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Craps: Introduction and Odds

Craps is a very cool game and preferred by us here at Quatloos! In summary form, the advantages are:

By playing the "odds", you can limit the House Advantage to less than 1%. In a casino which allows you to bet 100:1 "odds", the House's advantage is a approximately 1/10th of a percent -- almost no advantage at all.
Even in casinos where you can't get 100:1but the more common 2:1 "odds", by playing the "Parity Line Bet System" of betting "odds", you should be able to keep the House advantage well under 1% and thus a "Statistical Dead Heat" with the casino.
By playing the complex system known as "Parity Hedge System" (a complex variation of the Parity Line Bet System) you can even gain a very small statistical advantage over the House.

Introduction

Craps has lost much of its allure in the casino, simply because younger players are not willing to learn its nuances. This is a shame, because with a proper betting system it is possible to bring the House's advantage well below 1% -- a "statistical dead heat" meaning that the House's advantage will be insignificant over a few rolls, and even very small after hundreds of rolls. Indeed, it is possible to gain a slight statistical advantage over the House with a betting system known as the Parity Hedge System.

The Quatloos! rule about craps which you must remember is this: All of the craps bets you can see on the board are sucker bets, and the only craps bets you want to bother with (the "odds" bets) aren't even shown on the board!

In other words, if you can find the bet on the board, it is a lousy one. The best bets aren't even on the craps board!

Understanding Odds

The odds of a particular number being rolled is determined by how many combinations of the dice it takes to make that number:

Ways To Make

1 2 3 4 5 6

2 1 and 1

3 1 and 2 2 and 1

4 1 and 3 3 and 1 2 and 2

N 5 1 and 4 4 and 1 2 and 3 3 and 2

u 6 1 and 5 5 and 1 2 and 4 4 and 2 3 and 3

m 7 1 and 6 6 and 1 2 and 5 5 and 2 3 and 4 4 and 3

b 8 2 and 6 6 and 2 3 and 5 5 and 3 4 and 4

e 9 3 and 6 6 and 3 4 and 5 5 and 4

r 10 4 and 6 6 and 4 5 and 5

11 5 and 6 6 and 5

12 6 and 6

Ratios are determined by the likelihood that one number will come up before another number. For instance a 5 can be made by 4 combinations but a 7 can be made by 6 combinations. Therefore the odds that a 5 will come up before a 7 are 6:4, which is then usually reduced to 3:2

The Sucker Bets (the "Crazy Crapper Bets")

Since you can keep the House advantage under 1% by staying with the "odds" bets, there is no earthly reason why you should ever put money on any of the other bets (except to annoy the dealers if you are losing by putting their tips on these bets -- they know how bad they are!).

Here's a rundown of the sucker bets. If you see somebody making these bets, grant yourself a chuckle at their stupidity!

The following bets are called "Center Bets" or sometimes "Center Field Bets" because they are found on the center of the board. The are ALL without exception "Sucker Bets" and people who makes these bets either have too much money for their own good, are just idiots, or more likely are novices who have no conception of "odds".

Name & Description of Bet
Mathematical
Odds
Winning
Payout
House
Advantage

Hardways -- The idea is that the combination you bet on will come up before craps OR a "soft" version of the number (i.e., you make "4" by a 1 and 3 instead of 2 and 2)

----- Hard Four (2 and 2) or Hard Ten (5 and 5) 8:1 7:1 11.11%

----- Hard Six (3 and 3) or Hard Eight (4 and 4) 10:1 9:1 9.09%

Any Craps -- This is a one-roll bet that a 2,3 or 12 will come up on the next roll. 8:1 7:1 11.11%

Any Seven -- Another one-roll bet that a 7 will come up on the next roll. 6:1 4:1 16.67%

Two, Three, Eleven or Twelve -- These are one roll bets that the next roll will come up whatever number you bet on.

