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Regression Avoids Depression
Part VII

 It doesn't matter how well you CAN play.

It matters how well you DO play.

Your task as an advantage-player, is to figure out how good your own shooting actually is, and then match it with properly-sized exploitable wagers.

       The dice-set that you use and the indicative Foundation Frequencies that your toss-dynamic produces, is what yields your most recurrent outcomes…and your best, most predictable betting opportunities.

 

       Most dice-influencers use a different dice-set for the Come-Out portion of their hand than they use for their subsequent Point-cycle segment. 

 

       Though your dice-set may change from C-O cycle to Point-cycle, your basic dice-tossing dynamic does not. 

 

       As a result, the same Foundation Frequencies (primary-face hits, on-axis single-pitches, on-axis double-pitches, one dice off-axis, and both dice off-axis outcomes) that you produce with one dice-set will generally carry over to each and every other dice-set. 

 

The savvy Precision-Shooter not only recognizes how indicative his own Foundation Frequencies determine the Signature-Numbers that each dice-set produces; but in doing so, he often identifies here-before-unknown latent betting-opportunities. 

That brings us to a perennial wagering favorite among dice-influencers who use various permutations of the V-2 dice-set.

Outside-Bets

In a random outcome game, Outside wagers constitute 38.89% of all possible outcomes.  The Outside-bet covers the 4, 5, 9, and 10.

There are:

       Three ways to make a 4, and it pays 9:5, unless you buy it, in which case it pays out at 2:1, less the vigorish.

 

       Four ways to make a 5, and it pays 7:5.

 

       Four ways to make a 9, and it pays 7:5.

 

       Three ways to make a 10 and it pays 9:5, unless you buy it, in which case it pays out at 2:1, less the vigorish.

 

Therefore, Outside-numbers constitute 14-out-of-36 (38.89%) of all randomly-expected outcomes, and their average weighted-payout is $7.86 per hit.

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

Probability

16.67%

14.29%

12.5%

11.11%

7’s-per-36 rolls

6

5.14

4.5

4

 

 

 

 

 

Outside to Sevens Ratio

 

 

Random SRR 6

SRR 7

SRR 8

SRR 9

Outside-Numbers to Total Outcomes

14-out-of-36

14.40

14.70

14.93

Per-Roll

Probability

38.89%

40.00%

40.83%

41.47%

Outside -Numbers-to-7’s Ratio

2.3:1

2.8:1

3.3:1

3.7:1

 

 

 

 

 

 

 

 

 

 

Anatomy Of An Outside-Wager

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-bets.

$20-Outside 

Flat-bet

Return-on-Investment

 

Outside-Number Hits

Total Investment

Weighted

Payout

Return on Investment

Profit

0

$20

$0

0%

(-$20.00)

1

-

$7.86

39.30%

(-$12.14)

2

-

$7.86

78.60%

(-$4.28)

3

-

$7.86

117.90%

$3.58

 

 

 

 

 

 

A random-roller still has a greater chance of 7’ing-Out than he does of hitting enough Outside-numbers for this low hit-requirement bet to pay for itself on a consistent basis.  That is the nature of ANY randomly-based bets that you make.

However, in the hands of a modestly skilled dice-influencer, the Outside -bet can be a steady profit contributor to your bankroll.  Take a look:

Expected Flat-bet Win-Rate

$20-Outside

 

Expected Profit/Roll

Random SRR 6

SRR 7

SRR 8

SRR 9

Outside-Numbers-to-7’s Ratio

2.3:1

2.8:1

3.3:1

3.7:1

1

$7.86

$7.86

$7.86

$7.86

2

$7.86

$7.86

$7.86

$7.86

3

$2.36

Weighted payout

$6.29

Weighted payout

$7.86

$7.86

4

-

-

$2.36

Weighted payout

$5.50

Weighted payout

Total Expected Payout

$18.08

$22.01

$25.94

$29.08

Remaining Wager

$20.00

$20.00

$20.00

$20.00

Net-Profit

-$1.92

$2.01

$5.94

$9.08

Return-on-Investment

-9.6%

10.1%

27.7%

45.4%

 

 

 

 

 

 

 

 

As with Inside-Numbers and All-Across wagers; your Sevens-to-Rolls Ratio largely determines the average roll-duration of your Outside-bet hand.  Equally, your SRR also determines the decay-rate of your validated edge against any given bet and therefore establishes the optimal time to regress your initially large bet into a smaller, lower-value one.

