« Part 2: Learning the theory of dice influencing | Main | Ask the Mad Professor - Part 8 »

Regression Avoids Depression - Part 8

When compared to flat-betting, the use of an Initial Steep Regression (ISR) provides a superior return-on-investment that is just too darn good to ignore.

The Proof Is In The PROFIT

In case you haven't figured it out by now, the term "flat-bet" can just as easily be replaced with "Kelly Criterion bet".  The "Kelly" holds that you wager in direct proportion to your player-edge over a given bet, neither increasing nor decreasing it during any given hand. As such, Kelly-based flat-bets derive their net-profit from the average of short-hand losers and long-hand winners that your personal SRR-rate produces.  Unfortunately, despite its validity, you'll likely experience all kinds of wild bankroll volatility swings when using Kelly-style betting. Frankly, I am not fundamentally against the use of Kelly wagering; it's just that most players cannot endure the whipsaw ups and downs of the win-some, lose-a-lot results, and as such, their own actual shooting ability is negatively affected by the psychological toll that that kind of nerve-wracking unpredictability brings to their game.

Initial Steep Regressions take some of that volatility out of the game by offering a higher rate of predictability as well as providing an increased level of retained profit. At the end of the day, however, you have to make the decision as to how steadily and how profitably you want to take advantage of your own dice-influencing skills. The choice is entirely up to you.

Take a look at how Initial Steep Regressions stack up against flat Kelly-style wagering:

$110-Inside Flat-bet vs. $110-Inside Regressed to $22-Inside
SRR 7 SRR 8 SRR 9
$110-Inside Flat-bet Net-Profit/Hand $16.00 $33.50 $56.25
$110-Inside Regressed to $22-Inside Net-Profit/Hand $19.92 $89.69 $124.86
$-Difference $3.92 $56.19 $68.61
Increased Return-on-Investment 3.56% 51.08% 62.67%
$160-Across Flat-bet vs. $160-Across Regressed to $32-Across
SRR 7 SRR 8 SRR 9
$160-AcrossFlat-bet Net-Profit/Hand $24.80 $55.60 $86.40
$160-AcrossRegressed to $32-Across Net-Profit/Hand $52.34 $90.52 $129.27
$-Difference $27.54 $34.92 $42.87
Increased Return-on-Investment 50.68% 38.57% 33.16%
$100-Outside Flat-bet vs. $100-Outside Regressed to $20-Outside
SRR 7 SRR 8 SRR 9
$100-OutsideFlat-bet Net-Profit/Hand $2.79 $21.14 $35.83
$100-OutsideRegressed 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%

While most gamblers are trying to figure out ways to make money off of random-rollers, smart players are taking some or all of that needlessly imperiled negative-expectation money, and deploying it on positive EV (expected-value) ISR wagers where they not only have a positive-expectation of profit; but where they have a superior expected rate-of-return over flat Kelly-based wagering too.

Some people like to gamble, and some people like to win.

In most cases, the difference comes down to how you specifically wager your money.

As a modestly skilled dice-influencer, Steep Regressions offer a tangible way to turn some of the casinos money into YOUR money, instead of the other way around; and when it comes right down to it, that is what advantage-play is all about.

Even-Number Bets

In a random outcome game, Even-number wagers constitute 44.44% of all possible outcomes. The Even-Number bet covers the 4, 6, 8, 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. Five ways to make a 6, and it pays 7:6.
  3. Five ways to make an 8, and it pays 7:6.
  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, the Even-Number wager constitutes 16-out-of-36 (44.44%) of all randomly-expected outcomes, and their average weighted-payout is $7.75 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
Even-Numbers to Sevens Ratio
Random SRR 6 SRR 7 SRR 8 SRR 9
Even-Numbers to Total Outcomes 16-out-of-36 16.46 16.80 17.07
Per-Roll Probability 44.44% 45.72% 46.67% 47.42%
Even -Numbers- to-7's Ratio 2.67:1 3.20:1 3.73:1 4.27:1

Anatomy Of An Even-Number 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 Kelly-style bets.

Even-Number Flat-bet Repayment Rate
Even-Number Hits Total Investment Weighted Payout Return on Investment Profit
0 $22 $0 0% (-$22.00)
1 - $7.75 35.23% (-$14.25)
2 - $7.75 70.45% (-$6.50)
3 - $7.75 105.68% $1.25

As with any other bet, a random-roller still has a greater chance of 7'ing-Out than he does of hitting enough Even-number bets for it to pay for itself on a consistent basis. That is the nature of ANY randomly-based bets that you make. Again, if you are chasing random-rollers and trying to make a steady profit off of them, then your money would be better deployed on your very own validated advantage-play wagers.

