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Regression Avoids Depression Part - 6

A Word About Global Bets

I refer to multi-number wagers like Inside (5, 6, 8, and 9), Across (4, 5, 6, 8, 9, and 10), Outside (4, 5, 9, and 10), Even (4, 6, 8, and 10), Iron Cross (5, 6, 8, and Field) and similar, as "global bets", because they are semi or fully-encompassing wagers that cover several numbers at the same time.

In the hands of a random-roller, NONE of those bets hold ANY merit whatsoever, and frankly NONE of your money should be ventured on ANY of them if you want your advantage-play bankroll to stay in positive-expectation territory.

Conversely, each one of those bets holds their own special place in the world of dice-influencing. Your task as an advantage-player, is to figure out how good your own shooting ability is; and then determine which bets are best suited to those talents.

Your Betting Should Be Dictated By How Good Your Shooting Is

Frankly, the lion's share of your betting-weight should be wagered on your top one or two Signature-Numbers.

  1. Your S-N's are determined by the particular dice-set that you use and the consistency in which you throw. I refer to that influence-rate/dice-set consistency as "Foundation Frequencies".
  2. The more consistent your toss is, the more dominant certain dice-outcomes will be when you are using a given dice-set.

For a full discussion on Signature-Numbers, I would invite to you read the six-part series, The When, Where, Why, What and How of Signature-Numbers.

  1. When you spread your money across a wider range of bets, your volatility decreases but your bet-exposure increases.
  2. By far, the absolute best way to exploit your advantage over the house is to put your money where your greatest advantage is.
  3. If you reduce the amount of money that you wager on your strongest-edge bet just so you can wager on additional numbers; then you may be unfairly diminishing your profit.
  4. That means you may unwittingly be surrendering more profit in favor of more frequent hits on a wider range of bets and still emerge from that transaction with less net-revenue than your shooting-skill deserves.

That sort of deleterious betting problem is not foreign to anyone who has sought to exploit their dice-influencing edge over this game. However that is precisely WHY the carefully considered use of Initial Steep Regressions is so important to intermediate and advanced Precision-Shooters.

The ISR betting-formulas that we are discussing in this series solve that age-old problem with all kinds of new profit-making opportunities.

In Parts Two, Three, Four and Five, we validated the use of Initial Steep Regressions on the Inside-bet in a way that permits even a modestly skilled dice-influencer to satisfy both the desire of a satisfyingly high hit-rate with the necessity of a fully utilized SRR-based profit-generator.

Your shooting-skill dictates where your money should be wagered. As such, a savvy player has to consider his skills in context with a wide range of betting choices. The prudent use of SRR-based ISR's can often delineate and more fully exploit those choices within a global-bet context.

All-Across Bets

In a random outcome game, Across-the-Board or All-Across wagers constitute 66.67% of all possible outcomes. The Across-bet covers all of the box-numbers (4, 5, 6, 8, 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. Five ways to make a 6, and it pays 7:6.
  4. Five ways to make an 8, and it pays 7:6.
  5. Four ways to make a 9, and it pays 7:5.
  6. 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, Across-the-board numbers constitute 24-out-of-36 (66.67%) of all randomly-expected outcomes, and their average weighted-payout is $7.50 per hit.

Your Mileage May Vary

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

  1. The less the 7 shows up within a given sampling-group, the more other non-7 outcomes will take its place.
  2. 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.
  3. In the samples that I've used in this series, I've evenly spread those replacement numbers across the entire outcome spectrum.
  4. As such, your expectancy-chart may look somewhat different than the generic ones here; so for even more betting-accuracy, you may want to tailor your wagers to more closely match up with your actual numerically-significant roll-sample outcomes.

Although your Sevens-to-Rolls ratio is not the only dice-influencing metric that matters, many dice-influencers often underutilize it when it comes to shaping and structuring betting-methods and their related same-bet, press or regress trigger-points.

How many incredibly skilled Precision-Shooters do you know who have endured years of suffering through the "Please lawrd, just gimme one more hit" syndrome of improperly timed same-bet, press or regress trigger-points. Sooner or later, most players come to realize that it is NOT their shooting that is needlessly keeping them on the break-even or minor losing side of the ledger it is THEIR BETTING.

If you ignore or dismiss your SRR-rate; you are not only overlooking your best indicator of average hand-duration, but you are also rejecting the best gauge by which to successfully structure a consistently productive multi-number betting-method.

Intelligent advantage-players aren't so quick to turn their backs on such an important profit-patterning benchmark.

If you ignore what your skill-based sevens-appearance-rate is trying to tell you; then don't be surprised if consistently produceable profit ignores you too.

The 7 is the omnipresent roll-ender for every Rightside bettor.

