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Part XIV No
matter how good your dice-influencing skills are, you will generally have more short
(1 to 8 roll) point-cycle hands than you do of the medium (9 to 20 roll) variety. Moreover, you will have even fewer long
(21 to 50 point-cycle rolls), even fewer mini-mega (51 to 70 rolls) ones, and
finally much a smaller amount of mammoth (70+) point-cycle hands. That
is the nature of craps regardless of your skill-level.
In
essence it means that most hands will have at least two, three or four
point-cycle rolls in them regardless of their eventual duration, but fewer hands will have
ten, eleven, or twelve rolls in them, again, regardless of their eventual duration. Some
hands do go on to have 20, 30, or 40 point-cycle rolls before the 7 shows up, but each of
them starts out at the roll #1 starting-point and proceeds from there. When you look at a graph for a SRR-8 shooter for
example
Ø
Hell
survive the first point-cycle roll approximately 87% of the time.
Ø
Hell
survive the second point-cycle roll about 76% of the time.
Ø
Hell
survive the third point-cycle roll around 67% of the time.
Ø
Hell
survive the fourth point-cycle roll approximately 58% of the time.
Ø
By
the time we get to the tenth p-c roll, hell have a 26% statistical chance of getting
to his eleventh one.
Ø
On
his twentieth point-cycle roll, hell have a 7% chance of emerging from that to make
his twenty-first p-c toss. If
you look at each roll as an independent-trial, then his SRR-8 chances of rolling a 7
remains at 1-in-8 (12.5%) on each and every roll; however the cumulative-effect
that his SRR-rate has on roll-duration survivability does not remain static. Now
before anyone tries to tells you that this has anything to do with due number
theory; I can state quite emphatically that it does not. Instead, it has everything to do with the reality
of dice-throwing and the expected duration of a given hand based on your Sevens-to-Rolls
Ratio (SRR). For
a random-roller, we never know how long one particular hand will last, but we can
make some general observations about how long most of them will last and
specifically how often a roll will endure to a certain point. Equally, we can do the same for any SRR-rate that
is either higher or lower than random, and from there we can map out the likelihood
of your chances of having a 1-roll Point-then-Out hand or a 50-roll point-cycle hand and
everything in between
and that is exactly what we are going to do today. Using SRR To
Determine Roll-Duration Range In a moment, you
are going to see a chart which shows how each SRR skill-level will generally fair when the
dice are thrown during the point-cycle. That
is, we are going to look at the prospects of how likely it is for a given shooter to get
up to his 50th point-cycle roll without a hand-ending 7 getting in the way. Before we do
that however, many curious players want to understand how and why the SRR-based 7s
appearance-rate affects each and every subsequent throw that they make
and Im
happy to provide the answer.
The chance of a
7 showing up on any given roll is determined by each players validated in-casino SRR-rate,
and that in turn not only determines his expected roll-duration, but it also determines
the decay-rate of any given hand. For instance, we
know that a random-rollers SRR of 1:6 means that on any given throw there is a 16.67%
chance that it will result in a 7, and an 83.33% chance that it wont. Now this is the point where most math-guys turn
off their brains and turn on their myopic-vision blinders.
They see and understand single-event independent trials of one throw each,
but they cant comprehend how SRR-rates affect the groupings of more than one throw
in a chain of outcomes. For
example:
Ø
Everyone
understands that a SRR-6 random-roller will survive his first point-cycle roll about 83%
of the time, while an SRR-8 shooter will survive his first point-cycle roll about 87%
of the time.
Ø
On
the second point-cycle roll, there is a 69% chance that the SRR-6 guy will get past
it, while the SRR-8 shooter has a 76% chance of surviving.
Ø
By
the third point-cycle roll, the R-R will survive this one 57% of the time, while
the SRR-8 shooter will get past it 67% of the time.
Ø Though the roll-duration/bet-survival rate for both shooters decays with each and every subsequent point-cycle roll that they make, the rate of decline is quite different for each.
