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Regression Avoids Depression
Part XI

The use of Initial Steep Regressions control and regulate the amount of negative volatility that your bankroll will have to endure during any given session. 

       Two of the primary aspects of that control come from the roll-duration decay-rate and the bet-survival rate that your currently valid in-casino SRR-rate produces for each bet.

       These fundamental volatility-range determinants are especially useful for global (multi-number, multi-decision) types of wagers.

       Your Expected-value (EV) on any given bet is affected by the positive magnitude and range of your ability to influence the dice. That is, the more influence you have over the dice, the stronger your EV will be on certain bets, and therefore your session bankroll will endure less whipsaw volatility because of it.

       Each dice-set and its resultant Sevens-to-Rolls-Ratio (SRR) has its own deviation range over which some bets fall into positive territory and some fall onto the negative side of it. 

       Each dice-set produces its own array of high-EV, low-EV, and negative-EV wagers.  Wagering on a few high-EV bets will almost always be more profitable than spreading the same amount of money across a wider range of lower-EV wagers.

Putting the 5 and 9 Place-bet Under a Microscope

With the use of certain dice-sets, the 5 and 9 often turn out to be the most dominant Signature-Numbers that you produce.  It is heartening to see an increasing amount of skilled players take advantage of the Signature Numbers that their current dice-influencing skills are producing instead of betting on outcomes that they wish they could produce.

       In random-expectancy, we’ll see four 5’s and four 9’s against six appearances of the 7, which equates to eight appearances of the 5 and 9 for every six appearances for the 7.

 

       That 8:6 ratio means a random-roller can expect a 5’s-and-9’s-to-7’s appearance-rate of 1.33:1, and even though a winning Place-bet pays 7:5, it is still not enough to overcome the house-edge.  As a result, random-rollers stay on the negative-side of the expectation curve with this bet, while dice-influencers cross over into positive territory on a regular basis.

 

Why ISR’s Work So Well With Simple 5 & 9 Place-bets

In a random outcome game, the 5 and 9 constitutes 22.22% of all possible outcomes. 

There are:

       Four ways to make a 5.

 

       Four ways to make an 9.

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

 

 

 

 

 

5’s & 9’s-to-Sevens Ratio

 

Random SRR 6

SRR 7

SRR 8

SRR 9

5’s and 9’s to Total Outcomes

8-out-of-36

8.23

8.40

8.54-out-

of-36

Per-Roll

Probability

22.22%

22.86%

23.33%

23.71%

5’s and 9’s-

to-7’s Ratio

1.33:1

1.6:1

1.87:1

2.14:1

 

 

 

 

 

 

 

 

 

Although the sheer number of 5’s and 9’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 5’s and 9’s than a random-roller does (8.5 versus 8.0).  However, since his dice-influencing produces a lower overall sevens-appearance-rate, his actual 5’s-and-9’s-to-7’s ratio improves by more than 62% (from 1.33 to 2.14).

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

Anatomy Of a 5 & 9 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.

5 & 9 Flat-bet

Repayment Rate

 

5 & 9 Hits

Total Investment

Single

Payout

Return on Investment

Profit

0

$10

$0

0%

(-$10.00)

1

-

$7.00

70%

(-$3.00)

2

-

$7.00

140%

$4.00

 

 

 

 

 

 

Place-betting the 5 and 9 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 5 or 9 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:

 

$5  5 & 9 Place-bet
Expected Flat-bet Win-Rate

 

Expected Profit/Roll

Random SRR 6

SRR 7

SRR 8

SRR 9

5’s & 9’s-to-7’s Ratio

1.33:1

1.6:1

1.87:1

2.14:1

1

$7.00

$7.00

$7.00

$7.00

2

$2.31

Weighted payout

$4.20

Weighted payout

$6.09

Weighted payout

$7.00

3

-

-

-

$0.98

Weighted payout

Total Expected Payout

$9.31

$11.20

$13.09

$14.98

Remaining Wager

$10.00

$10.00

$10.00

$10.00

Net-Profit

-$0.69

$1.20

$3.09

$4.98

Return-on-Investment

-6.9%

12%

31%

49%

 

 

 

 

 

 

How this works is that an SRR-7 flat-bet shooter will sometimes meet or exceed the two-winning-hits-required threshold…but sometimes he won’t.  Over all though, he’ll nonetheless be able to eke out a meager profit since his player-edge against this bet is still assertive enough to overcome the house-edge.  Obviously though, he’ll have to be extremely careful in protecting his freshly made profit by avoiding any bets that have a lower EV (expected value) than the ones he is making on the 5 and 9.  

