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Regression Avoids Depression
Part X

Why ISR’s Offer More Profit Predictability 

The intelligent use of Initial Steep Regressions (ISR's) is the closest a player can come to accurately projecting his profit on a session-to-session, day-to-day, week-to-week, month-to-month and year-to-year basis.  Nothing else comes closer to predicting how much profit an advantage-player can yield on a per-hand basis.

       By taking a players entire SRR-predictive range of roll-outcomes (from the shortest Point-then-7-Out to the longest mega and mini-mammoth hands) for each Sevens-to-Rolls Ratio; and then counterposing and evaluating every global (multi-number/multi-decision) bet on the table, we can determine the optimal regression point for each bet-type and skill-level.

 

       Since volatility-measurement and volatility-management is built into each of the optimal regression trigger-points for each of the bet-types we are discussing in this series; a player can determine how many rolls and winning-hits he can generally expect from each hand depending on his current in-casino SRR-rate.

 

       The charts in this series not only show how it is done, but also why ISR's are truly superior to other wagering methods and why they work so well.  The only thing the shooter has to do is to control his betting-discipline as much as he controls the dice at his current SRR skill-level.

For example…

       If he knows how many turns with the dice he’ll have during an average session; then using the SRR-tables in this series, he can look at his current SRR dice-influencing skill-level and his current bankroll, plus his current wager-size comfort-level; and then determine the appropriate ISR betting method (Inside-Numbers, All-Across wagers, Outside-Numbers, Even-Numbers, the Iron Cross, or simple 6 & 8, 5 & 9, or 4 & 10 regressions, or even more exotic multi-stage Place-Come-Place staggered regression-type wagers) and determine not only the bet-type that is just right for him, but also how much money he’ll likely make from those ISR-wagers during an average session.

 

How ISR’s Offer Better Profit Dependability 

       If a player has a fairly good dice-tossing consistency, yet he has a hard time getting to any level of revenue-consistency; then chances are, he hasn't properly matched his shooting prowess with his betting prowess.

 

       ISR’s are especially useful to players who have developed a modest ability to influence the dice, but haven't yet been able to turn their skills into steady earnings.

 

With the use of Initial Steep Regressions, a novice player can reap a larger degree of the rewards that his de-randomized throws are offering; while an advanced player can extract even more income from his current skill-set on a much more predictable basis...with each player accomplishing his profit-objective more often and with less overall risk than flat or pressed-up wagering.

Putting the 6 and 8 Place-bet Under a Microscope

So far we’ve looked at how well ISR’s work on several global-type bets that cover four numbers (Inside, Outside, and Even), six numbers (Across) and even ten numbers (Iron Cross) at the same time.   However, let’s say you are just considering Place-betting your two most dominant Signature-Numbers like the 6 and 8.

       In random expectancy, we’ll see five 6’s and five 8’s against six appearances of the 7, which equates to ten appearances of the 6 and 8 for every six appearances for the 7.

 

       That ratio of 10:6 means a random-roller can expect a 6’s-and-8’s-to-7’s appearance-rate of 1.67:1. 

 

       As you know, the difference in that ratio is not enough to make up for the cost of a 7-out which would wipe out both Place-bet wagers; and even though a winning hit pays 7:6…it is still not enough to overcome the house-edge.

 

       A simple look at the combined value of both bets against their single-hit payoff quickly exposes where all of that negative-expectation comes from.  

 

       A simple $6 Place-bet on both the 6 and 8 offers a $7 payoff for $12 of risk. 

 

       In that light, the 10:6 (1.67:1) Sixes-&-Eights-to-Sevens ratio doesn’t look all that appealing even with the better than even-money payoff that those winning Place-bets pay.

 

       As a result, random-rollers stay on the negative-side of the expectation curve, while dice-influencers cross over into positive territory on a regular basis.

 

       By using an ISR, the talented shooter can capitalize on those positive-side raids in a much more reliable way.

