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Regression Avoids Depression
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…

       He’ll survive the first point-cycle roll approximately 87% of the time.

 

       He’ll survive the second point-cycle roll about 76% of the time.

 

       He’ll survive the third point-cycle roll around 67% of the time.

 

       He’ll survive the fourth point-cycle roll approximately 58% of the time.

 

       By the time we get to the tenth p-c roll, he’ll have a 26% statistical chance of getting to his eleventh one.

 

       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:

       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.

 

       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.

 

       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...

       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.

 

       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

 

SRR-7

 

SRR-8

 

SRR-9

 

R
O
L
L
S

Survival Rate

Cumulative Odds against a 7

Surv’l Rate

Cum. Odds against a 7

Surv’l Rate

Cum. Odds against a 7

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:

       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.

 

       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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