**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 MathematicalOdds WinningPayout HouseAdvantage

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 Least12.5%

Hop Bet -- A one-roll bet that a particular combination will come up, such as
a 2 and a 5. Varies Varies At Least11.11%

The 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 MathematicalOdds WinningPayout HouseAdvantage

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 MathematicalOdds WinningPayout HouseAdvantage

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 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.

DesiredResult MathematicalOdds WinningPayout YOURAdvantage

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 MathematicalOdds WinningPayout HOUSEAdvantage

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 MathematicalOdds WinningPayout CumulativeHOUSEAdvantage

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 MathematicalOdds WinningPayout YOURAdvantage

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.

DesiredResult MathematicalOdds WinningPayout HOUSEAdvantage

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 MathematicalOdds WinningPayout CumulativeHOUSEAdvantage

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 MathematicalOdds WinningPayout HOUSEAdvantage

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 MathematicalOdds WinningPayout HOUSEAdvantage

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't Pass/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.

Craps: Strategies

This page considers several Craps strategies which will keep the House Advantage
down to less than 1%.

Note that these systems will only get you close to a statistical zero House
Advantage. It will not guarantee you success, or even that you can stay at the
table for a long period of time. As we have discussed elsewhere, statistics
only give the House an advantage because it rolls the dice tens-of-thousands
of times per day and can statistically expect certain results. As a bettor who
may only roll the dice a hundred times or so, you will be subject to much wilder
short-term swings of luck, good AND bad.

So, no system or "statistical dead heat" will guarantee you anything.
If you are unlucky, you will still get clobbered no matter what system you will
use.

What we can do is get you close enough to "even odds" that the House
Advantage will not wear you down. In other words, you will win or lose depending
on whether you are lucky or not, and not a foreordained result such as long-term
betting with a poor-odds game like Roulette.

In other words, we can't tell you that you will win, or even that you will not
lose. What we can tell you is that the following systems mathematically make
the most sense, and are utilized by the most sensible and experienced craps
players.

The Basic Strategy

The Basic Strategy for craps is thus very simple: You make a bet on Pass, Come,
Don't Pass or Don't Come, and you place as much in odds on that bet as you can
afford commensurate with your money management strategy. Simple as that.

Example: Let's say you are playing at a table with 3x Odds. Your strategy is
to make a $10 Pass bet, and then once the point is established you make a $30
Odds bet on the point. On the first roll (a/k/a the "Come Out Roll"),
your Pass bet will win on a 7 or 11 but lose on a 2, 3 or 12. Once the number
is made, if your number is rolled again you will win only 1:1 although the true
odds are 2:1, 3:2 or 6:5 depending on what the number is. This creates a House
Advantage of 1.41% on your Pass Bet, which you then "dilute" to 0.35%
by placing the 3x Odds.

The Parity Line Bet System (a/k/a "The Doey-Don't")

The Parity Line Bet System is popularly called the "Doey-Don't" after
the label given to it in Frank Scoblete's classic book: Beat the Craps Out of
the Casinos and Play Craps and Win, p. 39 (Bonus Books, 1991). To understand
the Parity Line Bet System, you must first have a solid understanding of the
Line Bets and of placing Free Odds. If you don't understand those bets thoroughly,
what we're about to discuss will probably just give you a big headache.

You will recall that the Odds bets are great bets, and would be perfect bets
except that you also have to make a Pass, Come, Don't Pass, or Don't Come bet
before you can take advantage of the Odds. The Parity Line Bet System is a simple
twist on the basic strategy which seeks to minimize the Pass, Come, Don't Pass,
or Don't Come bet, by the simple expedient of betting equal, offsetting amounts
on both the Pass and Don't Pass lines, or the Come and Don't Come bets. The
idea here is that you essentially "wash out" the Pass or Don't Pass
bet, by making it's counterpart. Then, by placing as much Odds as is possible,
you essentially water down the House's Advantage even further.

