Can You
Have Your 6 and 8 it Too?
By D.C. Wizard
Some new place-betting systems for the 6 and 8?
It was raining here. I must have been bored. So, this weekend I decided to take
another look at the collection of place-betting systems that I have in my
library. Then, I compared these systems to some of the place-betting systems
that have been written about here. (DiceSetter.com) I discovered nothing new. As expected, I
found mostly run of the mill "up and pull" systems that have sustained casino
profits for years.
With place betting, “winning” more bets than
pass-line bettors comes at the cost of greater risk and larger losses. The
“fuzzy math” that I’ve seen to support 6/8 systems misses this unpleasant fact.
Yes, if one bets both the six and eight, chances are that either the six or the
eight will hit before a seven is rolled. However, when the seven does roll, (and
it will roll on average once in every six rolls no matter how many bets are on
the table), the player who places both the six and eight is going to lose both
bets (or 2 units). Likewise, the player, placing all six numbers is going to
lose 6 units to the seven out while the largest possible win is limited to 1.8
(9 to 5 which is paid when hitting either the four or ten). In my opinion, it
is much better to risk (and to lose) 1 unit rather than to risk 2 or more
units. And, if he confines himself to betting the pass line and the pass line
alone, 1 unit is the most that the pass-line better will ever lose on one roll
of the dice.
From time to time, I hear place bettors suggest
that their increasing the number of bets helps overcome the nasty seven. For
example, place both the 6 and the 8 … Ten ways to win and 6 ways to lose…Sounds
good to a novice player, I am sure…However, here is the skinny. Placing more
than one number increases both the chance of winning a little and of losing a
lot. No place-betting system can rectify this.
Another serious problem with place betting is
that when the place bet does win, it pays less than the true mathematical odds.
(In the case of the 6 and 8, the pay-out is 7/6 instead of 6/5). Bad player odds
and increased player risk explain why the casinos best customers are place
bettors. Hits on the six or eight, are only going to pay about 1.17 units (7 to
6), while a hit on the seven is going to cost 2 units. On the other hand, while
pass-line bettors who parlay naturals and take the odds "win" less often than
place bettors, pass-line bettors lose much less money to the inevitable seven.
Equally important, when the pass-line bettor
does win, he wins more money than he has put at risk. Following our pass-line
system, a win on the pass line will either represent completion of a parlay
(that parlay will pay either 3 or 7 times the original amount put at risk), or
payment of a pass-line bet in which we have taken double odds. In either case,
the payout will always exceed the amount put at risk to a seven-out.
So why do so many players find place betting
alluring? As a pit boss once told me, "all systems work some of the time".
And, when place betting is working, everyone knows it! When the seven
disappears for 15 to 30 minutes, it is almost like an all-you-can-grab money
buffet. Hot tables are certainly a memorable event, one where place bettors are
making more than almost anybody else at the table...Including, pass-line
bettors...My estimate is that during hands where there are say 20 to 30 box
numbers between sevens, the place bettor will make 3 to 5 times to that of a
pure pass-line bettor.
The trouble is, hands with 20 or 30 box numbers
between sevens, don't occur often enough for the place bettor to keep his head
above water. One can go days without seeing such a hot table. The seven is a
diligent worker that rarely takes much time off. More often than not, the seven
is showing, and when the seven is showing, the place bettor is going to lose far
bigger than pass-line bettors.
A friend of a friend of mine has coined a term
he calls “selective memory”. In my opinion, "selective memory" is the perfect
term for what goes on in the mind of a place bettor. It's easy to remember
everything about the hot shoot…The guy who placed all the numbers could well
make 50 or 100 times his original buy in. Or, how about the guy who parlayed the
hard eight three times? Why that paid over 500 to 1!!!
"To the moon" systems, however, seem much less
inviting when we consider how much cash the place bettor blew through either
waiting for that hot hand, or over-betting a hand that he thought was hot. The
old song "Memories" comes to mind. Specifically, memories "too painful to
remember we simply choose to forget...". [Gosh to think I'm quoting Barbara
Streisand. I really am old!!!]
Here’s a bit of the math. Most everyone that has
ever read a book on craps must have seen this somewhere. It’s the old cumulative
probabilities that most every beginning craps book offers. See the table below
for the probabilities of each number and each number expressed as odds. It is
the wins to losses that I want to focus on.
Number |
Expectation Out of 36 |
Chance of
Rolling |
Expressed
as Odds |
Number of
Wins To Losses |
2 |
1 |
1/36 |
35:1 |
0 |
1 |
3 |
2 |
2/36 |
17:1 |
0 |
2 |
4 |
3 |
3/36 |
11:1 |
1 |
2 |
5 |
4 |
4/36 |
8:1 |
1.6 |
2.4 |
6 |
5 |
5/36 |
6.2:1 |
2.27273 |
2.72727 |
7 |
6 |
6/36 |
5:1 |
6 |
0 |
8 |
5 |
5/36 |
6.2:1 |
2.27273 |
2.72727 |
9 |
4 |
4/36 |
8:1 |
1.6 |
2.4 |
10 |
3 |
3/36 |
11:1 |
1 |
2 |
11 |
2 |
2/36 |
17:1 |
2 |
0 |
12 |
1 |
1/36 |
35:1 |
0 |
1 |
Total |
36 |
36/36 |
-- |
17.74546 |
18.25454 |
Now, for the fun part. Add up the total ways
to win and the total ways to lose.