 

Why ISR’s Work So Well With Simple 6 & 8 Place-bets

We know that for a random-roller, the 7 is expected to show up once every six rolls.  With a 16.67% appearance-rate, that DOES NOT mean that the 7 will show up like clockwork on each and every sixth roll.  Instead, it means that its appearance-rate will average out to once every six rolls.  That’s the nature of the beast that we call volatility.  

As dice-influencers we know that the further we move our shooting away from the randomly-expected SRR-6, the better we are at keeping the 7 at bay.

In a random outcome game, the 6 and 8 constitute 27.78% of all possible outcomes. 

There are:

       Five ways to make a 6, and a Place-bet pays 7:6.

 

       Five ways to make an 8, and a Place-bet pays 7:6.

 

Therefore, the Place-bet 6 and 8 wager constitutes 10-out-of-36 (27.78%) of all randomly-expected outcomes, and its payout for a $6 bet is $7.00 per winning hit.

As with every Rightside bet, how often the 7 appears is dictated by your skill-based SRR-rate.

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%

12.5%

11.11%

7’s-per-36 rolls

6

5.14

4.5

4

 

 

 

 

 

6’s & 8’s-to-Sevens Ratio

 

Random SRR 6

SRR 7

SRR 8

SRR 9

6’s and 8’s to Total Outcomes

10-out-of-36

10.29

10.50

10.67-out-

of-36

Per-Roll

Probability

27.78%

28.57%

29.16%

29.63%

6’s and 8’s-

to-7’s Ratio

1.67:1

2:1

2.33:1

2.67:1

 

 

 

 

 

 

 

 

 

Although the sheer number of 6’s and 8’s doesn’t rise that dramatically when your shooting-skill improves; the real difference comes in the reduced appearance-rate of hand-ending 7’s.  In the chart above, an SRR-9 shooter only generates slightly more 6’s and 8’s than a random-roller does (10.67 versus 10.00).  However, since his dice-influencing produces a lower overall sevens-appearance-rate, his actual 6’s-and-8’s-to-7’s ratio improves by more than 62% (from 1.67 to 2.67).

That is a healthy increase that a savvy advantage-player simply cannot ignore.

Anatomy Of a 6 & 8 Place-bet

The primary advantage-play rule-of-thumb is:

The fewer advantaged bets that you spread your money over, the fewer winning hits you will need in order to produce a net-profit.

 

6 & 8 Flat-bet

Repayment Rate

 

6 & 8 Hits

Total Investment

Single

Payout

Return on Investment

Profit

0

$12

$0

0%

(-$12.00)

1

-

$7.00

58.33%

(-$7.00)

2

-

$7.00

116.67%

$2.00

 

 

 

 

 

 

Place-betting the 6 and 8 only requires two winning hits to repay your initial base-bet before breaking into net-profitability.

As a flat-betting advantage-player, two hits on either the 6 and 8 seems like a modest goal; but you have to maintain perspective and think about all of the times when you’ve only hit one of them.  If you add up all of those frustrating one-roll-short-of-a-profit losses; you’ll quickly see that the number of winning hands that you need to throw, actually exceeds that two-hits-required mark because of all those one-hit-isn’t-enough performances.

In other words, the more you miss, the more you have to hit…just to break even.

To be totally fair though, it still doesn’t take very much dice-influencing skill for this wager to be a steady profit contributor, even if you do decide to strictly adhere to flat-bets only.  Take a look:

$6  6 & 8 Place-bet
Expected Flat-bet Win-Rate

 

Expected Profit/Roll

Random SRR 6

SRR 7

SRR 8

SRR 9

6’s & 8’s-to-7’s Ratio

1.67:1

2:1

2.33:1

2.67:1

1

$7.00

$7.00

$7.00

$7.00

2

$4.69

Weighted payout

$7.00

$7.00

$7.00

3

-

-

$2.31

Weighted payout

$4.69

Weighted payout

Total Expected Payout

$11.69

$14.00

$16.31

$18.69

Remaining Wager

$12.00

$12.00

$12.00

$12.00

Net-Profit

-$0.31

$2.00

$4.31

$6.69

Return-on-Investment

-2.58%

16.67%

39.92%

55.75%

 

 

 

 

 

 

Your Sevens-to-Rolls Ratio largely determines the average roll-duration of your 6 & 8 Place-bet. 