Example: Same table with 3x Odds. Instead of making a single $10 Pass, you make
a $10 Pass bet AND a $10 Don't Pass bet. If a 7 or 11 is rolled, your Pass bet
wins but your Don't Pass bet loses, so that is a wash. if you roll 3 or a 12
(or a 2 in some casinos) then your Don't Pass bet wins and your Pass bet losses,
so that washes out. If you roll a 2 (or a 12 in some casinos), then ONLY your
Pass bet loses (your Don't Pass bet doesn't win). If "numbers" (4,
5, 6, 8, 9, or 10) are rolled, you then place $30 Odds on either Pass or Don't
Pass (whichever you choose). With the Parity Line Bet System, you odds of losing
your Pass Bet are 1 in 36, which gives the House a 2.8% advantage. Note that
this is HIGHER than the House Advantage for either the Pass/Come or Don't Pass/Don't
Come Bets. The important difference is that those bets become bad bets on a
little more than half the rolls, whereas with the Parity Line Bet System, it
is only a bad bet the 1 in 36 times that a 12 shows up on the dice.

Keep in Mind: Even with the Parity Line Bet System, the dice are either bouncing
your way or they are not. If the dice are bouncing your way, you would be better
off betting the Pass/Come or Don't Pass/Don't Come bets to maximize your income.
If the dice aren't bouncing your way, you won't lose as much, but you will still
be losing. The Parity Line Bet System very slightly helps your chances over
the basic game, but it doesn't automatically make you a winner, or even switch
the advantage to your favor.

Analysis: One way to think of this is as a "tax" which you pay every
36 rolls to allow you to play the casino with no advantage. But another way
to look it this as a 36 roll "Risk Cycle", i.e., every 36 rolls the
Casino will be up on you one bet. Then, compare it to the Risk Cycles for the
Pass/Don't Pass and Come/Don't Come Bets -- those Risk Cycles are nearly twice
as long at approximately 70 rolls before the House can expect an advantage!
So, you are really half as well off with the Parity Line Bet System as you are
with the Basic Strategy (so there is no point in pursuing this strategy).

The Parity Hedge System

This is the legendary craps "system" which was utilized by a Japanese
businessman in the mid-1970s to clean several Las Vegas casinos out of more
than a hundred million dollars -- which infuriated the casino bosses so much
that only a couple of days later he was found dead in the desert! After that,
the few people who knew and understood the system quit using it and moved on
to other games, or at best used it sparingly.

The Parity Hedge System is so complicated that it is beyond the description
of this website. Suffice it to say that it is a sophisticated variant of the
Parity Line Bet System (with a unique twist!), and has probably ever been known
only by a handful of the very best craps players. It is so little known and
complicated that we seriously doubt that any of today's so-called craps "experts"
or even any of today's pit bosses, could spot the strategy if it were being
used.

Since we first published our pages on craps, we have been literally inundated
with requests for an article explaining the Parity Hedge System. So, we will
probably try to do an article on this by early 2001 -- watch our (free) newsletter
for more details! Keep in mind that the Parity Hedge System gives about the
same edge to the craps player as does counting cards at Blackjack, meaning that
even it will not overcome bad luck. But with a good player -- and competent
dealers -- the system does create a slight mathematical edge over the House.
(And, no, we will not "sell" or auction this system to anybody though
we've had many e-mail requests to do this -- when we write about it, we will
do so for free and post it on this site so that everybody can scrutinize it).

Offsetting Bet Systems

Over the years, lots of people have attempted to come up with "offsetting"
bet systems, where they bet a few chips here, and then a few more chips to protect
those chips against bad rolls, and so forth and so on. Indeed, it is an attraction
of craps to attempt to work out the "perfect" system whereby you never
lose and the House never wins (sort of like those people who cover all the squares
in Roulette).

Well, give it up folks. Mathematically, you cannot make a good bet out of two
or more bad ones. Several doctoral thesis have conclusively proven this fact.
Yet, much of the allure of craps to neophytes is the idea that they can place
several bets and somehow shift the odds into their favor -- and this is encouraged
by the Center Field Sucker Bets (the "Crazy Crapper Bets"), which
give you the opportunity to "hedge" against the seven on particular
rolls -- though at a steep cost.