You can pretend that it's not there, and you can hope that it never shows up, and you can wish that your hand will last long enough to show a net-profit; but if your betting-method structure doesn't recognize the 7's appearance-rate or the resultant roll-duration decay-rate that accompanies your SRR; then don't be surprised or disappointed if your skill-based profits continue to be far lower than your dice-influencing abilities indicate they should be.

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
All-Across to Sevens Ratio
Random SRR 6 SRR 7 SRR 8 SRR 9
Across-Numbers to Total Outcomes 24-out-of-36 24.69 25.20 25.60
Per-Roll Probability 66.67% 68.58% 70.00% 71.11%
Across-Numbers-to-7's Ratio 4:1 4.8:1 5.6:1 6.4:1

The randomly-expected SRR-rate is one-in-six (16.67%) on any given roll, while a novice SRR-7 shooter only has to contend with a 14.29% per-roll (1-in-7) chance of it appearing. At first glance that 2.38% difference looks pretty small, but it actually equates to a very exploitable 14% disparity between a random SRR-6 shooter and a SRR-7 dice-influencer. Within that small margin of improvement over random is where dice-influencers can find all kinds of money, but you have toproperly wager your money on that differencefor it to do you any good.

Anatomy Of An Across-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.

If, for example, you flat-bet $32-Across (neither increasing nor decreasing your wager at any point during the point-cycle of your hand); then you need to make five successful Across-Number hits BEFORE reaching net-profitability.

$32-Across Flat-bet Return-on-Investment
Across-Number Hits Total Investment Payout Return on Investment Profit
0 $32 $0 0% (-$32.00)
1 - $7.50 23.44% (-$24.50)
2 - $7.50 46.88% (-$17.00)
3 - $7.50 70.31% (-$9.50)
4 - $7.50 93.75% (-$2.00)
5 - $7.50 112.00% $5.50

As attractive and enticing as the idea of covering all of the box-numbers is, with the Across-bet constituting fully two-thirds (66.67%) of all possible random-outcomes; the sad fact is that a random-roller still has a greater chance of 7'ing-Out than he does of hitting enough box-numbers for that 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 Across-bet can be a steady profit contributor to your bankroll.

Expected Flat-bet Win-Rate $32-Inside
Expected Profit/Roll Random SRR 6 SRR 7 SRR 8 SRR 9
Across Numbers to 7's Ratio 4:1 4.8:1 5.6:1 6.4:1
1 $7.50 $7.50 $7.50 $7.50
2 $7.50 $7.50 $7.50 $7.50
3 $7.50 $7.50 $7.50 $7.50
4 $7.50 $7.50 $7.50 $7.50
5 - $6.00 Weighted payout $7.50 $7.50
6 - - $4.50 Weighted payout $7.50
7 - - - $3.00 Weighted payout
Total Expected Payout $30.00 $36.00 $42.00 $48.00
Remaining Wager $32.00 $32.00 $32.00 $32.00
Net-Profit -$2.00 $4.00 $10.00 $16.00
Return-on-Investment -6.25% 12.50% 31.25% 50.00%

As with Inside-wagers, your Sevens-to-Rolls Ratio largely determines the average roll-duration of your Across-bet hand.  At the same time, 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.

Across-Bet Survival-Rate
Across Number Hit rate Random SRR 6 SRR 7 SRR 8 SRR 9
1 66.67% 68.58% 70.00% 71.11%
2 55.56% 58.78% 61.25% 63.21%
3 46.29% 50.38% 53.59% 56.19%
4 38.58% 43.18% 46.89% 49.94%
5 32.15% 37.01% 41.03% 44.40%
6 26.79% 31.72% 35.90% 39.46%
7 22.32% 27.19% 31.42% 35.08%
8 18.60% 23.30% 27.49% 31.18%
9 15.50% 19.97% 24.05% 27.72%
10 12.92% 17.12% 21.05% 24.64%
11 10.76% 14.67% 18.42% 21.90%
12 8.97% 12.58% 16.11% 19.47%

As I just mentioned:

  1. If we know how long our hand generally stays in positive-expectation territory for the Across-Number bets we are making; then we can easily determine the ideal time to regress them from their initially high starting-value.
  2. 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 all-encompassing Across-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 $160-Across versus the use of an initial $160-Across wager that is steeply regressed to $32-Across at the appropriate trigger-point.

