moaning over the results of any throw of the dice. Some players want to win a lot of money on a small bet. They might bet that the outcome of the next roll will be a 2 (“snake-eyes”). That pays off at 30 to 1, so even a measly \$5 bet pays off at \$150.

Other players like to play a close to even game with an even-money payoff. Those players will bet on the pass line and take as big an odds bet as they can. If you can find a casino offering you the option of betting 10X odds, the house edge for all the money you have in action on that combination of bets is only 0.184%.

The house edge, by the way, is just another way of expressing the expected value. In this case, it’s the amount of money the casino expects to win from each bet over the long run. If the house edge for a bet is 1%, the casino expects to win \$1 on average every time you bet \$100. With a house edge of 0.184%, your expected loss on a \$100 bet is only 18.4 cents—less than a quarter!

## What I Hate about Craps, Though

The large variety of bets is a 2-edged sword. It’s a feature but also a drawback. With such a large number of bets to choose from, it’s easy to choose bad bets—wagers with a high negative expectation. In fact, when it comes to craps, there are far more bad choices you can bet on than good ones.

What does this mean in practical terms? It means if you choose the right bets, you can play for a long time on very little money. You can also get reasonable odds of walking away a winner during any given gambling session. Games of chance are streaky, and with a low house edge, the probability of having a winning streak is better.

But if you choose the wrong bets—the wagers with the highest house edge—you can lose your entire bankroll faster than you ever thought possible. Lots of players make those bets, too, and the casinos even encourage their employees at the craps table to hustle those bets and encourage players to make them.

## More about the House Edge and How the Casino Makes Its Money

The best way to think about how the casino makes its money at craps is to realize that one of 2 things is always happening with a craps bet:

• The casino wins more often than the player on an even money proposition
• The casino gets a cut of our winnings on any bets that you win

These are 2 sides of the same coin. Let me explain how those concepts work to make the casino a fortune:

The most common bets in craps are the pass line bet and the come bet. These are the most basics bets in the game—bets that the shooter will succeed. In the long run, over 495 “rounds,” the casino will win either of those bets on average 251 times. The player will only win an average of 244 of those bets. That’s a difference of 7 bets over the course of 495 rounds of play (7/495 = 1.41%). By taking the odds bet, you can reduce that even further. In a casino where you can take 10X odds, the house edge is reduced to 0.18%, and in a casino where you can take 100X odds, the house edge is reduced to 0.02%.

This means with \$100 in action, you’re looking at losing an average of just 20 cents or just 2 cents, respectively. That’s a lot of entertainment, cheap. It’s also a great possibility of winning, because you don’t need standard deviation to fall far the other direction to come out ahead. Of course, a lot of casinos only allow 2X odds. That’s okay, even though it’s not great. It still reduces the house edge to 0.61%. Let’s talk about the casino’s cut of winnings, too. It’s best explained using an example—the worst bet at the craps table.

### The Any 7 Bet Is a Great Example

The “any 7” bet is a one-roll bet that the next roll will be a 7. You have 6 ways of making a 7 when rolling 2 dice:

• 1, 6
• 2, 5
• 3, 4
• 4, 3
• 5, 2
• 6, 1

That means the probability of winning this bet is 6 divided by 36. (There are 36 possible outcomes when you roll 2 6-sided dice.) This means you’ll win 1 bet out of 6, which also means that your odds of winning are 5 to 1. If you bet \$10 repeatedly on the “any 7” bet, you’ll lose \$10 on 5 rolls out of 6, or \$50.

If you were playing in a “break-even” game—one where the payout odds and the odds of winning were the same—you’d get 5 to 1 on your money, meaning you’d win \$50 on the one roll out of 6 where you won. Since you lose \$50 and win \$50, you break even. But the casino wouldn’t make any money that way. What the casino does, instead, is take a cut of those winnings. Instead of paying off at 5 to 1, this bet pays off at 4 to 1, which means you’ll win \$40 and lose \$50, for a net loss of \$10 over those 6 dice throws.

