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House
Advantage Control
By Mike In Hawaii
It has taken a long trip to get to a
bottom line with Dice Control. First we had to determine if such a thing
could exist. Could it have a physical basis in a learnable skill? We found
a promising mechanism in axial control, and a more remote possibility in
facial control.
Once a mechanism was available, we could
create a spreadsheet that would calculate how that assumed level of
control would effect the percentage appearances of the 36 possible dice
rolls. From there we had to calculate the effect on the 11 numbers that
drive the game of Craps. We even reasoned out how to go from a statement
of "I can control the dice one out of X rolls" to facial percentages that
would need to be used to simulate that level of dice control.
This finally gives interesting tables and
pretty charts showing that indeed the six basic axial control dice sets do
indeed change the distribution of numbers in a potentially significant way
with levels of dice control that while difficult, are not super human. We
had to consider all the physical constraints that construction of each die
demanded. And be clear that we cannot "rob Peter" unless we "pay Paul". We
must end up with certain totals right at 100%. If control enhances
percentages in one area, it must suppress percentages somewhere else to
restore balance.
Finally we came up with a model to convert
from assumed dice control to a bottom line. All shooters are random
rollers. No one can call with absolute certainty the next roll of the
dice. Therefore all participants in a game of Craps will see their
results, their winnings and loses vs. sequential rolls as a random walk. A
random walk around a baseline.
Since the house has designed the game of
Craps to have a house advantage, that is be less than a zero sum, fair bet
game, the baseline will slope downwards at the house advantage loss rate.
How steep your personal baseline is will depend on what bets you make
since in Craps you are faced with some of the lowest and some of the
highest house advantages in the casino, all mixed together on the felt. In
other words, on the composite house advantage of your betting strategy.
Where true dice control comes in, is its
ability to potentially alter the house advantage on specific bets. Any
dice control that moves the distribution of the 36 outcomes from flat, all
equal at about 2.78% each, will cause the house advantage on all Craps
bets to potentially change. Some actually can remain virtually unchanged.
Others will be quite sensitive to change.
Here we have a bottom line that we can
examine. Finally we have slashed our way through the mathematical
undergrowth of the jungle far enough to create a trail from an assumed
level of dice control to a "show me the money" type of answer.
The Hardways Set
Let's look at actual numbers for a classic
1-6 1-6 axial, symmetrical set called the "Hardways Set". It is so called
because when ready to throw, the top, bottom, front and back face pairs
all make "hardways". Specifically, 2-2, 3-3, 4-4, and 5-5. The hard four,
hard six, hard eight and hard ten.

What would this set actually accomplish if
one could throw it with high quality dice control? Exactly how would you
have to change your betting strategy to compensate for the effect such
control would have on the 36 rolls? How would that control percolate down
to the bottom line, advantageous changes in the house advantages on
various bets, and disadvantageous changes in house advantage on various
bets?
This is very critical information! Without
it, you are far better off working hard to NOT control the dice, but have
them behave in a totally random fashion. Why? When you start messing with
the 36 possible results of a throw of the dice, when you move those
percentages off a flat line of 2.78% each, you are going to change
everything, somehow. Many bets will potentially become considerably worse
for the player. If you do not know exactly which ones, you are in big
trouble.
At least for the true random roller, the
house advantages are well known and easy to calculate. Any betting
strategy will have a composite house advantage that is knowable.
You start actually achieving some level of
dice control, you give up this information and absolutely MUST get it
back.
So let's look. This set is very well
named. We will assume a level of control of one roll in 12. We will assume
you can get it to work one out of every 12 tries. This is perhaps possible
with a lot of practice, study and coaching. By selecting such a high level
of control, we can get a clearer picture of where a given dice set is
headed. Which house advantages it is targeting in a positive and negative
direction.

