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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 I've 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
7's 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-numbers to 7's 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-numbers to 7's 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-numbers to 7's 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-numbers to 7's 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 7's 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
6's & 8's to 7's 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
5's & 9's to 7's 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
4's & 10's to 7's 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

7's per 36-rolls is simply the average number of 7's that will show up in a range of 36-rolls. For a random-roller it is six 7's 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 rolls, on average, you will see between 7's.

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 7'ing-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 7's ratio is the specific expected hit-rate for each of these multi-number wagers (Inside, Outside, Even, etc.) when compared to the frequency of 7's for each SRR skill-level. For example, we'd 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 7's, the SRR-7 shooter enjoys a much higher 4.8 Across-numbers-to-7's 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 Regressingis 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 let's 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 he'd 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 he'd 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. We'll explore the best ways to safely utilize your edge without imperiling your bankroll, and we'll 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 you'll join me for that. Until then,

Good Luck & Good Skill at the Tables and in Life.


The Mad Professor

Copyright © 2006

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This page contains a single entry from the blog posted on January 19, 2007 3:51 AM.

The previous post in this blog was Walking with a Vegas Ghost - Part 2.

The next post in this blog is Ask the Mad Professor - Part 19.

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