----- 2 or 12 35:1 30:1 13.89%

----- 3 or 11 17:1 15:1 11.11%

Horn Bet a/k/a " Horn High Bet" a/k/a "Craps & Eleven" a/k/a "C&E" -- Bets that the next roll will be a 2, 3, 11 or 12 Varies Varies At Least
12.5%

Hop Bet -- A one-roll bet that a particular combination will come up, such as a 2 and a 5. Varies Varies At Least
11.11%

he foregoing sucker bets are often called the "Crazy Crapper" Bets after being labeled such by Frank Scoblete in his Beat the Craps Out of the Casinos: How to Play Craps and Win, p. 27 (Bonus Books, 1991) ("Unless you're insane and enjoy throwing away money, these bets offer nothing but the prospect of substantial losses in the long run."). Notice that with these bets the House Advantage is never less than at least an insane 11%.
Big 6 and Big 8 -- On the corners of the board is a good-sized area which says "Big" and with the numbers 6 and 8. This is a mega-sucker bet, since the House advantage is a "Big" 9.09%! Another good place to leave tips for dealers you don't like.

Field Bet

Although not as bad as the "Crazy Crapper" Center Bets, the Field Bet should also be avoided.

The Field Bet is on a very large area on the board which says "Field" and with the numbers 3-4-9-10-11 and the numbers 2 and 12 circled. If you hit any of these numbers, you win 1:1 except for the 2 and 12 which pay 2:1. This is a lousy bet, since the real odds are 11:7 though it pays at 1:1 (paying double on the 2 and 12 brings the odds to 2.78%). Note that this is still better odds than you can get at, say, Roulette, but not nearly as good as taking odds bets (described below).

The only good thing about the Field Bet is that it occupies a large area on the board and is hard to miss when you are throwing a chip on the board to tip the dealers. Otherwise, avoid the Field Bet.

The Place and Don't Place Bets

Place Bets -- The Place Bets are located in large areas on both sides of the craps board, with blocks of numbers 4, 5, 6, 8, 9, and 10, and usually the words "Place Bets". While the Place Bets aren't the worst bets on the board, they are at best a mediocre bet that you shouldn't make -- simply because there are bets available that will give you a much higher payout on the same roll of the dice.
Essentially, a Place Bet is a bet that a given number (4, 5, 6, 8, 9 or 10) will be rolled before a 7 is rolled. When a 7 is rolled, the number loses. If the number comes up before the 7 comes up, you will be paid at a ratio relative to the mathematical odds as follows

Number Bet On Mathematical
Odds Winning
Payout House
Advantage

4 or 10 2:1 9:5 6.67%

5 or 9 3:2 7:5 4.00%

6 or 8 6:5 7:6 1.52%

So, the best you can do with a Place Bet is 1.52% if you bet on the 6 or 8. Not acceptable odds.

Buying the 4 and 10 -- The 6.67% House Advantage for a Place Bet on the 4 or 10 is really horrendous, and would discourage bettors from the most common type of Place Bet strategy, which is "Covering the Numbers", i.e., making bets on all of the 4, 5, 6, 8, 9, and 10. So, the House allows a bettor to do what is known as "Buy" the 4 and the 10 (or either one -- you don't have to "buy" both), which means that you pay the House a 5% tax, or "Vig", and instead you get the 4 and the 10 at true odds of 2:1, less your 5% tax, which always makes your payoff a still-unacceptable 4.76%.

Most of the craps books written by the "experts" will tell you that you can spot the "sophisticated player" because they will "Buy" the 4 and the 10. Throw these books in the trash. As shown, even buying these numbers gives you odds of 4.76%, which is really horrendous and not acceptable to us.

Don't Place Bets -- You can also Don't Place Bet, which is a bet that the 7 will appear before the number, i.e., it is the reverse of the Place Bet. This is also known as a "Laying Bet" as in "Laying the 9", which means that you have bet that the 7 will appear before the 9.

Here are the odds for the Don't Place Bets:

Number Bet On Mathematical
Odds Winning
Payout House
Advantage

4 or 10 1:2 5:11 3.03%

5 or 9 2:3 5:8 2.50%

6 or 8 5:6 4:5 1.82%

So, the best Don't Place Bet gives the House a 1.82% Advantage, making Don't Place Bets a bet which is not acceptable for our purposes.

The Bad Bets which gets you to the Good Bets -- Understanding the "Line Bet" a/k/a "Pass Line" and "Don't Pass" Bets, and the "Come Bets" and "Don't Come Bets"

The Pass Bet -- The Pass and the Don't Pass Bets (a/k/a the "Line Bets") are the heart of craps (and Free Odds, described below, are the soul). These bets are of a rare type in the casino because the odds immediately change after the first roll of the dice.