       Now we all know that sometimes a random-roller will throw all kinds of 6’s and 8’s, while at other times they can’t produce them to save their life.

 

       On average though, the house wins out on the randomly-wagered 6 and 8…and at the end of the day, it remains a net-detractor to your bankroll.  

 

       On the other hand, even a flat-betting SRR-7 shooter can produce a net-profit with this wager.  Sure, sometimes he’ll throw a 7-Out before producing the two required winning hits that it takes to make this bet net-profitable; but over time, even flat betting it will produce a decent profit for this caliber of shooter by providing an average return of 16% profit on each and every hand that he throws.  For the SRR-8 shooter, that rate-of-return jumps to nearly 40% R.O.I. per hand.

 

As good as A-P flat-betting can be; there is an even better way for the modestly skilled Precision-Shooter to produce steadier and larger profits from the exact same skill-level. 

       Your SRR determines the ability for any given wager to survive over multiple Point-cycle rolls. 

 

       That survival rate is determined by the ever-present 7. 

 

       As your SRR-rate improves over random, your chances of a given bet surviving for additional rolls, increases. 

 

       The higher your SRR-rate is, the longer a given bet has a chance to survive…and THRIVE!

 
As with a random-roller, each SRR-rate produces its own roll-duration decay-rate against which your validated edge against any given wager has to fight.   

       When we compare your bet-survival-rate and pit it against the roll-duration decay-rate of your current Sevens-to-Rolls-Ratio (SRR), we can establish the optimal time at which to regress your initially large bet into a smaller, lower-value one. 

 

As we’ve seen in previous chapters, the per-roll decay-rate is different for each SRR-rate as well as each type of wager.  Here is what it looks like for the 6 and 8 Place-bet point-cycle: 

6 & 8 Place-Bet Survival-Rate

6 & 8

Hit-rate

Random SRR 6

SRR 7

SRR 8

SRR 9

1

27.78%

28.57%

29.16%

29.63%

2

23.15%

24.49%

25.52%

26.34%

3

19.29%

20.99%

22.33%

23.41%

4

16.07%

17.99%

19.53%

20.81%

5

13.39%

15.42%

17.09%

18.50%

6

11.16%

13.22%

14.96%

16.44%

7

9.30%

11.33%

13.09%

14.62%

8

7.75%

9.71%

11.45%

12.99%

9

6.46%

8.32%

10.02%

11.55%

10

5.38%

7.13%

8.77%

10.27%

11

4.48%

6.11%

7.67%

9.13%

12

3.73%

5.24%

6.71%

8.11%

Although the percentages for each SRR proficiency-rate may appear to be relatively close to each other, and not significantly better than random; it is in that small degree of positive-expectation variance that we find all kinds of reliable profit.  This is especially true in the first couple of point-cycle rolls during any given hand.

As we’ve discussed previously, your per-roll chances of rolling a 7 stays exactly the same.  For a random-roller it remains steady at 16.67% per-roll, and for the SRR-7 shooter it stays locked in at 14.29% per point-cycle roll.  However, the cumulative roll-ending effect of the 7 does not remain stable.  As a result, your chances of having a long non-7 hand decays with each and every subsequent point-cycle roll that you make.  Sure, you may sometimes produce a headline-making mega-roll, but most times you won’t. 

Advantage-play means taking profitable advantage of what your dice-influencing skills are most capable of producing.  You can try to bet like EVERY hand will be a mega-hand, but frankly you are going to be disappointed many more times than you’ll be elated.