As a flat-betting advantage-player, it takes three winning same-bet hits before this $22 Even-Number wager breaks into profitability. Fortunately, in the hands of a modestly skilled dice-influencer, the Even-number bet can be a steady profit contributor to your bankroll, even if you do decide to strictly adhere to flat-bets with it. Take a look:

Expected Flat-bet Win-Rate $22 Even-Number bet
Expected Profit/Roll Random SRR 6 SRR 7 SRR 8 SRR 9
Even-Numbers-to-7's Ratio 2.67:1 3.20:1 3.73:1 4.27:1
1 $7.75 $7.75 $7.75 $7.75
2 $7.75 $7.75 $7.75 $7.75
3 $5.19 Weighted payout $7.75 $7.75 $7.75
4 - $1.55 Weighted payout $5.66 Weighted payout $7.75
- - - $2.09 Weighted payout
Total Expected Payout $20.69 $24.80 $28.91 $33.09
Remaining Wager $22.00 $22.00 $22.00 $22.00
Net-Profit -$1.31 $2.80 $6.91 $11.09
Return-on-Investment -5.94% 12.73% 41.41% 50.41%

As with Inside-Numbers, All-Across and Outside-wagers; your Sevens-to-Rolls Ratio largely determines the average roll-duration of your Even-number bet. 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.

Even-Number Bet Survival-Rate
Even-Number Hit-rate Random SRR 6 SRR 7 SRR 8 SRR 9
1 44.44% 45.72% 46.67% 47.42%
2 37.03% 39.19% 40.84% 42.15%
3 30.86% 33.59% 35.71% 37.47%
4 25.71% 28.79% 31.27% 33.31%
5 21.43% 24.67% 27.36% 29.61%
6 17.85% 21.15% 23.94% 26.32%
7 14.88% 18.13% 20.95% 23.39%
8 12.40% 15.53% 18.33% 20.79%
9 10.33% 13.32% 16.04% 18.43%
10 8.61% 11.41% 14.03% 16.43%
11 7.17% 9.78% 12.28% 14.60%
12 5.98% 8.38% 10.74% 12.98%

As usual:

  1. If we know how long our hand generally stays in positive-expectation territory for the Even-Number bets we are making; then we can easily determine the ideal time to regress them from their initially high starting-value.
  2. Even though advantage-play flat-betting can produce a net-profit for us, the use of ISR's substantially increase our same-skill profit-rate.
  3. 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 Even-number wager correctly factors in the modified sevens-appearance-rate for any given SRR; which in turn then produces the optimal regression trigger-point for each skill-level.

  1. 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.
  2. Regression-betting does not mean that we remove our bets once they have paid for themselves; rather, it means that we reduce the initial large-bet into a still-active small-bet while concurrently locking in a profit at the optimal trigger-point. Not only will more of our short hands produce a tangible profit, but the long ones will continue to produce revenue too.
  3. We produce many more short hands than we produce long ones. Why not capitalize on it instead of fighting it? Why not use most of our short hands to produce a profit instead of hoping and praying that each and every hand will be long enough to produce sufficient multiple Kelly-based flat-bet wins to produce an overall profit?
  4. The more profit our bankroll accumulates, the more adaptable and aggressive our wagering can become.  ISR'slet us get there sooner and with much less volatility.
  5. The Kelly Criterion can accurately tell us how much of our total bankroll we should be wagering against a given player-advantage bet. I have no problem with that at all. In fact I use a partial-Kelly specifically for that bet-sizing purpose as well as using it to determine my total bet-exposure value.
  6. However, Steep Regressions take much of the volatility-sting out of erosive loses on global (multi-number, multi-hit-requirement) bets where multiple winning wagers are hit but unfortunately not enough of them are steadily produced to improve a players overall shooting confidence. This series is all about putting steady and predictable profit INTO your hands while concurrently boosting your overall Precision-Shooting confidence.
  7. Nobody is saying that your reduced-bets have to stay at their lower level if your hand surpasses your average roll-duration point, as it often will. Instead,ISR's let you make more money from a greater number of hands than flat-betting does, thereby giving you even MORE bet-flexibility once you get past your average roll-duration point.

A Practical Comparison

Let's look at how this works when we compare flat-betting $110 on the Even-Numbers versus the use of an initial $110 Even-Number wager that is steeply regressed to $22-Even at the appropriate trigger-point.

Flat-betting $110 Even-Numbers Return-on-Investment
Random SRR 6 SRR 7 SRR 8 SRR 9
Even-Numbers-to-7's Ratio 2.67:1 3.20:1 3.73:1 4.27:1
Flat Bet $110.00 $110.00 $110.00 $110.00
Single-hit Weighted-Payout $40.25 $40.25 $40.25 $40.25
Expected Total Payout $107.47 $128.80 $150.13 $171.87
Remaining Exposed Wagers $110.00 $110.00 $110.00 $110.00
Net-Profit -$2.53 $18.80 $40.13 $61.87
Return-on-Investment -2.3% 17.1% 36.5% 56.2%

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 $110 Even-Numbers Regressed at Optimal Trigger-Point to $22 Even-Numbers Return-on-Investment
SRR 7 SRR 8 SRR 9
Even-Numbers-to-7's Ratio 3.20:1 3.73:1 4.27:1
Initial Large Bet $110.00 $110.00 $110.00
Subsequent Small Bet $22.00 $22.00 $22.00
1st Hit $40.25 $40.25 $40.25
2nd Hit Post Regression $7.52 Weighted payout $40.25 $40.25
3rd Hit - $40.25 $40.25
4th Hit - Post Regression $6.82 Weighted payout $40.25
5th Hit - - Post Regression $7.27 Weighted payout
Total Expected Payout $47.77 $127.57 $168.27
Remaining Exposed Wagers $22.00 $22.00 $22.00
Net-Profit per-Hand $25.77 $105.57 $146.27
Return-on- Investment 23.43% 95.97% 132.97%