What happens is this: If the Shooter (the person who rolls the dice) has made a Come bet and rolls either a 7 or an 11, then the Shooter wins immediately, and is paid by the casino at 1:1. However, if the Shooter rolls a 2, 3 or 12 ("Craps") then the Shooter loses immediately. So this starts off as a great bet, since the odds are 8 in 36 that the Shooter will roll a 7 or an 11, but are only 4 in 36 that the Shooter will roll a 2, 3 or 12.

So this starts off as a really great bet! The odds are 8:36 that you will win, but only 4:36 that you will lose -- meaning that the odds of you winning on the come out roll are twice your odds of losing. Whoo Hoo! Sell the cow, we're movin' to Las Vegas.

Not quite. You see this leaves a lot of "Numbers" in the middle, namely 4, 5, 6, 8, 9 and 10. If the Shooter rolls any of these numbers, then the Shooter neither wins or loses, but instead a "Point" is established. The Shooter must then roll that Point again before he rolls a 7 or he loses. Here, the odds have deteriorated because there are six ways to roll a 7, but only five ways to roll 6 or 8, four ways to roll a 5 or a 9, and three ways to roll a 4 or a 10. The problem is that the bet still pays off only 1:1, although the "true odds" of these bets are 5:6, 2:3, and 1:2 respectively.

Worse, the Shooter is required to keep his bet on the table and keep rolling until a 7 comes up. He can only hope that he makes his number before the nasty 7 appears.

Ouch! Put the cow back in the barn.

The truth is that the Pass Bet is a lousy bet, but it DOES qualify you to place "Free Odds" -- one of the most favorable bets in the whole casino -- on the point made. This is described below.

Mechanics -- To make a Pass Bet, you simply place your chips on the Pass Line on the Come Out Roll. The Come Out Roll occurs whenever a 7 has just been rolled, or the point number was rolled (a/k/a "made"). If a "number" (4, 5, 6, 8, 9 or 10) is rolled on the Come Out Roll, then a marker is placed on that number signifying that it is the "point" to be made. If the point is made before a 7 is rolled, there is a new Come Out Roll and a new point is established.

Once you have made a Pass Bet you cannot take your chips off the table until either the 7 is rolled or the point is made.

Put Bet -- Before we move on, we should tell you about the Put Bet. This is a bet made on the pass line after the Come-Out Roll, which essentially allows you to "Choose Your Own Point" by betting or not betting depending on what the point is. This is a completely stupid bet, which pays at 1:1 even though your odds vary from the 6:5 (point is 6 or 8), 3:2 (point is 5 or 9) or 2:1 (point is 4 or 10), and you've missed your chance to win at 1:1 on the Come Out Roll, when the odds were 2:9 against you! The odds for the Put Bet are so embarrassingly bad that they have been banned in Atlantic City and several other gambling resort cities!

The Come Bet -- On any roll after the Come Out Roll, you can make a Come Bet. The Come Bet is almost exactly like a Place Bet, insofar as your odds are good on the first bet since you can win on a 7 or an 11, but only lose on a 2, 3 or 12. However, if "numbers" (4, 5, 6, 8, 9 or 10) come up, your chips are then placed in that box, and you will only win if that number is rolled again before a 7 appears. If your number is rolled before the 7 appears, you will be paid at 1:1.

To make a Come Bet you simply place your chips in the Come Bet box.

The House Advantage on the Pass and Come Bets -- The odds for Pass and Come Bets are identical, as indicated by the following chart:

Come Out Roll for the Pass Bet / First Roll for the Come Bets

Your best best as a Pass or Come bettor is on your first roll, as you can make a 7 or 11 in eight ways, but you can only lose on a 2, 3 or 12, which can only be made four ways.

Desired
Result Mathematical
Odds Winning
Payout YOUR
Advantage

Win 2:9 1:1 11.11%

Pass 2:3 None 55.55%

Subsequent Rolls for Pass Bet / Come Bets

The trouble, of course, is that if you don't win and a number is made you are forced to leave your bet on the table at unfavorable odds of 6:5, 3:2 or 2:1 (depending on the number), but your payoff is only 1:1.

Point	Mathematical Odds	Winning Payout	HOUSE Advantage
4 or 10	2:1	1:1	8.33%
5 or 9	3:2	1:1	5.55%
6 or 8	6:5	1:1	2.77%

Cumulative House Advantage

Depending on which number you bet on, the House still has the advantage because your being forced to leave your bet on the table is a worse bet than the House allowing you to win on the 7 or 11 in the first place.