The use of Initial Steep Regressions bring profit-reliability much closer to hand…much more often.

Your Mileage May Vary

As your Sevens-to-Rolls Ratio (SRR) improves, the appearance-rate for the 7 declines. 

       The less the 7 shows up within a given sampling-group, the more other non-7 outcomes will take its place.  Therefore, a reduced 7’s appearance-rate means an increased winning-bet rate.

 

       To give your dice-shooting skills the best opportunity to prosper, you should determine exactly which numbers are taking the place of those diminishing 7’s. 

 

       In the samples that I’ve used in this series, I’ve evenly spread those replacement numbers across the entire outcome spectrum.  As such, your expectancy-chart may look somewhat different than the generic ones here.

 

As we’ve discussed before:

       If we know how long our hand generally stays in positive-expectation territory; then we can easily determine a way in which to use an initially large “starting-level” wager, and then calculate when the ideal time to regress it down to a still productive post-regression value is.

 

       As I showed above; even though Kelly-style flat-betting can produce a net-profit, the use of ISR’s substantially increase our same-skill profit-rate.

 

       The closer your SRR is to random; the faster you will have to regress your bets in order to have the greatest chance of making a profit during any given hand.  Conversely, the higher your SRR is, the more time (as measured by the number of point-cycle rolls) you will have in which to fully exploit your dice-influencing skills.

 

Therefore, the expected roll-duration hit-rate chart for the 6 and 8 Place-bet that we just looked at, correctly factors in the modified sevens-appearance-rate for any given SRR; which in turn produces the optimal regression trigger-point for each skill-level. 

       Once we know where that positive-to-negative transition point is, we can use it as the trigger-point in which to optimally regress our large initial-wager down to a lower level.  In doing so, we concurrently lock-in a net-profit while still maintaining active but lower-value bets on the layout in the event that our hand-duration does exceed and survive that positive-to-negative transition point, as it often will. 

 

A Practical Comparison

Let’s look at how this works when we compare flat-betting $30 each on the 6 and 8 versus initially betting $30 each on the 6 and 8 then steeply regressing it to $6 each on the 6 and 8 at the appropriate trigger-point. 

 

Flat-betting

$30 Place-bet each on 6 and 8

Return-on-Investment

 

 

Random SRR 6

SRR 7

SRR 8

SRR 9

6’s and 8’s-to-7’s Ratio

1.67:1

2:1

2.33:1

2.67:1

Flat Bet

each

$30.00

$30.00

$30.00

$30.00

Per-hit

Payout

$35.00

$35.00

$35.00

$35.00

Expected

Total Payout

$58.45

$70.00

$81.55

$93.45

Remaining Exposed Wagers

$60.00

$60.00

$60.00

$60.00

Net-Profit

-$1.55

$10.00

$21.55

$33.45

Return-on-Investment

-2.58%

16.66%

35.92%

55.75%

 

 

 

 

 

 

I deleted any further references to SRR-6 random betting in the following charts simply because it always remains in negative-expectation territory.

Using an Initial Steep Regression (ISR) permits even the most modestly skilled dice-influencer to achieve a net-profit much sooner and on a much more consistent basis than if he is making comparably spread flat Kelly-style bets.

The following ISR chart utilizes the optimum SRR-based trigger-point at which the Large-bet-to-Small-bet regression takes place. 

Initial Steep Regression

$30 each Place-bet on 6 and 8

Regressed at Optimal Trigger-Point to

$6 each Place-bet on 6 and 8

Return-on-Investment

 

 