Ø
By
the time we get to the twelfth point-cycle roll, there is a 1-in-9 (11%) chance that the
random-roller will get this far, but a 1-in-5 (20%) chance that the SRR-8 shooter will
still have the dice. Again, the SRR-8
shooter might unleash an incredibly long and memorable hand that goes beyond twelve
p-c rolls; however there is an 80% (4-in-5) chance that he won't. Many
players bet like every hand will be THE hand-of-the-day (or the
century), but most times it isn't. That means that their bets are often disconnected from
the reality of their skills. Though their skills are readily apparent, their ability to
harvest a profit from their edge over the house is severely impaired by the way that they bet
their advantage. In
other words... While
their dice-influencing holds up its end of the advantage-play bargain (by providing an
edge over the casino), their BETTING fails to connect that skill with any level of
consistent profit. The use of
Initial Steep Regressions helps a player bridge that skill/profit gap. Weve seen
how the SINGLE-event chances of a 7 showing up on any particular roll is 16.67% for a
random-roller; 14.29% for an SRR-7 shooter; 12.5% for a SRR-8 player and 11.11% for a
SRR-9 Precision-Shooter. Now, lets look
at how the Cumulative-Odds against a 7 showing up on a roll-to-roll basis
affects his chances of getting to a certain point-cycle roll count:
ISRs
offer an incredible opportunity to profit from the fattest, most frequently occurring part
of the roll-duration expectancy-curve. For
example:
Ø
A
random-roller has a 5:1 chance of rolling at least one non-7 during the point-cycle
portion of his hand, but his chances of two non-7 outcomes in a row drops to 4.2:1. When
you think about the odds of him getting to the tenth point-cycle roll, there is only a
0.9:1 chance that hell actually get there.
Ø
An
SRR-8 shooter has a 7:1 chance of rolling at least one non-7 during the point-cycle
portion of his hand, while his chances of two non-7 outcomes in a row drops to 6.1:1. When
you think about the odds of him getting to the tenth point-cycle roll, there still a 2.1:1
chance that hell make it.
So
although there is only a moderate difference between those two shooters surviving their first
point-cycle roll (83.33% vs. 87.50%); by the time they get to their tenth roll
there is an ever-widening gap (16.14% vs. 26.31%). Again,
the chances of a 7-Out occurring on any given roll remains rock solid at 16.67% for the
random-roller, and 12.50% for the SRR-8 shooter; but each of those 1-in-6 (for the R-R)
and 1-in-8 (for the SRR-8 shooter) per-roll 7s occurrence-rates affects how long, on
average, each player can expect to hold the dice. That brings us
to the cumulative-odds of a non-7 roll occurring; for example
~A
SRR-8 shooter is 270% more likely to throw a 20-roll hand than a random-roller is, and
450% more likely to throw a 30-roll hand. By the time we get to a 40-roll expectancy;
there is a 685% difference; and finally, a 2600% disparity between the expectancy of a
SRR-6 and a SRR-8 shooter having a 50-roll point-cycle hand. Still though,
you have to ask yourself; if that huge roll-duration difference is enough to keep your
bets at their high starting value for the duration of each hand, or whether you should use
the fattest portion of the roll-duration curve to lock-in a profit before regressing to a
lower-value as roll-duration expectancy declines. Take a look and
decide for yourself
One
more thing that I should point out is that, this chart does not include those hands where
you will establish a multi-Point hand that is interspersed with Come-Out 7-winners. Rather, it is illustrative of the fact that it is
difficult to have a 50-roll point-cycle that is undisturbed by either a PL-Point winner or
a hand-ending 7-Out loser. What
To Do With What Youve Got
One
of the most basic elements of dice-influencing that players fail to understand is that
their short-hands will always outnumber their long-hands...and it is what
they do with the MAJORITY of their hands that determines just how much money they
will earn from an average non-headline-making session. Anyone
can and should make money off of 20, 30, 50 and 70-roll hands; but how many players
make consistent profit off of their 2, 3, 4 and 5-roll hands? The
simple truth about dice-influencing is that regardless of how skilled you are, your
point-cycle will always contain a declining number of tosses when you look at your
roll-duration outcomes on a chart. Savvy
ISR dice-influencers profitably exploit the fattest, most frequently-occurring portion of
the roll-duration curve, while flat-bettors hope to get far, far beyond that point. Both
Flat-bettors and ISR-bettors can make money off of their SRR-8 skills. The ISR-user gets his profit more
consistently and much earlier, while the Flat-bettor gets it less frequently and quite a
bit later. But
at the end of the day, how you profitably exploit your advantage over the house is
entirely up to you. Good
Luck & Good Skill at the Tables
and in Life. Sincerely, The
Mad Professor
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