Point	Mathematical Odds	Winning Payout	Cumulative HOUSE Advantage
4 or 10	2:1	1:1	2.77%
5 or 9	3:2	1:1	1.11%
6 or 8	6:5	1:1	0.76%

Using weighted averaging, the House Advantage for the Pass Line is 1.41% -- still an unacceptable bet.

The Don't Pass Bet -- The Don't Pass Bet is the flipside of the Pass Bet. It is a bet that once the point is made that a 7 will be rolled before the point. To bet the Don't Pass Bet simply place a chip on the Don't Pass line. On the Come Out roll, you win if a 2 or 3 is rolled, you immediately win. If a 7 or 11 is rolled, you immediately lose. If a number ( 4, 5, 6, 8, 9 or 10) is rolled, then that is the point, and the House will pay you 1:1 if a 7 appears before the number.

The Don't Come Bet -- The Don't Come Bet is the flipside of the Come Bet. It is a bet that a 7 will be rolled before a number is rolled. On the first roll of a Don't Come Bet, if you roll a 2 or 3 you win immediately, and if you roll a 7 or 11, you immediately lose. If a number ( 4, 5, 6, 8, 9 or 10) is rolled, then that is your number, and the House will pay you 1:1 if a 7 appears before the number.

Important: The Standoff "12" -- Note that on the first roll of a bet if you are a Pass Line or Come bettor you can win on a 7 or 11, but can lose on the 2, 3 or 12 (a/k/a "Craps"). But if you are a Don't Pass or Don't Come bettor you can lose on a 7 or 11, but you can only win on the 2 or the 3 -- not the 12 too. If the 12 is rolled, you neither win nor lose -- your chip just stays on the table (unless you want to pick it up). What gives?

The truth is that if the Don't Pass or Don't Come bettor could also win on the 12, he would have a slight mathematical advantage over the House. Since this is of course intolerable, the House will not let the Don't bettor win on the 12.

In some casinos, the Don't bettor can't win on the 2 instead of the 12. Mathematically, it doesn't matter much because the 2 and 12 are equals, but you should ask before you start to play.

It is important to understand the Standoff "12" because it makes a big difference in the betting strategy known as the Parity Line Bet System, described below.

The Don't Pass Bet and Don't Come Bet Odds -- So why do people make Don't Pass and Don't Come bets? Simply because these bets pay out at 1:1 although the odds are actually greater.

Subsequent Rolls for Don't Pass Bet / Don't Come Bets

If you can avoid the 7 or 11 on the first roll, you are in great shape because you will be paid 1:1 although your chances of losing are much less than that since the most likely thing which will happen is that a 7 will be rolled.

Point Mathematical
Odds Winning
Payout YOUR
Advantage

4 or 10 1:2 1:1 8.33%

5 or 9 2:3 1:1 5.55%

6 or 8 5:6 1:1 2.77%

Come Out Roll for the Don't Pass Bet / First Roll for the Don't Come Bets

The trouble is, to get to where the odds are in your favor, you must run the gauntlet of the first roll, where the House can win on a 7 or an 11 but you can only win on a 2 or 3.

Desired Result	Mathematical Odds	Winning Payout	HOUSE Advantage
Win	3:36	1:1	8.33%
Pass	2:3	None	55.55%

Cumulative House Advantage

The House's advantage on the first roll is simply too great to overcome.

Point	Mathematical Odds	Winning Payout	Cumulative HOUSE Advantage
4 or 10	2:1	1:1	-0.35%
5 or 9	3:2	1:1	1.95%
6 or 8	6:5	1:1	3.95%

Using weighted averaging, the House Advantage for the Don't Pass Line is 1.40% -- still an unacceptable bet.

Free Odds

If -- and only if -- you make a Pass, Don't Pass, Come, Don't Come bet, you are then allowed to make a separate bet on that bet, i.e., if you have made a Come bet and the number is 4, you can then make an additional bet against the House that the 4 will come up. Another way to look at this is that it is a "side bet" that the 4 will be made. If you are Don't Pass or Don't Come bettor, your "side bet" will be that the number will NOT be made, i.e., a 7 will be rolled first.

These "side bets" are called "Odds" and they are the most important bet in Craps and possibly the best bet in the entire casino!

