« Part 3: The Practice Rig | Main | Ask the Mad Professor - Part 7 »

Regression Avoids Depression Part 7

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.

  1. 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.
  2. 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.
  3. Though your dice set may change from C O cycle to Point cycle, your basic dice tossing dynamic does not.
  4. 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:

  1. 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.
  2. Four ways to make a 5, and it pays 7:5.
  3. Four ways to make a 9, and it pays 7:5.
  4. 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%
  1. 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.
  2. 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

  1. The steeper the regression ratio is; the higher, earlier and more often a Net Profit will be secured.
  2. 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

Do you have questions or comments about the articles and subjects discussed here at the Dice Institute? Sign up for our member's forum and share them with us!

About

This page contains a single entry from the blog posted on January 7, 2007 5:52 PM.

The previous post in this blog was Part 3: The Practice Rig.

The next post in this blog is Ask the Mad Professor - Part 7.

Many more can be found on the main index page or by looking through the archives.

Creative Commons License
This weblog is licensed under a Creative Commons License.
Powered by
Movable Type 3.34