Here's a summarized comparison between flat-betting the Even-Numbers versus the use of an Initial Steep Regression:

$110 Even-Numbers Flat-bet vs. $110 Even-Numbers Regressed to $22-Even
SRR 7 SRR 8 SRR 9
$110 Even-NumberFlat-bet Net-Profit/Hand $18.80 $40.13 $61.87
$110 Even-NumbersRegressed to $22-Even Net-Profit/Hand $25.77 $105.57 $146.27
$-Difference $6.97 $65.44 $84.40
Increased Return-on-Investment 27% 62% 58%

For novice, intermediate and even advanced dice-influencers, regression-betting enjoys a wide return-on-investment advantage over flat-betting.

  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. ISR's permit us to derive profit from the fattest positive-expectation portion of our point-cycle, while the newly reduced lower-value bets remain in action when our hand does exceed it expected average duration.
  3. In future chapters of this series, we will take a serious look at how to properly ramp up your bets on those rare but welcome long hands.

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 your net-profit will be.

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

Even-Number Profit Projections using various Steepness Ratios SRR-7
Ratio 2:1 3:1 4:1 5:1 10:1
Initial Large Bet $44 $66 $88 $110 $220
Subsequent Small Bet $22 $22 $22 $22 $22
1st Hit Weighted Value$15.50 Weighted Value$23.25 Weighted Value $32.13 Weighted Value$40.25 Weighted Value $80.50
2nd Hit Post Regression $7.52 Weighted payout Post Regression $7.52 Weighted payout Post Regression $7.52 Weighted payout Post Regression $7.52 Weighted payout Post Regression $7.52 Weighted payout
Total Expected Payout $23.02 $30.77 $39.65 $47.77 $88.02
Remaining Exposed Wagers $22.00 $22.00 $22.00 $22.00 $22.00
Net-Profit $1.02 $8.77 $17.65 $25.77 $66.02
Return-on- Investment 2.32% 13.29% 20.06% 23.43% 30.00%

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

Even-Number Profit Projections using various Steepness Ratios SRR-8
Ratio 2:1 3:1 4:1 5:1 10:1
Initial Large Bet $44 $66 $88 $110 $220
Subsequent Small Bet $22 $22 $22 $22 $22
1st Hit Weighted Value$15.50 Weighted Value$23.25 Weighted Value $32.13 Weighted Value$40.25 Weighted Value $80.50
2nd Hit $15.50 $23.25 $32.13 $40.25 $80.50
3rd Hit $15.50 $23.25 $32.13 $40.25 $80.50
4th Hit Post Regression $6.82 Weighted payout Post Regression $6.82 Weighted payout Post Regression $6.82 Weighted payout Post Regression $6.82 Weighted payout Post Regression $6.82 Weighted payout
Total Expected Payout $53.32 $76.57 $103.21 $127.57 $248.32
Remaining Exposed Wagers $22.00 $22.00 $22.00 $22.00 $22.00
Net-Profit $31.32 $54.57 $81.21 $105.57 $226.32
Return-on- Investment 71.18% 82.68% 92.28% 95.97% 102.87%

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; 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 Even-Numbers bet that we've been discussing today, he'll generally get the benefit of four pre-regression hits before optimally reducing his bet-exposure.

Even-Number Profit Projections using various Steepness Ratios SRR-9
Ratio 2:1 3:1 4:1 5:1 10:1
Initial Large Bet $44 $66 $88 $110 $220
Subsequent Small Bet $22 $22 $22 $22 $22
1st Hit Weighted Value$15.50 Weighted Value$23.25 Weighted Value $32.13 Weighted Value$40.25 Weighted Value $80.50
2nd Hit $15.50 $23.25 $32.13 $40.25 $80.50
3rd Hit $15.50 $23.25 $32.13 $40.25 $80.50
4th Hit $15.50 $23.25 $32.13 $40.25 $80.50
5th Hit Post Regression $7.27 Weighted payout Post Regression $7.27 Weighted payout Post Regression $7.27 Weighted payout Post Regression $7.27 Weighted payout Post Regression $7.27 Weighted payout
Total Expected Payout $69.27 $100.27 $135.79 $168.27 $329.27
Remaining Exposed Wagers $22.00 $22.00 $22.00 $22.00 $22.00
Net-Profit $47.27 $78.27 $113.79 $146.27 $307.27
Return-on- Investment 107.43% 118.59% 129.31% 132.97% 139.67%

Part Nine in this series tackles the venerable Anything-but-7 Iron Cross bet. I hope you'll join me for that. 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 8, 2007 7:56 PM.

The previous post in this blog was Part 2: Learning the theory of dice influencing.

The next post in this blog is Ask the Mad Professor - Part 8.

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