[Ironically, the "Parity Hedge System" is an offsetting bet system,
though it takes into account a unique twist which recognizes that on certain
bets the odds change (something never covered in any of the doctoral thesis).]

Craps: Helpful Hints and Craps Crap

Here we are going to go through some helpful hints and tips about playing craps,
as well as debunk some of the more popular superstitions and rumors.

Helpful Hints -- In addition to the general Helpful Hints and Tips for the casino
in general, these are specifically for the craps table:

· Get a corner spot close to the dealers -- If you can't get a spot,
wait! There are MANY important reasons for this:

o You are going to betting only Pass/Don't Pass, Come/Don't Come or Odds, so
you need to be close to those bets so that you can get your bets down quickly
and efficiently.

o You will be talking to the dealer nearest you, and telling him where to place
your odds and how. If you are in the corner space, you will standing next to
him and can speak in his ear so that it will be difficult for him to misunderstand
you.

o You will be able to look down the "line" at your bets, and more
efficiently check to see that you are being paid the correct amounts on a win.

o You don't have to worry about people being behind you, or watching the action
on one side while somebody steals your chips or wallet on the other side, and
you can protect your chips with one hand.

o You will not be forced to break your concentration to make conversation with
people on both sides of you.

o You will not be making any Center Bets ("Crazy Crapper Bets"), so
you don't need to be close to the center of the table -- and being as far away
from those bets as possible reduces the possibility of an "irresistible
impulse" bet.

· Touch and throw the dice with your forefinger and thumb only, and make
sure the dice hit the backboard -- Some "experts" say "Never
throw the dice" while other "experts" have written whole books
on "Rhythmic shooting" and how you can magically cause the desired
numbers to appear. This is all crap (excuse the pun). Throwing the dice is a
fun part of craps which you should learn how to do, but at the same time do
it right by using only two fingers and keeping the dice in sight of the box
man at all times. When you throw the dice, make a nice arc which causes the
dice to land right in front of the wall, hit the wall, and then bounce back
on the table. This (common) method of shooting will draw the least amount of
attention to you by the casino personnel, which correspondingly will keep your
own stress level low. Oh, and don't believe for a second that you can cause
the dice to land any particular way, because you can't.

· Keep an eye on the payouts -- It is not that dealers are dishonest,
but there is a lot of action going on whenever a craps table is "hot"
and they are human and make mistakes. If they do make a mistake against you,
point it out, and if disputed ask the box man for a ruling. If they make a mistake
in your favor -- keep your mouth shut! If you don't know what the payouts should
be, you have no business gambling.

· Avoid Crowded Tables -- Although crowded tables are generally more
fun, there is also a much higher likelihood that the dealers will get distracted
and screw up your bets. So don't play at crowded tables. The best tables are
often empty tables. There is NO truth -- nada, none, zilch -- to the statement
that "an empty table is a cold table". Dice have no memory, and if
you are the only bettor you can play at your own pace without much chance of
the dealers screwing up your bets.

· Beware Superstition -- On each and every roll, the odds of a particular
number coming up are exactly the same. Dice have no memory and are controlled
by nothing other than gravity, momentum, and random chance. Do not think that
because the dice have been "cold" that it means they will eventually
"warm up" or that because they have been "hot" they must
now go "cold". You must wash all such thoughts from your mind, and
concentrate on the odds on each individual roll.

Superstition/Craps Crap

· "Because Something Happened, the Next Roll Will Be a _____"
-- Usually, when you hear this line it will end with "7", such as
in "If one of the dice bounces off the table the next roll will be a 7".
And in fact a 7 is the most likely roll, because it is easier to make a 7 than
any other number. But this has to do with statistics, and nothing to do with
luck. The dice are little cubes of clear plastic, and do not remember what object
they last hit.

· The Rhythmic Shooter -- Some (self-proclaimed) experts will state that
some craps players are "Rhythmic" shooters, meaning that they can
roll the dice in such a fashion that the 7 never appears, or does appear depending
on what is needed. This is completely bogus. Because of the felt table, and
the serrated foam wall, it is impossible to throw a certain number or predict
what numbers might appear. People who claim that they can do this are "full
of it".

