Quatloos! > Quatloosia! > Quatloosian
Guide to Gambling > Craps
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 oneroll bet that a 2,3 or 12 will come up on the next
roll. 
8:1 
7:1 
11.11% 
Any Seven  Another
oneroll 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 oneroll
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 goodsized area which says "Big" and with the numbers
6 and 8. This is a megasucker 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 3491011 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 stillunacceptable 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 ComeOut 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/DP/DC
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/DP/DC
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

Have a question for Quatloos?
Ask
TonytheWonderLlama
Quatloosia
Good Life
A discussion of the better things in life, including music, the arts, wine,
beer, cigars, scotch, gambling the Quatloosian way, travel, sports, and many
other topics.