SRR 7

SRR 8

SRR 9

6’s and 8’s-to-7’s Ratio

2:1

2.33:1

2.67:1

Initial

Large Bet

$30.00

each

$30.00

each

$30.00

each

Subsequent Small Bet

$6.00

each

$6.00

each

$6.00

each

1st Hit

$35.00

$35.00

$35.00

2nd Hit

$35.00

$35.00

$35.00

3rd Hit

Post-Regression $5.53

Weighted payout

$35.00

$35.00

4th Hit

-

Post-Regression $5.63

Weighted payout

$35.00

5th Hit

-

-

Post-Regression $5.71

Weighted payout

Total Expected Payout

$75.53

$110.63

$145.71

Remaining Exposed Wagers

$12.00

$12.00

$12.00

Net-Profit per-Hand

$63.53

$98.63

$133.71

Return-on- Investment

105.88%

164.38%

222.85%

 

 

 

 

 

Here’s a summarized comparison between flat-betting the 6 and 8 Place-bet versus the use of an Initial Steep Regression:

$30 each Place-bet on 6 and 8 Flat-bet

vs.

$30 each Place-bet on 6 and 8

Regressed to $6 each Place-bet on 6 and 8

 

SRR 7

SRR 8

SRR 9

$30 each

Flat-bet

Net-Profit/Hand

$10.00

$21.55

$33.45

$30 each Regressed

to $6 each Profit/Hand

$63.53

$98.63

$133.71

$-Difference

$53.53

$77.08

$100.26

Increased

Return-on-Investment

84.26%

78.15%

74.98%

I don’t know about you, but most players want to get the most bang for their buck. 

       A $10 per-hand profit for a SRR-7 flat-bettor is good, but a $63 per-hand profit for the same guy using a Steep Regression is a whole lot better. 

 

       In both cases, each scenario starts off with the same bet, $30 each on the 6 and 8.  The big difference comes when the smart player regresses his initially large wager down to a more reasonable one when it is approaching negative-expectation territory…thereby locking up a profit no matter what happens during the rest of the hand.

 

Now the argument could be made that the guy who never regresses his bets will make more money in the event that this hand turns out to be THE hand of the century.  That assumption of course is correct for long hands; however, we are talking about your average-hand and your average-session shooting where your skills should be producing a profit for you…but they currently aren’t.   

No one in their right mind is saying that you can’t press-up your regressed bets with ongoing winning-wager revenue if your longer-duration hand does continue to produce money; however the fact remains that MOST of your barely-better-than-random hands don’t get to that point; yet they can STILL be net-profitable if you bet them properly. 

Anyone can make money off of 20, 30, 50 and 70-roll hands, but it takes an acute sense of skills-awareness and betting-efficiency to take advantage of the short and mediocre ones too.

SRR-based ISR’s help you accomplish that.

Using Different Steepness Ratios

       The steeper the regression-ratio is; the higher, earlier and more often a net-profit will be secured. 

 

       The shallower the regression-ratio is; the less frequent and lower your net-profit will be.

 

Take a look at how various steepness ratios affect your profitability.

Place-bet on 6 and 8

Profit Projections using various Steepness Ratios

SRR-7

Ratio

2:1

3:1

4:1

5:1

10:1

Initial

Large Bet

$12.00

each

$18.00

each

$24.00

each

$30.00

each 

$60.00

each

Subsequent Small Bet

$6.00

each

$6.00

each

$6.00

each

$6.00

each

$6.00

each

1st Hit

$14.00

$21.00

$28.00

$35.00

$70.00

2nd Hit

$14.00

$21.00

$28.00

$35.00

$70.00

3rd Hit

Post-Regression

$5.53

Weighted payout

Post-Regression

$5.53

Weighted payout

Post-Regression

$5.53

Weighted payout

Post-Regression

$5.53

Weighted payout

Post-Regression

$5.53

Weighted payout

Total Expected Payout

$33.53

$47.53

$61.53

 

$75.53

 

$145.53

Remaining Exposed Wagers

$12.00

$12.00

$12.00

 

$12.00

 

$12.00

Net-Profit

$21.53

$35.53

$49.53

$63.53

$133.53

Return-on- Investment

89.71%

98.69%

103.2%

105.9%

111.3%

As your SRR-rate improves, so does your return on investment:

 