· An Empty Table is a Cold Table -- Empty tables are neither "hot"
nor "cold" (remember, the plastic dice cubes have no memory).

Craps Trivia

· The dice are clear plastic -- This is so that the box man who examines
the dice can look for weighted inserts which cause the dice to roll or not roll
some number more than others. These are known as "loaded" dice, and
they do exist. Usually, the cheater will take some dice and bore holes in them,
and fill the holes with lead. But they can be quickly caught with clear dice.

· There is a mirror on the wall opposite the box man -- This is so the
box man can see the back of people's hands when they are rolling, and can look
out for either changes in dice or somebody stealing chips.

· "Right" bettors bet on Pass and Come, and "Wrong"
bettors bet on Don't Pass and Don't Come -- The famous gambler known and "Jimmy
the Greek" was a "wrong" gambler, meaning he always bet with
the House that the 7 would appear before the number. Of course, Jimmy was best
known for setting the spread the year Joe Namath and the New York Jets won the
Super Bowl -- heavily against the Jets (in retrospect, Jimmy the Greek was a
really lousy gambler). But whichever way you bet, the odds are about the same.

Craps: The Parity Hedge System

This is the forgotten system that took the gambling world by storm for a few
brief weeks in the early 1970s. After we first mentioned the Parity Hedge System
in 1998, we have received literally thousands of e-mails requesting more information
about the system, who developed it, why it never became public information,
and what happened to it.

The Parity Hedge System derives in part from the Doey-Don't System immortalized
in Frank Scoblete's classic book: Beat the Craps Out of the Casinos and Play
Craps and Win, p. 39 (Bonus Books, 1991). You have to understand what makes
that strategy successful before you can delve into the intricacies of the Parity
Hedge System.

The Unofficial History of the Parity Hedge System

The originators of the Parity Hedge System were too smart to make themselves
known. It is believed that they were nuclear physicists and theoretical mathematicians
who were working at the Nevada Test Range, located just north of Las Vegas.
During the daytime, they put their skills to the test by creating new and unusual
types of hydrogen bombs and measuring their yields. In the evening, they made
their way into Las Vegas where they put their statistical know-how to the test
on the Blackjack and Craps tables. This was a group of very sharp young minds
who had studied under such geniuses as Von Neumann and Teller, and who knew
how to "think outside the box".

Whether they picked up the Doey-Don't from other gamblers, or they figured the
system out themselves is not known. At any rate, they quickly realized the nearly
risk-free arbitrage nature of the "DD", and in their slack time at
the test range began to theorize about how to improve on the Doey-Don't. Eventually,
they were to develop their strategy into a situational algorithm that is much
like a basic computer program. Depending on the situation, betting a certain
way will either slightly improve the odds, or will negate odds that have become
heavily in the house's favor.

Realizing that an overly complex system was unworkable with a fast-paced game
such as craps, these kid geniuses simplified the system into the "11 keys"
that characterizes the system. They also realized that if the casinos ever figured
out the Parity Hedge System, the casinos could make slight rule changes to negate
the system's advantages (To jump ahead for a moment, they were wrong - even
years after studying the few film tapes of people using the Parity Hedge System,
the casino's mathematicians were unable to crack the system, and so no changes
were ever made. But the casinos were to handle the matter differently, as we
will soon relate).

Of course, the kid geniuses tried to keep the system to themselves. They wouldn't
play when other experienced gamblers were around, but played only in the early
morning hours while the least knowledgeable security crews were working and
most of the casino personnel were focused on clearing the slot machines' take
from the previous night. They made small bets, and were for a while content
to supplement their government salaries with repeated small but consistent payoffs.

But greed begets greed. As détente and the nuclear arms accords began
to spell an end to many of the nuclear testing programs, some of those knowledgeable
about the system began to think of ways to make a really big "hit"
on the casino.

The Parity Hedge System gives gamblers a slight edge over the casino. For small
bets, this means small gains. Bigger gains require bigger bets, and bigger bets
attract more attention. And the kid geniuses did not want their system to go
away. But they didn't want to retire on their government pensions, either.

