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Regression Avoids Depression

Part 19 

 

My over-riding passion in writing all of these articles, and frankly in ultimately allowing Stanford Wong to publish my book; is so that players can finally bridge the gaping and disappointingly wide chasm between the edge that their de-randomized throws produce...and the profits that their skills should be generating.


Making the connection between the edge that you currently shoot with and the profit that those same skills should be earning you; is actually easier than it appears, although admittedly, most players will continue to make it unnecessarily difficult on themselves.

 

This entire series is all about how to safely make more money from your current skills.  In most cases, that means showing you what you could accomplish if you simply wagered on your current advantage the way it  should be bet.

 

I like to make as much money with as little risk from my D-I skills as possible.  I do that by focusing the bulk of the money that Ive allocated on a per-hand basis, to those validated positive-expectations wagers that I know I am most likely to collect from during the point-cycle. 

 

The following chart will help you determine where your own opportunities are; and when you regress your wagers at the optimal regression point, this chart also shows what your true edge over these multi-number global-bets really is.

 

Your true edge, when broken out on a per-roll basis, is critical in helping you determine the proper size of your pre-regression wagers in relation to the boundaries of your current total gaming bankroll.

 

Player-Edge

using Optimized Regression

 

SSR-7

SSR-8

SSR-9

7s per 36-rolls

5.14

4.5

4.0

7-Out Probability/Roll

14.29%

12.50%

11.11%

Average
Point-Cycle
Roll-Duration

7

8

9

Average Rolls/PL or 7-Out Decision

4.2

5.0

5.8

Inside

 

 

 

Inside-numbers to 7s ratio

3.6:1

4.1:1

4.75:1

Inside-number

Probability/Roll

51.19%

52.08%

52.78%

Optimal Hits before Regressing

1

3

4

Cumulative Pre-Regression Edge on this Wager based on Bet-Survival Curve

2.00%

6.23%

12.36%

Overall

Edge-per-Roll

0.48%

1.25%

2.13%

Across

 

 

 

Across-numbers to 7s ratio

4.8:1

5.6:1

6.4:1

Across-number

Probability/Roll

68.58%

70.00%

71.11%

Optimal Hits before Regressing

2

3

4

Cumulative Pre-Regression Edge on this Wager based on Bet-Survival Curve

1.78%

5.84%

11.97%

Overall

Edge-per-Roll

0.42%

1.17%

2.06%

Outside

 

 

 

Outside-numbers to 7s ratio

2.8:1

3.3:1

3.7:1

Outside-number

Probability/Roll

40.00%

40.83%

41.47%

Optimal Hits before Regressing

1

2

4

Cumulative Pre-Regression Edge on this Wager based on Bet-Survival Curve

1.40%

5.10%

10.70%

Overall

Edge-per-Roll

0.33%

1.02%

1.85%

Even

 

 

 

Even-numbers to 7s ratio

3.20:1

3.73:1

4.27:1

Even-number

Probability/Roll

45.72%

46.67%

47.42%

Optimal Hits before Regressing

1

3

4

Cumulative Pre-Regression Edge on this Wager based on Bet-Survival Curve

1.82%

5.86%

12.09%

Overall

Edge-per-Roll

0.43%

1.17%

2.08%

Iron Cross

 

 

 

IC-numbers to 7s ratio

6:1

7:1

8:1

IC-number

Probability/Roll

85.72%

87.50%

88.89%

Optimal Hits before Regressing

2

3

4

Cumulative Pre-Regression Edge on this Wager based on Bet-Survival Curve

1.68%

5.59%

11.64%

Overall

Edge-per-Roll

0.40%

1.12%

2.01%

6 and 8

 

 

 

6s & 8s to 7s ratio

2:1

2.33:1

2.67:1

6 & 8

Probability/Roll

28.57%

29.16%

29.63%

Optimal Hits before Regressing

2

3

4

Cumulative Pre-Regression Edge on this Wager based on Bet-Survival Curve

2.42%

7.42%

14.00%

Overall

Edge-per-Roll

0.58%

1.48%

2.55%

5 and 9

 

 

 

5s & 9s to 7s ratio

1.6:1

1.87:1

2.14:1

5 & 9

Probability/Roll

22.86%

23.33%

23.71%

Optimal Hits before Regressing

1

3

4

Cumulative Pre-Regression Edge on this Wager based on Bet-Survival Curve

1.70%

5.60%

11.70%

Overall

Edge-per-Roll

0.40%

1.12%

2.02%

4 and 10

 

 

 

4s & 10s to 7s ratio

1.2:1

1.4:1

1.6:1

4 and 10

Probability/Roll

17.14%

17.5%

17.78%

Optimal Hits before Regressing

1

2

4

Cumulative Pre-Regression Edge on this Wager based on Bet-Survival Curve

1.10%

4.60%

9.60%

Overall

Edge-per-Roll

0.26%

0.92%

1.67%

 

 

What It Means

 

7s per 36-rolls is simply the average number of 7s that will show up in a range of 36-rolls.  For a random-roller it is six 7s per 36-rolls, but as your Sevens-to-Rolls Ratio (SRR) improves, this number drops to 5.14 for SRR-7, 4.5 for SRR-8, and 4.0 for SRR-9.

  

7-Out Probability/Roll represents the likelihood of a 7 showing up on any given roll.  Given your SRR-rate, this can be expressed as a percentage.  For a random-roller, the probability of a 7 showing up on any given roll is 16.67%, for a SRR-7 shooter it is 14.29%; for a SRR-8 dice-influencer it is 12.5% on any given roll, and for a SRR-9 precision-shooter, it is 11.11%.

