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Regression Avoids Depression - Part 14

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

  1. He'll survive the first point cycle roll approximately 87% of the time.
  2. He'll survive the second point cycle roll about 76% of the time.
  3. He'll survive the third point cycle roll around 67% of the time.
  4. He'll survive the fourth point cycle roll approximately 58% of the time.
  5. By the time we get to the tenth p c roll, he'll have a 26% statistical chance of getting to his eleventh one.
  6. On his twentieth point cycle roll, he'll 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 7's appearance rate affects each and every subsequent throw that they make and I'm happy to provide the answer.

Sevens Appearance Rate
Random SRR 6 SRR 7 SRR 8 SRR 9
Appearance Ratio 1 in 6 1 in 7 1 in 8 1 in 9
Per Roll Probability 16.67% 14.29% 12.50% 11.11%
7's per 36 rolls 6 5.14 4.5 4

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 won't. 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 can't comprehend how SRR rates affect the groupings of more than one throw in a chain of outcomes.

For example:

  1. 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.
  2. 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.
  3. 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.

You can easily see where this is heading...

  1. 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.
  2. 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.

We've 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, let's 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:

Roll Duration Survival Rate Cumulative Odds against a 7 showing up on a roll to roll Basis
SRR 6 Survival Rate Cumulative Odds against a 7 SRR 7 Surv'l Rate Cum. Odds against a 7 SRR 8 Surv'l Rate Cum. Odds against a 7 SRR 9 Surv'l Rate Cum. Odds against a 7
1 83.33% 5:1 85.72% 6:1 87.50% 7:1 88.89% 8:1
2 69.44% 4.2:1 73.47% 5.14:1 76.56% 6.1:1 79.01% 7.1:1
3 57.86% 3.5:1 62.97% 4.4:1 66.99% 5.4:1 70.24% 6.4:1
4 48.22% 2.9:1 53.97% 3.8:1 58.62% 4.7:1 62.43% 5.6:1
5 40.18% 2.4:1 46.26% 3.3:1 51.29% 4.1:1 55.50% 5.0:1
6 33.48% 2.0:1 39.65% 2.8:1 44.88% 3.6:1 49.33% 4.4:1
7 27.90% 1.7:1 33.98% 2.4:1 39.27% 3.1:1 43.85% 3.9:1
8 23.25% 1.4:1 29.13% 2.0:1 34.36% 2.7:1 38.98% 3.5:1
9 19.37% 1.2:1 24.97% 1.7:1 30.07% 2.4:1 34.65% 3.1:1
10 16.14% 0.9:1 21.40% 1.5:1 26.31% 2.1:1 30.80% 2.8:1
11 13.45% 0.8:1 18.34% 1.3:1 23.02% 1.8:1 27.38% 2.5:1
12 11.21% 0.7:1 15.72% 1.1:1 20.14% 1.6:1 24.34% 2.2:1