Place-bet on 6 and 8

Profit Projections using various Steepness Ratios

SRR-8

 

Ratio

2:1

3:1

4:1

5:1

10:1

Initial

Large Bet

$12.00

each

$18.00

each

$24.00

each

$30.00

each 

$60.00

each

Subsequent Small Bet

$6.00

each

$6.00

each

$6.00

each

$6.00

each

$6.00

each

1st Hit

$14.00

$21.00

$28.00

$35.00

$70.00

2nd Hit

$14.00

$21.00

$28.00

$35.00

$70.00

3rd Hit

$14.00

$21.00

$28.00

$35.00

$70.00

4th Hit

Post-Regression

$5.63

Weighted payout

Post-Regression

$5.63

Weighted payout

Post-Regression

$5.63

Weighted payout

Post-Regression

$5.63

Weighted payout

Post-Regression

$5.63

Weighted payout

Total Expected Payout

$47.63

$68.63

$89.63

 

$110.63

 

$215.63

Remaining Exposed Wagers

$12.00

$12.00

$12.00

 

$12.00

 

$12.00

Net-Profit

$35.63

$56.63

$77.63

$98.83

$203.63

Return-on- Investment

148.5%

157.3%

161.7%

164.4%

169.7%

 

 

 

 

 

 

 

Again, as your SRR improves over random, the higher your rate of return will be.  Obviously, the better funded your session bankroll is, the better you’ll be able to take full advantage of your current dice-influencing skills.

It is important to note that each SRR-level forces a different bet-reduction trigger-point.  While the SRR-7 shooter has to immediately regress his large initial bet after just two hits; the SRR-8 dice-influencer can reasonably keep them up at their initial large size for the first three point-cycle rolls before needing to steeply regress them.  In the case of a SRR-9 shooter using the 6 and 8 Place-bet that we’ve been discussing today, he’ll generally get the benefit of four pre-regression hits before optimally reducing his bet-exposure.

Place-bet on 6 and 8

Profit Projections using various Steepness Ratios

SRR-9

 

Ratio

2:1

3:1

4:1

5:1

10:1

Initial

Large Bet

$12.00

each

$18.00

each

$24.00

each

$30.00

each 

$60.00

each

Subsequent Small Bet

$6.00

each

$6.00

each

$6.00

each

$6.00

each

$6.00

each

1st Hit

$14.00

$21.00

$28.00

$35.00

$70.00

2nd Hit

$14.00

$21.00

$28.00

$35.00

$70.00

3rd Hit

$14.00

$21.00

$28.00

$35.00

$70.00

4th Hit

$14.00

$21.00

$28.00

$35.00

$70.00

5th Hit

Post-Regression

$5.71

Weighted payout

Post-Regression

$5.71

Weighted payout

Post-Regression

$5.71

Weighted payout

Post-Regression

$5.71

Weighted payout

Post-Regression

$5.71

Weighted payout

Total Expected Payout

$61.71

$89.71

$117.71

$145.71

 $285.71

Remaining Exposed Wagers

$12.00

$12.00

$12.00

 $12.00

 $12.00

Net-Profit

$49.71

$77.71

$105.71

$133.71

$273.71

Return-on- Investment

207.1%

215.9%

220.2%

 222.9%

 228.1%

 

 

 

 

 

 

 

As I mentioned above; the fewer advantaged bets that you spread your money over, the fewer winning hits you will need in order to produce a net-profit.

By limiting your wagers to just two Place-bets like the 6 and 8; the required number of winning hits to break through to net-profit is minimal.   As we’ll see in future chapters of this series, this rule-of-thumb will hold us in good stead when we are converting our SRR-based skill into a 90% winning-session rate that produces a steadily reliable 30% return-on-investment per session.

You do the math.  If that kind of profit-consistency interests you; I hope you’ll join me as we explore how regression-betting truly does avoid bankroll-depression.   Until then,

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

Sincerely,

The Mad Professor


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