The reason the Odds bets are so good is that the House has no advantage. Nada, none, zilch. What the real mathematical odds are is what the House pays off at.

Pass and Come Odds (a/k/a "Pass Odds" or "Placing Odds")

These are the odds if you have made a Pass or Come bet, and wish to Place Odds for that number. The Odds will pay off when the bet pays off, and your Odds bet will be lost if a 7 is rolled before the number.

Point Mathematical
Odds Winning
Payout HOUSE
Advantage

4 or 10 2:1 2:1 0.00%

5 or 9 3:2 3:2 0.00%

6 or 8 6:5 6:5 0.00%

Don't Pass and Don't Come Odds (a/k/a "Don't Odds" or "Laying Odds")

These are the odds if you have made a Don't Pass or Don't Come bet, and wish to Lay Odds against that number. The Odds will pay off if a 7 is rolled before the number, and the Odds will lose if the number is rolled before the 7.

Point	Mathematical Odds	Winning Payout	HOUSE Advantage
4 or 10	1:2	1:2	0.00%
5 or 9	2:3	2:3	0.00%
6 or 8	5:6	5:6	0.00%

Mechanics of Odds

So you are probably saying: "That sounds like a great bet! But I don't see 'Odds' anywhere on the crap table?"

The reason for this is that Odds are not shown on the craps table, and if you are not familiar with the rules of craps you would never know this bet existed.

To place an Odds bet, you must first make a Pass, Don't Pass, Come or Don't Come bet. After the point is made or a number is rolled, you place the necessary chips on the table and tell the dealer that you want to place or lay odds on the number, whatever the case may be. The dealer will then take your chips and lien them up against your bet, signifying that those are the Odds bets.

Multiple Odds

So how much in Odds can you make on a give bet? This depends on the casino. The odds are usually shown on a small placard on the side of the craps table, with the amount of the odds allowed and a small "x".

All casinos will give what are called "1x" odds, meaning that your odds can be as large as your Pass/Come/Don't Come/Don't Pass bet. Almost all casinos will give you at least "2x" odds, meaning that the size of your odds bet can be twice as large as your P/C/D-P/D-C bet. Most casinos on the Las Vegas Strip will give you at least "3x" odds, meaning that the size of your odds bet can be three times as large as your P/C/D-P/D-C bet. Many casinos on the northern part of the Strip will give you "10x" odds (ten times as large as your bet), and some casinos in downtown Las Vegas will even give you "100x" odds.

Historical Note: Binions casino used to (may still) let you choose your own odds, which are determined by your first bet, i.e., if you place 2x or 2,000x odds on your first bet, that is what you must play with thereafter!

Importance of Multiple Odds

The Odds are definitely a great bet, because the House's advantage is zero. If the Odds were the only bet you could make, you would theoretically be able to play the House dead even all day. The trouble is that the Odds aren't the only bet you are making -- to get to the odds you must make a Pass, Don't Pass, Come or Don't Come bet. And although the Odds themselves are a great bet, these bets aren't so hot: About a 1.4% House Advantage whether you play Pass/Come or Don'tPass/Don't Come.

The truth is that the House does have an advantage when you play the Odds, because you had to make a bad bet against the House when you made your Pass, Come, Don't Pass or Don't Come bet. However, this advantage is "diluted" by the amount of the odds you play:

Odds Played Cumulative House Advantage

None 1.41%

1x 0.71%

2x 0.47%

3x 0.35%

5x 0.24%

10x 0.13%

100x 0.01%

So, even if you play just 2x Odds, the House advantage is less than 1%, meaning that for all practical purposes you are in a "statistical dead heat" with the House. At 3x Odds, the House Advantage is about 1/3 of a percent, meaning that unless you play A LOT of craps, the House Advantage is statistically meaningless.

Because of these very low House Advantage with Multiple Odds, it simply doesn't make any sense for you to make any bet other than one which takes the best advantage of the Odds.

Additional Pages on Craps

Craps Strategies -- Analysis of the basic craps strategies, and several popular strategies for betting.
Craps Crap -- Superstitions and Trivia
The Parity Hedge System -- Short history of the Craps system that took the gambling world by storm in the early 1970s -- until the system's most prolific gambler was found dead in the desert!

Books on Craps

For additional reading on Craps, vist our Gamblers' Reading Room

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