Outside-Bet Survival-Rate

Outside-Number

Hit-rate

Random SRR 6

SRR 7

SRR 8

SRR 9

1

38.89%

40.00%

40.83%

41.47%

2

32.41%

34.28%

35.73%

36.86%

3

27.00%

29.38%

31.26%

32.77%

4

22.50%

25.19%

27.35%

29.13%

5

18.75%

21.59%

23.93%

25.89%

6

15.62%

18.50%

20.94%

23.01%

7

13.02%

15.86%

18.32%

20.46%

8

10.85%

13.59%

16.03%

18.18%

9

9.04%

11.65%

14.03%

16.16%

10

7.53%

9.98%

12.28%

14.37%

11

6.28%

8.56%

10.74%

12.77%

12

5.23%

7.34%

9.40%

11.35%

As usual:

       If we know how long our hand generally stays in positive-expectation territory for the Outside-Number bets we are making; then we can easily determine the ideal time to regress them from their initially high starting-value.

 

       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; and obviously 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 for the Outside-number wager has to factor in the modified sevens-appearance-rate for any given SRR; which in turn then 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 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 $100-Outside versus the use of an initial $100-Outside wager that is steeply regressed to $20-Outside at the appropriate trigger-point.

Flat-betting

$100-Outside

Return-on-Investment

 

 

Random SRR 6

SRR 7

SRR 8

SRR 9

Outside-Numbers-to-7’s Ratio

2.3:1

2.8:1

3.3:1

3.7:1

Initial Large Bet

$100-Outside

$100-Outside

$100-Outside

$100-Outside

Single-hit Weighted-Payout

$36.71

$36.71

$36.71

$36.71

Expected

Total Payout

$84.43

$102.79

$121.14

$135.83

Remaining Exposed Wagers

$100

$100

$100

$100

Net-Profit

-$15.57

$2.79

$21.14

$35.83

Return-on-Investment

-15.6%

2.79%

21.14%

35.83%

 

 

 

 

 

 

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

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

Initial Steep Regression

$100-Outside

Regressed at Optimal Trigger-Point to

$20-Outside

Return-on-Investment

 

 

SRR 7

SRR 8

SRR 9

Outside-Numbers-to-7’s Ratio

2.8:1

3.3:1

3.7:1

Initial
Large Bet

$100-Outside

$100-Outside

$100-Outside

Subsequent Small Bet

$20-Outside

$20-Outside

$20-Outside

1st Hit

$36.71

$36.71

$36.71

2nd Hit

Post-Regression

$7.67

Weighted payout

$36.71

$36.71

3rd Hit

-

Post-Regression

$7.82

Weighted payout

$36.71

4th Hit

-

-

$36.71

5th Hit

-

-

Post-Regression

$7.69

Weighted payout

Total Expected Payout

$44.38

$81.24

$154.53

Remaining Exposed Wagers

$20.00

$20.00

$20.00

Net-Profit per-Hand

$24.38

$61.24

$134.53

Return-on- Investment

24.38%

61.24%

134.53%

 

 

 

 

 

Here’s a comparison between flat-betting the Outside-bet versus the use of an Initial Steep Regression:

$100-Outside Flat-bet

vs.

$100-Outside Regressed to $20-Outside

 

SRR 7

SRR 8

SRR 9

$100-Outside Flat-bet

Net-Profit/Hand

$2.79

$21.14

$35.83

$100-Outside Regressed

to $20-Outside

Net-Profit/Hand

$24.38

$61.24

$134.53

$-Difference

$21.59

$40.10

$98.70

Increased

Return-on-Investment

87.80%

65.48%

73.37%

 

       By using a Steep Regression to lock in a quick profit while our wagers are still in positive-expectation territory, and still permitting a much-reduced set of post-regression wagers to stay in place once our roll-duration surpasses that point; we get to benefit from the best of both worlds.

 

       By using an Initial Steep Regression (ISR), we derive profit from the fattest positive-expectation portion of our point-cycle, while our newly reduced lower-value bets remain in action when our hand exceeds its expected average duration, as it often will.

 

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 our net-profit will be.