13 9.34% 0.6:1 13.47% 0.9:1 17.62% 1.4:1 21.63% 1.9:1
14 7.78% 0.5:1 11.55% 0.8:1 15.42% 1.2:1 19.23% 1.7:1
15 6.49% 0.4:1 9.90% 0.7:1 13.49% 1.1:1 17.09% 1.5:1
16 5.41% 0.3:1 8.48% 0.6:1 11.80% 0.9:1 15.19% 1.4:1
17 4.50% 0.27:1 7.27% 0.5:1 10.33% 0.8:1 13.50% 1.2:1
18 3.75% 0.22:1 6.23% 0.4:1 9.04% 0.7:1 12.00% 1.1:1
19 3.13% 0.19:1 5.34% 0.37:1 7.91% 0.6:1 10.67% 1.0:1
20 2.60% 0.16:1 4.58% 0.32:1 6.92% 0.5:1 9.49% 0.9:1
21 2.17% 0.13:1 3.92% 0.26:1 6.06% 0.48:1 8.43% 0.8:1
22 1.81% 0.11:1 3.36% 0.23:1 5.30% 0.42:1 7.50% 0.7:1
23 1.51% 0.09:1 2.88% 0.20:1 4.64% 0.37:1 6.66% 0.6:1
24 1.26% 0.08:1 2.47% 0.17:1 4.06% 0.32:1 5.92% 0.5:1
25 1.05% 0.06:1 2.12% 0.15:1 3.55% 0.28:1 5.26% 0.47:1
26 0.87% 0.05:1 1.82% 0.13:1 3.11% 0.25:1 4.68% 0.42:1
27 0.73% 0.04:1 1.56% 0.11:1 2.72% 0.22:1 4.16% 0.37:1
28 0.61% 0.04:1 1.33% 0.093:1 2.38% 0.19:1 3.70% 0.33:1
29 0.50% 0.03:1 1.14% 0.080:1 2.08% 0.17:1 3.29% 0.30:1
30 0.42% 0.02:1 0.98% 0.069:1 1.82% 0.15:1 2.92% 0.26:1
31 0.35% 0.020:1 0.84% 0.056:1 1.59% 0.13:1 2.60% 0.23:1
32 0.29% 0.017:1 0.72% 0.050:1 1.39% 0.11:1 2.30% 0.21:1
33 0.24% 0.014:1 0.62% 0.043:1 1.22% 0.10:1 2.05% 0.18:1
34 0.20% 0.012:1 0.53% 0.037:1 1.07% 0.09:1 1.82% 0.16:1
35 0.17% 0.010:1 0.45% 0.030:1 0.93% 0.07:1 1.62% 0.15:1
36 0.14% 0.008:1 0.39% 0.027:1 0.82% 0.065:1 1.44% 0.13:1
37 0.12% 0.007:1 0.33% 0.023:1 0.72% 0.057:1 1.28% 0.12:1
38 0.10% 0.006:1 0.29% 0.020:1 0.63% 0.050:1 1.14% 0.10:1
39 0.08% 0.005:1 0.25% 0.017:1 0.55% 0.044:1 1.01% 0.09:1
40 0.07% 0.004:1 0.21% 0.015:1 0.48% 0.038:1 0.90% 0.08:1
41 0.06% 0.0035:1 0.18% 0.013:1 0.42% 0.034:1 0.80% 0.07:1
42 0.05% 0.0029:1 0.15% 0.010:1 0.37% 0.030:1 0.71% 0.06:1
43 0.04% 0.0024:1 0.13% 0.009:1 0.32% 0.025:1 0.63% 0.057:1
44 0.03% 0.0018:1 0.11% 0.0076:1 0.28% 0.022:1 0.56% 0.050:1
45 0.02% 0.0012:1 0.10% 0.0070:1 0.25% 0.020:1 0.50% 0.045:1
46 0.01% 0.0006:1 0.08% 0.0055:1 0.22% 0.018:1 0.44% 0.040:1
47 0.008% 0.00047:1 0.07% 0.0049:1 0.19% 0.015:1 0.39% 0.035:1
48 0.007% 0.00042:1 0.06% 0.0042:1 0.17% 0.014:1 0.35% 0.032:1
49 0.006% 0.00036:1 0.05% 0.0034:1 0.15% 0.012:1 0.31% 0.028:1
50 0.005% 0.00030:1 0.04% 0.0029:1 0.13% 0.010:1 0.28% 0.025:1

ISR's offer an incredible opportunity to profit from the fattest, most frequently occurring part of the roll duration expectancy curve.

For example:

  1. 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 he'll actually get there.
  2. 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 he'll 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 7's 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