As good as advantage-play 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 over any given wager has to fight. 

       When we compare your bet-survival-rate 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 5 and 9 Place-bet point-cycle:

 

5 & 9 Place-Bet Survival-Rate

5 & 9

Hit-rate

Random SRR 6

SRR 7

SRR 8

SRR 9

1

22.22%

22.86%

23.33%

23.71%

2

18.52%

19.59%

20.41%

21.08%

3

15.43%

16.79%

17.86%

18.73%

4

12.86%

14.39%

15.63%

16.65%

5

10.71%

12.34%

13.68%

14.80%

6

8.93%

10.57%

11.97%

13.16%

7

7.44%

9.06%

10.47%

11.69%

8

6.20%

7.77%

9.16%

10.39%

9

5.17%

6.66%

8.02%

9.24%

10

4.30%

5.71%

7.01%

8.21%

11

3.59%

4.89%

6.14%

7.30%

12

2.99%

4.19%

5.37%

6.49%

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.

A Practical Comparison

Let’s look at how ISR’s work when we compare flat-betting $25 each on the 5 and 9 versus initially betting $25 each on the 5 and 9 then steeply regressing it to $5 each on the 5 and 9 at the appropriate trigger-point. 

 

Flat-betting

$25 Place-bet each on 5 and 9

Return-on-Investment

 

 

Random SRR 6

SRR 7

SRR 8

SRR 9

5’s and 9’s-to-7’s Ratio

1.33:1

1.6:1

1.87:1

2.14:1

Flat Bet

$25.00

$25.00

$25.00

$25.00

Per-hit

Payout

$35.00

$35.00

$35.00

$35.00

Expected

Total Payout

$46.55

$56.00

$65.45

$74.90

Remaining Exposed Wagers

 

$50.00

 

$50.00

 

$50.00

 

$50.00

Net-Profit

-$3.45

$6.00

$15.45

$24.90

Return-on-Investment

-6.9%

12%

31%

49%

 

 

 

 

 

 

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

$25 each Place-bet on 5 and 9

Regressed at Optimal Trigger-Point to

$5 each Place-bet on 5 and 9

Return-on-Investment

 

 

SRR 7

SRR 8

SRR 9

5’s and 9’s-to-7’s Ratio

1.6:1

1.87:1

2.14:1

Initial

Large Bet

$25.00

each

$25.00

each

$25.00

each

Subsequent Small Bet

$5.00

each

$5.00

each

$5.00

each

1st Hit

$35.00

$35.00

$35.00

2nd Hit

Post-Regression $6.40

Weighted payout

$35.00

$35.00

3rd Hit

-

$35.00

$35.00

4th Hit

-

Post-Regression $5.40

Weighted payout

$35.00

5th Hit

-

-

Post-Regression

$6.30

Weighted payout

Total Expected Payout

$41.40

$110.40

$146.30

Remaining Exposed Wagers

$10.00

$10.00

$10.00

Net-Profit per-Hand

$31.40

$100.40

$136.30

Return-on- Investment

62.8%

200.8%

272.6%

 

 

 

 

 

Here’s a summarized comparison between flat-betting the 5 and 9 Place-bet versus the use of an Initial Steep Regression:

 

$25 each Place-bet on 5 and 9 Flat-bet

vs.