 

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

Outside-bet Regression

Various Steepness Ratios

SRR-7

 

Ratio

2:1

3:1

4:1

5:1

10:1

Initial

Large Bet

$40-Outside

$60-Outside

$80-Outside

$100-Outside

$200-Outside

Subsequent Small Bet

$20-Outside

$20-Outside

$20-Outside

$20-Outside

$20-Outside

1st Hit

Weighted Value

$15.72

Weighted Value

$23.58

Weighted Value

$32.71

Weighted Value

$36.71

Weighted Value

$73.42

2nd Hit

Post-Regression

$7.67

Weighted payout

Post-Regression

$7.67 

Weighted payout

Post-Regression

$7.67

Weighted payout

Post-Regression

$7.67

Weighted payout

Post-Regression

$7.67

Weighted payout

Total Expected Payout

$23.39

$31.25

$40.38

 $44.38

 $81.09

Remaining Exposed Wagers

$20.00

$20.00

$20.00

$20.00

$20.00

Net-Profit

$3.39

$11.25

$20.38

$24.38

$61.09

Return-on- Investment

8.48%

18.75%

25.48%

24.38%

30.55%

 

 

 

 

 

 

 

As your SRR-rate improves, so does your return on investment, even when you are using a shallow 2:1 regression ratio.

Outside-bet Regression

Various Steepness Ratios

SRR-8

 

Ratio

2:1

3:1

4:1

5:1

10:1

Initial

Large Bet

$40-Outside

$60-Outside

$80-Outside

$100-Outside

$200-Outside

Subsequent Small Bet

$20-Outside

$20-Outside

$20-Outside

$20-Outside

$20-Outside

1st Hit

Weighted Value

$15.72

Weighted Value

$23.58

Weighted Value

$32.71

Weighted Value

$36.71

Weighted Value

$73.42

2nd Hit

$15.72

$23.58

$32.71

$36.71

$73.42

3rd Hit

Post-Regression $7.82

Weighted payout

Post-Regression $7.82

Weighted payout

Post-Regression $7.82

Weighted payout

Post-Regression $7.82

Weighted payout

Post-Regression
$7.82

Weighted payout

Total Expected Payout

$39.26

$54.98

$73.24

$81.24

$154.66

Remaining Exposed Wagers

$20.00

$20.00

$20.00

 $20.00

$20.00

Net-Profit

$19.26

$34.98

$53.24

$61.24

$134.66

Return-on- Investment

48.15%

58.30%

66.55%

61.24%

67.33%

 

 

 

 

 

 

 

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 can take full advantage of your 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; the SRR-8 dice-influencer can reasonably keep them up at their initial large size for the first three point-cycle rolls before having to steeply regress them.

Outside-bet Regression

Various Steepness Ratios

SRR-9

 

Ratio

2:1

3:1

4:1

5:1

10:1

Initial

Large Bet

$40-Outside

$60-Outside

$80-Outside


$100-Outside


$200-Outside

Subsequent Small Bet

$20-Outside

$20-Outside

$20-Outside

$20-Outside

$20-Outside

1st Hit

Weighted Value

$15.72

Weighted Value

$23.58

Weighted Value

$32.71

Weighted Value

$36.71

Weighted Value

$73.42

2nd Hit

$15.72

$23.58

$32.71

$36.71

$73.42

3rd Hit

$15.72

$23.58

$32.71

$36.71

$73.42

4th Hit

$15.72

$23.58

$32.71

$36.71

$73.42

5th Hit

Post-Regression $7.69

Weighted payout

Post-Regression
$7.69

Weighted payout

Post-Regression $7.69

Weighted payout

Post-Regression
$7.69

Weighted payout

Post-Regression
$7.69

Weighted payout

Total Expected Payout

$70.57

$102.01

$138.53

 $154.53

 $301.37

Remaining Exposed Wagers

$20.00

$20.00

$20.00

 $20.00

 $20.00

Net-Profit

$50.57

$82.01

$118.53

$134.53

$281.37

Return-on- Investment

126.4%

136.7%

148.2%

134.5%

140.7%

 

 

 

 

 

 

 

I hope you’ll join me for Part Eight, when we take a fresh and new look at a venerable old bet.  Until then,

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

Sincerely,

The Mad Professor


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