The house edge on that bet—the average that you mathematically expect to lose on it—is 16.67%. For every \$100 you bet, you’re expected to eventually lose an average of \$16.67. That’s a big sum compared to the \$1.41 on the pass line bet, or the 61 cents on the pass line bet with 2X odds. This bet is often called “big red.” (I have an ex-girlfriend with the same nickname, but I won’t get into that here.) Since red is the color accountants use for negative numbers on a spreadsheet, this bet is appropriately named.  You can analyze any bet in craps this way.

### The Field Bet Is another Great Example

Another example is the “field” bet. That’s another one-roll bet, this time that the next number will be one of the following:

• 2
• 3
• 4
• 9
• 10
• 11
• 12

You have a total of 16 ways to make those numbers, out of 36 possible outcomes. That sounds pretty good. Also, most casinos pay out 2 to 1 if you get a 2 or 12. The field bet is still a lousy wager, though. The casino still has 22 ways to win compared to your 16 ways to lose. Even with the doubled payouts on the 2 and the 12, the casino comes out way ahead here. The house edge for this bet is the same as the house edge for an American roulette game—5.26%.

### The Hard Way Bets

Some craps players love long odds, though. These guys make “hard way” bets. A popular fictional character who does this is featured in the movie Hard Eight, which I recommend you see if you haven’t already.

You can make the following hard way bets:

• Hard 4
• Hard 6
• Hard 8
• Hard 10

These are called “hard way” bets because you’re betting that the corresponding total will be rolled as doubles—a pair of 2s for a total of 4, a pair of 3s for a total of 6, a pair of 4s for a total of 8, or a pair of 5s for a total of 10. You’re also betting that this will happen BEFORE the shooter rolls either a 7 or the corresponding total the “easy way.” For example, if you bet on “6 the hard way,” if the shooter rolls a 1, 5; a 2, 4; a 4, 2; or a 5, 1.

The odds of winning this bet are 10 to 1. There are 10 ways to lose. There are 6 ways to lose by rolling a 7. And there are 4 ways to roll a 6 the easy way. The payoff when you win, though? 9 to 1. Bet \$10 on 6 the hard way 11 times, and you’ll lose 10 times, or \$100. On the roll you win, you’ll win \$90. This means you’ll lose \$10 net on 11 bets, or 9.09%.

## Right Bettor Wagers, Payoffs, and the House Edge

A “right bettor” is someone who bets with the shooter. (It’s the opposite of a “wrong bettor.”) Basically, all the right bettor wagers are bets that the shooter will succeed before rolling a 7.

Whirl – This is the horn bet and the any 7 bet combined.

It’s actually more complicated than some other craps bets, because the payoffs depend on which number wins. For example, if you roll a 7, the payoff is actually nothing, because it’s treated as a push. (This is a tie where your bet is returned to you without any winnings.) That’s because when you win the any 7 bet, you’re still losing the horn bet.

On the other hand, the 2 or 12 pay off at 26 to 5, and the 3 or 11 pay off at 11 to 5. It’s a complicated bet, and the house edge is high. Don’t bet it. Some casinos and players call it the “world” bet. Your odds of winning are 2 to 1. The house edge is 13.33%.

2 – This is a one-roll bet that the next number rolled will be a 2. The odds of winning are 35 to 1, but it only pays off at 30 to 1. The house edge is 13.89%. This is also called “snake eyes.”

12 – This is a one-roll bet that the next number rolled will be a 12. The odds of winning are 35 to 1, but it only pays off at 30 to 1. The house edge is 13.89%. You’ll notice that the odds are the same as for the 2 bet.

Hop (doubles) – The hop bet isn’t listed on the table. It’s one of those “secret” craps bets. A hop bet is a wager that the dice will fall on a specific combination. In this case, we’re looking at doubles, so a 4 on the hop (doubles) would be a bet that the dice would land on 2, 2. (Yes, this is the same as a 4 the hard way.)

There are 2 big differences between betting on the hop and the hard way. A bet on the hop is a one-roll bet—you win or lose on the next roll. A normal hard way bet stays in action until it’s won or until the total is rolled (or a 7 is rolled.) That’s the 1st difference.