$25 each Place-bet on 5 and 9

Regressed to $5 each Place-bet on 5 and 9

 

SRR 7

SRR 8

SRR 9

$25 each

Flat-bet

Net-Profit/Hand

$6.00

$15.45

$24.90

$25 each Regressed

to $5 each Profit/Hand

$31.40

$100.40

$136.30

$-Difference

$25.40

$84.95

$111.40

Increased

Return-on-Investment

80.9%

84.6%

81.7%

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

       A $6 per-hand profit for a SRR-7 flat-bettor is fairly good, but a $31 per-hand profit for the same guy using a Steep Regression is a whole lot better.

 

       Likewise for the SRR-8 shooter; a $15 per-hand flat-bet profit is admirable, however a $100 per-hand profit for the ISR-user from EXACTLY the same skill-level is significantly better.

 

       In each scenario, both shooters start off with the same $25 bet on the 5 and 9.  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.

 

       The SRR-8 shooter has to ask himself if a $15 per-turn-with-the-dice profit is enough to sustain another lap around the table and whether it justifies his time and effort; or whether his interests are better served by deploying the exact same money in a more intelligent manner to produce an average of $100 profit every time the dice come around to him.

 

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 5 and 9

Profit Projections using various Steepness Ratios

SRR-7

Ratio

2:1

3:1

4:1

5:1

10:1

Initial

Large Bet

$10.00

each

$15.00

each

$20.00

each

$25.00

each 

$50.00

each

Subsequent Small Bet

$5.00

each

$5.00

each

$5.00

each

$5.00

each

$5.00

each

1st Hit

$14.00

$21.00

$28.00

$35.00

$70.00

2nd Hit

Post-Regression

$6.40

Weighted payout

Post-Regression

$6.40

Weighted payout

Post-Regression

$6.40

Weighted payout

Post-Regression

$6.40

Weighted payout

Post-Regression

$6.40

Weighted payout

Total Expected Payout

$20.40

$27.40

$34.40

$41.40

$76.40

Remaining Exposed Wagers

$10.00

$10.00

$10.00

$10.00

$10.00

Net-Profit

$10.40

$17.40

$24.40

$31.40

$66.40

Return-on- Investment

52%

58%

61%

63%

66%

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

Place-bet on 5 and 9

Profit Projections using various Steepness Ratios

SRR-8

 

Ratio

2:1

3:1

4:1

5:1

10:1

Initial

Large Bet

$10.00

each

$15.00

each

$20.00

each

$25.00

each 

$50.00

each

Subsequent Small Bet

$5.00

each

$5.00

each

$5.00

each

$5.00

each

$5.00

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

$5.40

Weighted payout

Post-Regression

$5.40

Weighted payout

Post-Regression

$5.40

Weighted payout

Post-Regression

$5.40

Weighted payout

Post-Regression

$5.40

Weighted payout

Total Expected Payout

$47.40

$68.40

$89.40

$110.40

$215.40

Remaining Exposed Wagers

$10.00

$10.00

$10.00

$10.00

$10.00

Net-Profit

$37.40

$58.40

$79.40

$100.40

$205.40

Return-on- Investment

187%

194.6%

198.5%

200.8%

205.4%

 

 

 

 

 

 

 

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 one hit with the 5 and 9 Place-bet; 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 5 and 9 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 5 and 9

Profit Projections using various Steepness Ratios

SRR-9

 

Ratio

2:1

3:1

4:1

5:1

10:1

Initial

Large Bet

$10.00

each

$15.00

each

$20.00

each

$25.00

each 

$50.00

each

Subsequent Small Bet

$5.00

each

$5.00

each

$5.00

each

$5.00

each

$5.00

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

$6.30

Weighted payout

Post-Regression

$6.30

Weighted payout

Post-Regression

$6.30

Weighted payout

Post-Regression

$6.30

Weighted payout

Post-Regression

$6.30

Weighted payout

Total Expected Payout

$62.30

$90.30

$118.30

$146.30

$286.30

Remaining Exposed Wagers

$10.00

$10.00

$10.00

$10.00

$10.00

Net-Profit

$52.30

$80.30

$108.30

$136.30

$276.30

Return-on- Investment

261.5%

267.6%

270.7%

272.6%

276.3%

 

 

 

 

 

 

 

 

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

Sincerely,

The Mad Professor


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