How Many Point cycle Hands Will Get This Far?
SRR 6 SRR 7 SRR 8 SRR 9
1 8.3 out of 10 8.5 out of 10 8.7 out of 10 8.9 out of 10
2 7 out of 10 7 out of 10 7.6 out of 10 7.9 out of 10
3 6 out of 10 6 out of 10 7 out of 10 7 out of 10
4 5 out of 10 5 out of 10 6 out of 10 6 out of 10
5 4 out of 10 4.6 out of 10 5 out of 10 5.5 out of 10
6 3 out of 10 4 out of 10 4.5 out of 10 5 out of 10
7 3 out of 10 3.4 out of 10 4 out of 10 4.3 out of 10
8 2.3 out of 10 3 out of 10 3.4 out of 10 4 out of 10
9 2 out of 10 2.5 out of 10 3 out of 10 3.5 out of 10
10 16 out of 100 21 out of 100 26 out of 100 31 out of 100
11 13 out of 100 18 out of 100 23 out of 100 27 out of 100
12 11 out of 100 16 out of 100 20 out of 100 24 out of 100
13 9 out of 100 13 out of 100 18 out of 100 22 out of 100
14 8 out of 100 11 out of 100 15 out of 100 19 out of 100
15 6 out of 100 10 out of 100 13 out of 100 17 out of 100
16 5 out of 100 8 out of 100 12 out of 100 15 out of 100
17 4 out of 100 7 out of 100 10 out of 100 13 out of 100
18 3.8 out of 100 6 out of 100 9 out of 100 12 out of 100
19 3 out of 100 5 out of 100 8 out of 100 11 out of 100
20 2.6 out of 100 4.5 out of 100 7 out of 100 9 out of 100
21 2 out of 100 4 out of 100 6 out of 100 8 out of 100
22 18 out of 1000 33 out of 1000 53 out of 1000 75 out of 1000
23 15 out of 1000 29 out of 1000 46 out of 1000 67 out of 1000
24 13 out of 1000 25 out of 1000 40 out of 1000 59 out of 1000
25 10 out of 1000 21 out of 1000 36 out of 1000 53 out of 1000
26 9 out of 1000 18 out of 1000 31 out of 1000 47 out of 1000
27 7 out of 1000 16 out of 1000 27 out of 1000 42 out of 1000
28 6 out of 1000 13 out of 1000 24 out of 1000 37 out of 1000
29 5 out of 1000 11 out of 1000 20 out of 1000 33 out of 1000
30 4 out of 1000 10 out of 1000 18 out of 1000 29 out of 1000
31 3.5 out of 1000 8 out of 1000 16 out of 1000 26 out of 1000
32 3 out of 1000 7 out of 1000 14 out of 1000 23 out of 1000
33 2.4 out of 1000 6 out of 1000 12 out of 1000 20 out of 1000
34 20 out of 10000 53 out of 10000 110 out of 10000 182 out of 10000
35 17 out of 10000 45 out of 10000 93 out of 10000 162 out of 10000
36 14 out of 10000 39 out of 10000 82 out of 10000 144 out of 10000
37 12 out of 10000 33 out of 10000 72 out of 10000 128 out of 10000
38 10 out of 10000 29 out of 10000 63 out of 10000 114 out of 10000
39 8 out of 10000 25 out of 10000 55 out of 10000 101 out of 10000
40 7 out of 10000 21 out of 10000 48 out of 10000 90 out of 10000
41 6 out of 10000 18 out of 10000 42 out of 10000 80 out of 10000
42 5 out of 10000 15 out of 10000 37 out of 10000 71 out of 10000
43 4 out of 10000 13 out of 10000 32 out of 10000 63 out of 10000
44 3 out of 10000 11 out of 10000 28 out of 10000 56 out of 10000
45 2 out of 10000 10 out of 10000 25 out of 10000 50 out of 10000
46 1 out of 10000 8 out of 10000 22 out of 10000 44 out of 10000
47 80 out of 100000 700 out of 100000 1900 out of 100000 3900 out of 100000
48 70 out of 100000 600 out of 100000 1700 out of 100000 3500 out of 100000
49 60 out of 100000 500 out of 100000 1500 out of 100000 3100 out of 100000
50 50 out of 100000 400 out of 100000 1300 out of 100000 2800 out of 100000

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 You've 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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This page contains a single entry from the blog posted on January 14, 2007 3:38 AM.

The previous post in this blog was Current Practice…Future Profitability - Part 7.

The next post in this blog is FAQ’s About The Choppy-Table/Short-Leash - Part 1.

Many more can be found on the main index page or by looking through the archives.

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