Flat-betting $160-Across Return-on-Investment
Random SRR 6 SRR 7 SRR 8 SRR 9
Across-Numbers-to-7's Ratio 4:1 4.8:1 5.6:1 6.4:1
Initial Large Bet $160-Across $160-Across $160-Across $160-Across
Single-hit Payout $38.50 $38.50 $38.50 $38.50
Expected Total Payout $154.00 $184.80 $215.60 $246.40
Remaining Exposed Wagers $160 $160 $160 $160
Net-Profit -$6.00 $24.80 $55.60 $86.40
Return-on-Investment -3.75% 15.50% 34.75% 54.00%

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 $160-Across Regressed at Optimal Trigger-Point to $32-Across Return-on-Investment
SRR 7 SRR 8 SRR 9
Across-Numbers-to-7's Ratio 4.8:1 5.6:1 6.4:1
Initial Large Bet $160-Across $160-Across $160-Across
Subsequent Small Bet $32-Across $32-Across $32-Across
1st Hit $38.50 $38.50 $38.50
2nd Hit $38.50 $38.50 $38.50
3rd Hit Post Regression $7.34 Weighted payout $38.50 $38.50
4th Hit - Post Regression $7.02 Weighted payout $38.50
5th Hit - - Post Regression $7.27 Weighted payout
Total Expected Payout $84.34 $122.52 $161.27
Remaining Exposed Wagers $32.00 $32.00 $32.00
Net-Profit per-Hand $52.34 $90.52 $129.27
Return-on- Investment 32.71% 56.58% 80.79%

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

$160-Across Flat-bet vs. $160-Across Regressed to $32-Across
SRR 7 SRR 8 SRR 9
$160 Across Flat bet Net-Profit/Hand $24.80 $55.60 $86.40
$160 Across Regressed 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%

While regression-betting still enjoys a wide return-on-investment advantage over flat-betting; that gap actually narrows as your SRR improves.

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

  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.

Across-bet Regression Various Steepness Ratios SRR-7
Ratio 2:1 3:1 4:1 5:1 10:1
Initial Large Bet $64-Across $96- Across $128- Across $160- Across $320- Across
Subsequent Small Bet $32-Across $32-Across $32-Across $32-Across $32-Across
1st Hit Weighted Value $15.00 Weighted Value$22.50 Weighted Value $30.75 Weighted Value $38.50 Weighted Value $77.00
2nd Hit $15.00 $22.50 $30.75 $38.50 $77.00
3rd Hit Post Regression $7.34 Weighted payout Post Regression $7.34 Weighted payout Post Regression $7.34 Weighted payout Post Regression $7.34 Weighted payout Post Regression $7.34 Weighted payout
Total Expected Payout $37.34 $52.34 $68.84 $84.34 $161.34
Remaining Exposed Wagers $32.00 $32.00 $32.00 $32.00 $32.00
Net-Profit $5.34 $20.34 $36.84 $52.34 $129.34
Return-on- Investment 8.34% 21.19% 28.78% 32.71% 40.42%

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

Across-bet Regression Various Steepness Ratios SRR-8
Ratio 2:1 3:1 4:1 5:1 10:1
Initial Large Bet $64-Across $96- Across $128- Across $160- Across $320- Across
Subsequent Small Bet $32-Across $32-Across $32-Across $32-Across $32-Across
1st Hit Weighted Value $15.00 Weighted Value $22.50 Weighted Value $30.75 Weighted Value $38.50 Weighted Value $77.00
2nd Hit $15.00 $22.50 $30.75 $38.50 $77.00
3rd Hit $15.00 $22.50 $30.75 $38.50 $77.00
4th Hit Post Regression $7.02 Weighted payout Post Regression $7.02 Weighted payout Post Regression $7.02 Weighted payout Post Regression $7.02 Weighted payout Post Regression $7.02 Weighted payout
Total Expected Payout $52.02 $74.54 $99.27 $122.52 $238.02
Remaining Exposed Wagers $32.00 $32.00 $32.00 $32.00 $32.00
Net-Profit $20.02 $42.54 $67.27 $90.52 $206.02
Return-on- Investment 31.28% 44.31% 52.55% 56.58% 64.38%

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 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 having to steeply regress them. Further to that, the SRR-9 Precision-Shooter can keep his big bet out there for four hits before regressing it to a smaller value.

Across-bet Regression Various Steepness Ratios SRR-9
Ratio 2:1 3:1 4:1 5:1 10:1
Initial Large Bet $64-Across $96- Across $128- Across $160- Across $320- Across
Subsequent Small Bet $32-Across $32-Across $32-Across $32-Across $32-Across
1st Hit Weighted Value $15.00 Weighted Value $22.50 Weighted Value $30.75 Weighted Value $38.50 Weighted Value $77.00
2nd Hit $15.00 $22.50 $30.75 $38.50 $77.00
3rd Hit $15.00 $22.50 $30.75 $38.50 $77.00
4th Hit $15.00 $22.50 $30.75 $38.50 $77.00
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 $67.27 $97.27 $130.27 $161.27 $315.27
Remaining Exposed Wagers $32.00 $32.00 $32.00 $32.00 $32.00
Net-Profit $35.27 $65.27 $98.27 $129.27 $283.27
Return-on- Investment 55.11% 67.99% 76.77% 80.79% 88.52%

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

Sincerely,

The Mad Professor

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This page contains a single entry from the blog posted on January 6, 2007 3:09 PM.

The previous post in this blog was Part 4: The Puppy's First Hunt.

The next post in this blog is Ask the Mad Professor - Part 6.

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