 

Point-Cycle Roll-Duration is just another way of expressing your SRR-rate, in that it represents how many roll, on average, you will see between 7s.

 

Average Rolls/PL or 7-Out Decision tells us how many rolls our SRR-driven skill will generate before either repeating our PL-Point or 7ing-Out.  Where this figure can be quite helpful is in figuring out how many PL-Points we are likely to repeat during an average hand.  The reason this number is lower than our point-cycle roll duration is due to those hands where multiple PL-Point numbers are made within a string of point-cycle rolls.  A random-roller will experience about 3.4 rolls per Passline decision, while an SRR-7 shooter will encounter an average of 4.2 rolls, an SRR-8 dice-influencer will throw an average of 5.0 rolls per Passline decision, and a SRR-9 precision-shooter will experience about 5.8 rolls per PL decision.

 

(Global-bet) to 7s ratio is the specific expected hit-rate for each of these multi-number wagers (Inside, Outside, Even, etc.) when compared to the frequency of 7s for each SRR skill-level.  For example, wed randomly expect to see 3.0 Inside-number hits for every one 7-Out, and Inside-numbers have a random per-roll expectancy-rate of 50%; however a SRR-7 player produces a slightly better Inside-Number expectancy of 51.19% per-roll, and can expect 3.6 Inside-number hits for each 7-Out that he throws.  Likewise, random-rollers expect to see 4.0 Across-numbers for each 7-Out (where the Across-wager accounts for 66.6% of all random outcomes); whereas in the hands of an SRR-7 shooter, Across-numbers generally account for a slightly higher 68.58% per-roll appearance-rate, but because of the lower frequency of 7s, the SRR-7 shooter enjoys a much higher 4.8 Across-numbers-to-7s ratio.

 

(Global-bet) Probability-per-Roll sets out, in general terms, what we can expect each of these bets to account for as far as per-roll probability is concerned.   For example, the Iron-Cross (everything but the 7) accounts for 83.33% of all random outcomes (the 7 accounts for the other 16.67%).  However, as your SRR-rate improves, so does the per-roll probability of this wager.  For example, an SRR-7 shooter can expect his I-C anything-but-7 outcomes to account for 85.72% of his outcomes, while the SRR-8 shooter can expect it 87.50% of the time; and for the SRR-9 shooter, the Iron Cross will account for 88.89% of his point-cycle results.
 

Optimal Hits Before Regressing is the number of winning hits this particular bet should remain at its initial large pre-regression level before optimally reducing it to a lower bet-amount.  For example, a SRR-7 shooter would ideally leave his Inside-Number wager at its large pre-regression starting value for one hit only; while the SRR-8 shooter can afford to leave it at its initial starting value for three paying hits before regressing to a lower amount of exposure.

 

 

Cumulative Pre-Regression Edge on this Wager based on Bet-Survival Curve is the aggregate advantage the player has over the house prior to regressing his chosen bet at the optimal time.  This figure gives you an idea of how powerful regression-betting can be when properly combined with dice-influencing.  By merging your skill-driven expected-roll-duration with a betting-method that utilizes and exploits the fattest, highest-survival portion of your point-cycle expectancy-curve; you derive benefit from the most frequently occurring opportunities, while concurrently reducing bankroll volatility and risk as your point-cycle bet-survival rate diminishes.

 

Overall Edge-per-Roll is the weighted advantage you have over the house during each toss in your point-cycle roll when using regression-style wagering.  To manage volatility and err on the ultra-conservative side of money management; this figure is used to indicate how much of your total gaming bankroll you can reasonably afford to expose to these multi-number global-wagers when starting with a larger initial bet and then reducing it at the optimal regression point. 

 

For example, an SRR-7 shooter who validates his edge over the Place-bet 6 & 8 and chooses to use a 5:1 steepness ratio ($30 each on the 6 & 8 regressed down to $6 each after the first hit); would divide his 0.58% regression-based true edge over this combined bet into the total initial bet-value of $60 ($60 / 0.0058) to determine that his total I-will-give-up-craps-if-I-lose-this-amount-of-money gaming bankroll should be around $10,344 for this skill-level and regressed steepness ratio. 

 

Likewise, an SRR-8 player making the very same bet, but with a 1.48% edge-per-roll over the Place-bet 6 & 8 wager, would optimally have a total I-will-give-up-craps-if-I-lose-this-amount-of-money gaming bankroll of $4054 for this wager ($60 / 0.0148).  If lets say, this same player decided to use a more modest 3:1 steepness ratio ($18 each on the 6 & 8 regressed down to $6 each after optimally enjoying three paying hits at the initial rate); then hed take the total initial wager of $36 ($18 on the Place-bet 6 + $18 on the Place-bet 8) and divide that by the same 0.0148 (his true regression-based edge per-roll over this wager) to determine that hed ideally have a total gaming bankroll of $2432 to back up this lower starting-value bet.

 

 Coming Up

 

In Part Twenty of this series, we are going to dive into the whole how-much-money-do-I-REALLY-need-to-properly-exploit-my-edge question in extraordinary detail.  Well explore the best ways to safely utilize your edge without imperiling your bankroll, and well run through each of these global-bets over a broad range of steepness-ratios to look at how big your overall bankroll really should be.

 

I hope youll join me for that.  Until then,

 

Good Luck & Good Skill at the Tablesand in Life.

 

Sincerely,

 

The Mad Professor

Copyright 2006

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