Eventually, they settled on a Japanese businessman who they knew through their
defense contacts. The Japanese businessman had cash and the mathematical skills
necessary to run the Parity Hedge System on a big-time basis. More importantly,
the Japanese businessman was already known around Las Vegas as a "whale"
who regularly dropped tens of thousands (remember, this was the mid-1970s) on
a single weekend - and even better the casinos knew him as a "hard luck"
gambler. If the Japanese businessman suddenly started winning, the casinos would
figure that his luck had simply changed and it would not attract attention.

So it was that on one of his many trips to Las Vegas to oversee a construction
contract that the kid geniuses took the Japanese businessman aside, and over
the course of a weekend had instructed him in the "basic" Parity Hedge
System.

Early on the following Monday morning, during the casino's most quiet time,
the Japanese businessman made his way to the crap table, took over an end, flopped
down $10,000 in cash, and started working the system. At first, the crew working
the table and the box men thought we was nuts, playing "offsetting"
bets that seemingly couldn't win. Yet, of the course of an hour and a half,
the Japanese businessman had very quietly doubled his money.

It had been decided beforehand that the Japanese businessman would spread his
money around several casinos, and so he did for the remainder of the week always
playing around the breakfast hour. He lost on one day only, and then by little
more than $200 after an hour and a half of play. The Japanese businessman concluded
his first visit up more than $15,000 - of which he split $7,500 with the kid
geniuses, as well as a promise to return. Everything had gone so smoothly that
the casinos hardly took notice of the Japanese businessman's suddenly improved
play.

The kid geniuses continued to perfect the Parity Hedge System, sublime in the
context of doing this over coffee while measuring underground atomic tests.
But they awaited the Japanese businessman's return, and their big payday.

The Japanese businessman played the role well, waiting until the several casino's
inevitable calls inviting him to return. He at first refused, and then acquiesced
on the condition that the casinos would allow him to play craps at a very high
dollar amount - placing up to $10,000 per roll. The casinos were probably overjoyed
when they heard this, and assured him that if he could bankroll it, they would
take his money. So, the Japanese businessman took the time to schedule another
"construction visit" to the Las Vegas area, this time wiring to each
of these casinos a large sum (believed to be around $600,000 each). Thus it
was that the Japanese businessman landed in Las Vegas on a Thursday, stayed
holed up in his hotel room through the weekend (except for a brief visit to
the Atomic Test Range), and then showed up at precisely 6:00 a.m. on Monday
to start gambling.

And gamble he did. Helped by an enormous streak of "good numbers",
the Japanese businessman was up $1 million by breakfast. He then spent the day
making a circuit of the other casinos, only losing once and cleaning the rest
out for amounts up to $2 million. At the end of the day, by making progressively
bigger bets with the casino's money that he had won, the Japanese businessman
was ahead a cool $11 million.

Nothing travels fasted in Las Vegas than the news of a big winner. While each
casino had "spotters" on the Japanese businessman - more looking for
ways to lure him back to their casino when his run of "luck" finally
broke - the casino bosses were meeting with their staffs to try to figure out
what had happened. Keep in mind that at this juncture in Las Vegas' history,
the casinos were being run mostly be ex-mobsters (and some not-so-ex-) and they
simply couldn't grasp the Parity Hedge System. For his part, the Japanese businessman
greeted his casino-appointed hosts cordially, and retired back to his hotel
room.

Truth is, he should have taken the first plane out of town. Instead, he again
appears promptly at 6:00 a.m. the next morning, per the kid geniuses' plan,
and starts gambling at the highest limit (which, of course, the casinos let
him do to try to get their money back). Again, the combination of his lucky
streak, the Parity Hedge System, and that he was now using the large sums of
casino money he had won the day before, resulted in gains of just under $10
million at each of a half-dozen casinos in town.

By this time, the casino bosses are really starting to panic. In the mid-1970s,
a $10 million loss was unthinkable. Because there was still a great deal of
"skimming" going on, the casinos basically had no cash reserves. Fortunately,
the Japanese businessman had deposited his winnings with the casino at the end
of each day as credit for the next day.