The 2nd difference is that the hop bet has a different payout. The odds of winning a hop bet are 35 to 1, but it pays off at 30 to 1. The house edge is 13.89% on this one, too.

Horn – This is a bet that the dice will land on 2, 3, 11, or 12. The odds of winning are 5 to 1. The payoff depends on the specific total, though. A 2 or 12 pays off at 27 to 4. A 3 or an 11 pays off at 3 to 1. The house edge on the horn bet is 12.5%.

Hop (not doubles) – This is a bet on a specific combination, like 4 on the hop that consists of a 3 and a 1. Since you don’t have to roll doubles, you have twice as many ways to win on the hop if you don’t choose doubles. This makes the odds of winning 17 to 1, and the payoff is 15 to 1. The house edge is 11.11%.

3 – This bet, like the hop bet that isn’t based on doubles, has odds of 17 to 1 of winning. The payoff is also 15 to 1, and the house edge is also 11.11%. This bet is also called “ace deuce.”

11 – This is the same as the bet on 3, but it wins if you roll an 11. The odds are the same as for a bet on 3.

Any Craps – This is also called the “3 way.” It’s a bet that the dice will land on 2, 3, or 12. The odds of winning are 8 to 1, and the payoff is 7 to 1. The house edge is 11.11%. Any craps is a one-roll bet.

Hard 4 – This is a bet that the dice will come up 2, 2 before coming up with a total of 7 or another total of 4 not comprised of doubles. The odds of winning are 8 to 1, the payoff is 7 to 1, and the house edge is 11.11%.

Hard 10 – This has the same odds of winning and same payoff odds as a hard 4, but you’re betting on the dice coming up 5, 5 instead of 2, 2.

C&E – This is a combination of the any craps bet and the yo bet. The any craps portion of the bet pays off if you hit 2, 3, or 12. The yo bet pays off if you hit an 11. The overall probability of winning is 5 to 1. The payout is 3 to 1 if the craps numbers come up, but it’s 7 to 1 if the 11 comes up. The house edge is 11.11%

Hard 6 – The hard 6 is the same as a hard 4 or a hard 10, but there are more ways to lose. (There are more ways to roll a 6 than there are ways to roll a 4.) The odds of winning are 10 to 1, but the payoff odds are 9 to 1. The house edge is 9.09%.

Hard 8 – Almost everything I wrote about hard 6 applies to hard 8, too. The only difference is that you’re betting on the dice coming up 4, 4 instead of 3, 3.

Big 6 – This is just a bet that the shooter will roll a 6 before rolling a 7. The odds of winning are 6 to 5, and the payoff is even money. The house edge is 9.09%.

Big 8 – This is just a bet that the shooter will roll an 8 before rolling a 7. The odds are the same for big 8 as they are for big 6.

Place 4 – This is a bet that the 4 will come up before the shooter rolls a 7. The odds of winning are 2 to 1, and the payoff is 9 to 5. The house edge is 6.67%.

Place 10 – The odds are the same as for the place 4 bet, but you’re betting on a total of 10 coming up before the shooter rolls a 7.

The Field – I wrote about the field bet earlier in this post. It’s a bet that the dice will land on 2, 3, 4, 9, 10, 11 or 12. The odds of winning are 5 to 4, and the payoff is even money, unless you roll a 2 or 12. If you roll one of those, you get a 2 to 1 payoff. The house edge is 5.26%.

Place 5- This is a bet that the 5 will come up before the shooter rolls a 7. The odds of winning are 3 to 2. The payoff is 7 to 5. The house edge is 4%.

Conclusion

In the next post in this series, I’m going to look at some more of your betting options. That’s right. Craps has so many betting options that I can’t cover them all in a single post. More importantly, I’ll start offering some advice about which bets you should actually be placing on a regular basis.

For now, take this away from this post: Craps is a negative expectation game, but if you stick with the right bets, the house edge is so low that you can often walk away a winner. The larger number of bets available at the craps table is one of the more confusing aspects of the game. The casino makes its money from craps by making sure they’re going to win more often than you do or by paying you at odds lower than the odds of actually winning. Depending on the bet, the house edge can be as low as 0.18% or as high as 16.67%.

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