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Is One Power-Number
Enough, or Does Betting it’s Ugly Twin-Sister Make Sense for Volatility
Control?
As dice-influencers, we understand
the need to bet our money on the wagers where we have the biggest edge over
the casino, and less money or none at all on the ones of lesser edge or
where our edge is negative.
We also understand that a limited bankroll is the mortal enemy of our being
able to take proper advantage of our D-I skills in an optimal way. That is,
we understand the deadly role that volatility can play in destroying
under-funded bankrolls even when we have a significant edge over the house.
That leads us to ask whether betting on our highest-edge Signature-Number is
enough, or whether it’s better to include its somewhat-less-pretty (okay,
she’s sometimes downright homely) twin-sister in our betting regimen.
When we talk about ‘twins’, we are really talking about the dice-matched
pairing that all of the box-numbers have. For example, the 4 and 10 are
twin-sisters who each have a 3-out-of-36 appearance rate, and they live
across from each other on the dice (for instance, if you flip over a 2/2
Hard-4 outcome, you’ll see it’s 5/5 Hard-10 twin-sister, and if you flip
over a 4/6 Easy-10 outcome, you’ll see its 3/1 Easy-4 twin-sister).
So each box-number has a twin-sister (4 and 10, 5 and 9, 6 and 8).
Regardless of the dice-set that you choose, each one will have an equal
amount of your potential power-number outcomes as it will of its
not-so-attractive twin-sister.
Let me repeat that again:
ALL
dice-sets, no matter which one you choose, will have the same number of your
potential power-number outcomes on its axial-faces as it will of its ugly
twin.
For example:
~The on-axis faces of the V-3 set
offer three 6’s as well as three 8’s.
~The V-2 set as well as the P-6 set
both offer the same number of on-axis 5’s as they do of on-axis 9’s.
~The X-6 set and the Hardway-set both
offer the same number of on-axis 4’s as they do of the on-axis 10.
~Heck, even the S-6 set offers no
on-axis 5’s nor does it offer any on-axis 9’s.
That means that if your power-number is there then its ugly twin-sister is
also right there, always close by in a supporting role for her
better-performing sibling. The fact that she isn’t always in the shadow and
that she sometimes does come out to play is where the volatility-reduction
factor of betting the pretty-sister/ugly-sister in combination with each
other comes into play.
So, is it possible that your super-model power-number’s less-than-trophy
twin-sister can add any happiness and enjoyment to your betting life…or at
least provide a less tumultuous, less dramatic, and less volatile ride along
the way?
I say she can.
I also say the cost of bringing your power-number’s homely twin-sister along
on a casino date is not as costly as you might think.
Let’s have a look:
To figure out the chance of a number
appearing before a 7-Out, we take its appearance-rate along with that of the
7, and divide it into the sum.
For example, the 5 has four ways of showing, while the 7 has six ways to
occur; so in relation to the 5, the 7 has a 6-out-of-10 chance of showing up
before the 5.
Stated another way, the 7 has a 60% chance of showing up before a 5; however
the 5’s appearance-rate does not mean it will show up the other 40% of the
time. Instead, we have to multiply the 7’s 60% appearance-rate by the 5’s
4-out-of-10 appearance-rate (40%) to calculate our chances of rolling a 5
before a 7.
When we do that, we discover that our chances of getting one paying-hit on
the 5 is only 24% in random-expectancy. If for example, a random-roller
wants or needs two hits on the 5 before a 7-Out; there is only a 9.6% chance
of that happening, and a 3.8% chance of getting three 5’s before a 7-Out.
However, when we include the 5’s twin-sister (the 9) into the betting-mix;
things start to look better in terms of hit-rate.
The random-expectancy chances of getting one paying-hit on either the 5 or
the 9 (when they are bet in combination with each other) is now 48%. If a
random-roller wants or needs two hits (before a 7-Out) on the 5 or 9 when
they are bet in combination with each other; there is a 19.2% chance of that
happening, and a 7.6% chance of getting three 5’s or 9’s or some combination
of the two before a 7-Out shows up.
The same holds true for the twin-sister 4 and 10, and the twin-sister 6 and
8.
Have a look:
# of Hits 4 OR
10 4 AND 10
0 66.6% 33.3%
1 22.2% 44.4%
2 7.4% 14.8%
3 2.5% 5.0%
4 0.8% 1.6%
# of Hits 5 OR
9 5 AND 9
0 60.0% 30.0%
1 24.0% 48.0%
2 9.6% 19.2%
3 3.8% 7.6%
4 1.5% 3.0%
# of Hits 6 OR
8 6 AND 8
0 54.5% 27.3%
1 24.8% 49.6%
2 11.2% 22.4%
3 5.1% 10.1%
4 2.3% 4.6%
When you look at the random-expectancy figures, you get a clear
sense of the role and volatility-reducing effect that adding the
‘ugly-sister’ into the Place-bet combination with its better performing
power-number twin can have in terms of increasing your hit-rate and reducing
your volatility.
When you pair dice-influencing with the reduced volatility of betting your
power-number with its twinned but-slightly-less-attractive sister; you
quickly realize how a modestly-bankrolled player can utilize its added
presence. Though this bringing-along-the-ugly-sister-on-a-date does mean
that you are accepting a slightly lower return-on-investment (ROI) on your
strongest edge power-number; it also means you are using a very effective
method to control volatility.
Oh, and in case it hasn’t occurred to you yet; this whole betting-the-twin
approach can also substantially reduce the frustration level that many
players experience when their power-number appears to go on an unannounced
vacation while it’s twin sister still shows up with a regularity that makes
you wonder why the heck you aren’t dating both of them at the same time…and
with each others open-minded permission.
To control volatility, especially with a modest bankroll that is not
financed to the point of being able to endure the whipsaw back-and-forth
action of only having your money on ONE power-number; you may choose to
accept a slightly lesser rate of return in exchange for a better chance of
getting any return at all during a given hand.
In order to enjoy less bankroll volatility,
Betting Your Power-Number’s Ugly Twin-Sister Can Make a Lot of Sense
as long as you don’t mind biting a slightly less-advantageous
bullet.
Good Luck & Good Skill at the
Tables…and in Life.
Sincerely,
The Mad Professor
Copyright © 2006
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