Total Ways to Win in 36 Rolls = 17.74546
Total Ways to Lose in 36 Rolls = 18.25454
Player’s Negative Expectancy
Without Odds
(18.25454 – 17.74546)
36
= 1.41%
Have you ever seen that percentage?
Here is a little secret tid-bit. The great Sam
Grafstein recognized the play, but I am sure any math he did was done on his
fingers. Still, the math affirms the greatness of the Dice Doctor’s system. See
if this adds up?
Wins Due to
Naturals = 8 (22.22222% of total occurrences
and 45.08% of total wins)
Natural 7 = 6 (16.66667% of total occurrences
and 33.81% of total wins)
Natural 11 = 2 (5.555556% of total occurrences
and 11.27% of total wins)
Wins Due to Shooter Making
the Point = 9.74546 (26.5959 % of total
occurrences and 54.92% of total wins)
Losses Due to Crap Rolls = 4
Losses due to the 7-Out = 14.25454
Adds up: 4 + 14.25454 =
18.25454
So, now you know where those numbers come from
and why the house advantage is what it is. Wadda mean? No!
Okay, here is how it comes about. The blue
numbers refer to the number of times over 36 rolls that a decision will be won
and the red numbers represent decisions lost. This is the mathematical break
down for any individual number that can be rolled on a come out.
Let's look first at the six. As we know, 5 times
out of 36, the shooter will establish
six as a point. If he does roll a six for a
point, there are 5 ways to roll a six before a seven (the shooter wins) and 6
ways to roll a seven before a six (the shooter loses). So the chance over 36
rolls of a shooter winning on a six is (5x5/11), or,
2.27273 times.
The chance that a shooter will seven-out (having
established six as the point) is
(5x6/11). Or, 2.72727
times. Note that 2.27273 + 2.72727 = 5 and recall
that 5 is the number of times over 36 rolls that a shooter will establish 6 as a
point. Cool?
The math for the eight is, of course, the same
as the math for the six.
As for the five and nine, we expect to roll both
the five and nine 4 times each over 36 rolls. When a five or nine is rolled,
there are 4 ways to make the point, and six ways to lose to a seven. So, the
number of decisions over 36 rolls that will be won on a five or nine is
((4x4)/10) or 1.6. The number of times over 36
rolls that a shooter will lose on a five or nine is 2.4
((4x6)/10).
I trust by now, you can figure out the math for
the four and ten. There are 3 ways in 36 rolls to establish either the four or
the ten. Having rolled the four (or a ten) as the point, there are 3 ways for
the shooter to roll a four (or a ten) before the seven, and six ways for a
shooter to roll a seven before a four (or a ten). So over 36 rolls, there will
be 1 decision won with four or ten as the point (3x1)/3, and 2 decisions where
the shooter sevened out with four or ten as the point (3x2)/3.
Lastly, there are come out naturals and craps. A
come out seven or eleven will occur 8 times (six times on the seven, two times
on the eleven). So, 8 out of 36 rolls will be instant pass-line winners. A come
out crap will occur four times. (1 in every 36 rolls for both the two or
twelve), and 2 in every 36 rolls for the three.) So 4 out of 36 rolls will be
immediate pass-line losers.
I originally developed the chart as a tool to
demonstrate the power of naturals, and to illustrate the number of pass-line
decisions that are won by seven and eleven. (Many crap players are unaware of
this, but naturals, on average, account for just over 45% of pass line
wins!) This chart, however, could also help your understanding of place betting.
Place bettors get no benefit from come out
sevens or elevens while sharing all the risk from the shooter sevening out. And,
place bettors get shorted more on the payout than do pass-line bettors. For
example, instead of getting 6 to 5 odds on the six, place bettors receive 7 to
6. Over 36 rolls, if a place bettor bets $12 on the six every roll, he will win
2.27273 times. He should receive a payout of $14.4 ($12 x 1.2). Instead,
however, the place bettor gets a payout of $14.00. Over 36 rolls this amounts to
a ($0.4 x 2.27273) or $0.91 tax for the $12 place bettor on the six or
eight... Do you see how it is a game of numbers? Do you see how over a lifetime
career of playing craps the house-advantage works against the player on every
roll?? The higher the house odds, the higher the tax the player pays. Even
though I live and make my living in the land of big government (Washington DC),
I still cringe when I hear the word tax! At least when I am the guy paying the
tax. How about you?
D.C. Wizard
© Copyright 2006
<back to
the top>
|