The casino bosses still didn't understand what was happening. The first thought
in their paranoid minds was that the Japanese businessman was cheating. By this
time, the Japanese businessman was being watched by probably 20 or 30 people
at each casino, so that was unlikely. The casino bosses simply couldn't get
it through their minds that there was some system that gave the Japanese businessman
a slight advantage over the house.

By the third morning, the casino bosses were in a panic. They knew that the
Japanese businessman was scheduled to leave, and they knew the odds were low
of winning his money back. And sure enough, at 6:00 a.m., sharp, he steps into
the first casino of the day, and starts playing the system at the highest level
allowed him by the house. And he is still hot.

By a little after 11:00, he's been through five casinos, and is up additional
tens of millions. Thus, the Japanese businessman (in a private limo - should
have been his first clue that something was amiss) started for the airport,
where he had instructed each of the casinos to meet him with a certified check
made to his order for the funds he had won.

He never made it to the casino and his body was never recovered. Courtesy of
the gang of Tony "The Ant" Spillotro, The Mob's local enforcer, the
Japanese businessman disappeared into the Las Vegas traffic - vaporized in thin
air as well as a direct hit by the kid geniuses' atomic bombs could have done.
And of course, the certified checks never made it to the airport, either.

During the second and third days of the Japanese businessman's run, the casinos
made movie-quality films of the Japanese businessman's play. Suspecting that
the Japanese businessman had accomplices, the casinos each made note of several
of the hallmarks of the Parity Hedge System (but they never really grasped the
basics of the strategy).

So what of the kid geniuses? To say that they were scared to death is an understatement.
Yes, they had nuclear weapons, but they weren't of much practical use. One of
the kid geniuses knew Benny Binion, the rough and tumble founder of the legendary
Binion's casinos. Whether or not the Japanese businessman visited Binion's is
not known. Certainly, Binion - and the casino owners who weren't visited by
the Japanese businessman - were as at risk to being tapped by future Parity
Hedge System players as the casinos that had suffered the (now disappeared)
losses.

What seems to have happened is that Benny Binion agreed, on behalf of the casino
owners and doubtless The Mob, to have accepted a complete analysis and breakdown
of the Parity Hedge System (and a promise not to use it anymore) in exchange
for protection. Truth is, only Binion was smart enough to understand the importance
of getting the breakdown on the Parity Hedge System, and was capable of bringing
the casino owners and The Mob together to cut the deal. Instead of further broadcasting
the existence of the system by bringing in people to analyze it (the only people
who would have the mathematical training and intellect to understand it could
also run the system, of course), Binion apparently just hid the system in his
home vault along with the last remaining film canisters of the Japanese businessman's
fateful three days.

The Parity Hedge System was apparently safe with Benny Binion through his death
in the early 1990s, then it was inherited by Binion's son, Ted Binion. By this
time, the Parity Hedge System and the Japanese businessman had been long forgotten,
and the canisters relating to the Parity Hedge System had been moved out of
Benny Binion's vault and into Ted Binion's closet. The Parity Hedge System itself
was cached in the desert, along with some millions in silver that Ted Binion
kept for emergencies.

At some point, Binion's new (former stripper) wife and her boyfriend were apparently
rummaging through Binion's stuff and came across the film canisters. Watching
the play, along with some narrative by a gaming analyst, they realized the important
of the Parity Hedge System. Rumor has it that Ted Binion's stripper wife and
her boyfriend then waylaid Binion and force-fed him heroin in an attempt to
make him reveal the whereabouts of the analysis and summary done by the kid
geniuses. But before the now-widow and her boyfriend could get to the spot in
the desert, they were arrested for Ted Binion's murder.

So where is the Parity Hedge System now?

It is unknown where the analysis and the summary that the kid geniuses did for
old man Binion have gone. What we do know is this: The group of mathematicians
and physicists (probably numbering less than a half dozen) whom we have referred
to as the "kid geniuses" knew about the system that they created.
We also know there were a few people who worked for the casinos during the Japanese
businessman's remarkable run that saw the system employed. There may have been
other films made other than those that Benny Binion ended up with. And we have
no idea what the Japanese businessman did to memorialize his rather amply demonstrated
knowledge of the complexities of the system.