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

**. In most cases, that means showing you what you**

*current skills***accomplish if you simply wagered on your current advantage the way it**

*could***be bet.**

*should*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.

SSR-7 | SSR-8 | SSR-9 | |
---|---|---|---|

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 | |||

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 | |||

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 | |||

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 | |||

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 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 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.**

*Sincerely,*

**The Mad Professor**

**Copyright © 2006**