Set up for just axial control, suppressing
to some extent (about 8.33%) the appearances of the ones and sixes which
we set on the horizontal side to side axis, we discover little effect on
the Sevens. Sevens is our heaviest number, it has the greatest mass. It is
the hardest number to control.
We do see a nice effect on the lighter
numbers, especially the Twos and 12's. Why? well if either die is
controlled and its One does not appear, then there are zero ways to make
the sum Two. If either dice is controlled so its Six does not appear,
then there are zero ways to make the sum 12. That is why I call these
numbers "light". They have no "backup plan" like Seven does. You take away
the One or the Six and Seven still has multiple ways to get created based
on Two, Three, Four and Five.
Notice that what we take away from these
numbers, we get back in the summed point numbers Six and Eight. Let's look
at the table:
|
Group |
Result |
Random |
Absolute |
Relative |
|
Craps |
9.97% |
11.11% |
-1.14% |
-11.39% |
|
N / C |
2.21 |
2.00 |
10.43% |
|
|
Wins |
22.03% |
22.22% |
-0.19% |
-0.87% |
|
Sevens |
16.72% |
16.67% |
0.06% |
0.34% |
|
Elevens |
5.31% |
5.56% |
-0.25% |
-4.72% |
|
|
|
|
|
|
|
Hardways |
12.05% |
11.11% |
0.94% |
7.83% |
|
Two & 12 |
4.67% |
5.56% |
-0.89% |
-18.97% |
|
Set Pt. |
68.00% |
66.67% |
1.99% |
2.99% |
|
6 and 8 |
28.69% |
27.78% |
0.91% |
3.19% |
|
5 and 9 |
22.67% |
22.22% |
0.44% |
1.95% |
|
4 and 10 |
16.64% |
16.67% |
-0.03% |
-0.17% |
Notice that the biggest hit is focused in
two places. First Craps. This makes sense. This set really targets the
light numbers Two and 12. It also beats up on the four ways to make Three
and 11. As a result, Craps catches the brunt of any control applied to
this particular dice set.
True to its name, this set also targets
the hardways, causing them to appear more often than they should. Hardways
have "low mass". Only one of the 36 possible results of rolling two dice
makes each of the hardways. You mess with the frequency of the face on a
given die that contributes to a specific hardway, and you mess with the
frequency of the that hardway in a rather focused manner.
What we end up with is a dice set that on
the come out roll will suppress immediate losses due to Craps. It will
have an increased chance of setting a point. When it does set a point it
will tend to set Six and Eight more than other points. It also slightly
favors the Five and Nine as points. Since it does not like 11's, its
effect on wins due to Naturals on the come out roll will be diluted,
actually pushed negative.
What about the bottom line? The effect on
house advantages? What about specific bets on the felt? In the table
below, "Random" is what a true random roller has as a house advantage.
"Control" is what this assumed level of control with this dice set
implies. "Variance" is the absolute change in percentage. "Relative" is
the relative change in percentage of house advantage.
|
|
Random |
Control |
Variance |
Relative |
|
Passline |
1.41% |
0.08% |
1.33% |
94.26% |
|
Don't Pass |
1.36% |
2.25% |
-0.89% |
-65.27% |
|
|
|
|
|
|
|
Hard 4 |
11.11% |
3.73% |
7.38% |
66.45% |
|
Hard 6 |
9.09% |
3.01% |
6.09% |
66.94% |
|
Hard 8 |
9.09% |
3.01% |
6.09% |
66.94% |
|
Hard 10 |
11.11% |
3.73% |
7.38% |
66.45% |
|
|
|
|
|
|
|
Place 4 |
6.67% |
6.99% |
-0.32% |
-4.84% |
|
PLace 5 |
4.00% |
3.06% |
0.94% |
23.49% |
|
Place 6 |
1.52% |
-0.04% |
1.56% |
102.76% |
|
Place 8 |
1.52% |
-0.04% |
1.56% |
102.76% |
|
Place 9 |
4.00% |
3.06% |
0.94% |
23.49% |
|
Place 10 |
6.67% |
6.99% |
-0.32% |
-4.84% |
|
|
|
|
|
|
|
Any Seven |
16.67% |
16.38% |
0.29% |
1.73% |
|
Any Craps |
11.11% |
20.20% |
-9.09% |
-81.82% |
|
Two |
2.78% |
2.33% |
0.44% |
15.95% |
|
Three |
5.56% |
5.56% |
0.00% |
0.00% |
|
11 |
5.56% |
5.31% |
0.25% |
4.51% |
|
12 |
2.78% |
2.33% |
0.44% |
15.95% |
Since it also increases the chances of
setting and then making a point, especially Sixes and Eights, the house
advantage on a pass line bet is down from 1.41% to close to zero, just
0.08%. Since it thumps on Craps and Craps is the wrong bettor's friend,
you can see that Don't Pass would not be a good bet with this set if
control is actually working. House advantage on that bet soars to 2.25%.
Take a hard look at the Place Six and
Place Eight bet. They actually go negative by a tiny amount. That means if
this were actually working as advertised, the baseline on these bets would
be better than square, they would slightly be in favor of the shooter, and
of course all of his friends along for the ride.
The Hard Six and the Hard Eight have
really been smacked around. Unfortunately those bets start with a whopping
9.09% house advantage. Slicing that to 3% is impressive, but that is still
a lot of house advantage.
What about Seven? People are always going
on about Sevens. Well betting Big Red is of course donating your money to
the "Casino Management Relief Fund", a non-tax deductible donation. But it
does provide a measure of dice control focused on Sevens. It slides a bit
in your favor, by a relative 1.73%. But it is still at a whopping "stick'um
up" 16.38%. And due to the suppression of Craps, the any Craps bet has
taken the lead as the worst bet in the entire Casino! It is now in the
House's favor by 20.20%, having beaten out Big Red for that dubious honor.
As bar graph these deviations it look like
this:

Here we have graphed the exaggerated
variations of the effect of this level of assumed axial dice control with
the Hardways Set. The two green lines are pass line and don't pass. The
purples are the four hardways, the light blues are the Place Four and Ten,
the oranges the Place Five and Nine and the yellows are the Place Six and
Eight. The reds are the selected prop bets with the big one heading
downwards into your pocket being the Any Craps bet.
So finally, bottom line. If you put in the
practice, if you had the professional coaching, if you had dice control,
you could mess with the distribution of the percentage appearances of the
36 possible outcomes of a roll of two dice. It takes several steps,
permutations if you will, to go from such an assumption to the effect on
the house advantages such control might offer.
It is critically important to know exactly
where all this is headed because some bets are going to get better for the
player/shooter, and some bets are going to get worse. If you do not adapt
your betting strategy exactly right, you could work hard, practice a lot
and get much better at shooting yourself in the foot.
Copyright © 2006 Mike in Hawaii
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