« Long Tables = Po$$ibilitie$ - Part 3 | Main | Mad Professor's Mini-Table Craps Tour with the Vegas Ghost - Part 15 »

Regression Avoids Depression - Part 12

With the use of Initial Steep Regressions, a novice dice-influencer can reap larger and much more consistent monetary rewards from the same skill-level and the same bet-level than flat-betting or ramped-up bet-pressing can.

Equally, an advanced player can extract a steadier and even higher income from his current skill-set on a much more predictable basis by simply utilizing the widest, most frequently occurring sector of his roll-duration range.

How does that work?

  1. Once a players point-cycle roll-duration extends past the Optimal Regression point for an initially positive-expectation bet, the expected-value (EV) quickly falls into negative-expectation territory. That is, the wager is now expected to bring in less money than its face-value.
  2. The higher a players SRR-rate is, the less problematic negative volatility becomes. Therefore, the higher his EV on a given bet; the longer negative volatility is held at bay...and obviously, the more profitable each of his properly wagered hands become.
  3. At the same time; the higher his EV is on a given bet, the fewer roll-decisions he will need for the bet to become net-positive, and therefore, the less volatility each of his hands will have to endure.
  4. ISR's are critically important for dice-influencers who have already validated their skill but haven't yet been able to translate that into any kind of reliably consistent profit.

Steep Regressions Are A Force-Multiplier

Initial Steep Regressions effectually leverage the Expected Value and realizable profit that a player can earn on every validated wager that he makes.

In other words, ISR's let an SRR-7 shooter make the profit that most SRR-9 or SRR-10 flat-betting or aggressive-pressing shooters only FANTASIZE about.

  1. By profitably exploiting more of his rolls from the fattest (most frequently occurring) portion of his roll-duration expectancy-curve; the ISR-user can make much more money with much less risk and much lower volatility than a better shooter who uses flat or aggressively pressed wagers can.
  2. The use of Steep Regressions for SRR-7 through SRR-10 shooters is where the MOST dice-influencing profit can be found; yet most players fail to seize it or even recognize that it's possible to extract that much profit from their current skill-rate.
  3. 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.

To accomplish that however, you have to wager your money in a manner which utilizes only your strongest-edge bets, and disregards or at least discounts all the rest.

Once you've done that; Steep Regressions leverage your current skills and multiply the force by which your dice-influencing abilities are profitably fulfilled and effectuated.

ISR'ssimply work better and are more effective at extracting additional profit out of the SAME skill-level than any other types of bet-management.

Putting the 4 and 10 Place-bet Under a Microscope

So far we've looked at how well ISR's work on several global-type bets that cover four numbers (Inside, Outside, and Even), six numbers (Across) and even ten numbers (Iron Cross) at the same time. However, let's say you are just considering Place-betting your two most dominant Signature-Numbers like the 4 and 10.

  1. In random expectancy, we'll see three 4's and three 10's against six appearances of the 7, which equates to six appearances of the 4 and 10 for every six appearances for the 7.
  2. That ratio of 6:6 means a random-roller can expect a 4's-and-10's-to-7's appearance-rate of 1:1.
  3. As you know, that even-ratio is not enough to make up for the cost of a 7-out which would wipe out both Place-bet wagers; and even though a winning hit pays 9:5 as a straight Place-bet and 2:1 as a buy-bet it is still not enough to overcome the house-edge.
  4. As a result, random-rollers stay on the negative-side of the expectation curve, while dice-influencers cross over into positive territory on a regular basis.

Why ISR's Work So Well With Simple 4 & 10 Place-bets

We know that for a random-roller, the 7 is expected to show up once every six rolls. With a 16.67% appearance-rate, that DOES NOT mean that the 7 will show up like clockwork on each and every sixth roll. Instead, it means that its appearance-rate will average out to once every six rolls. That's the nature of the beast that we call volatility.

As dice-influencers we know that the further we move our shooting away from the randomly-expected SRR-6, the better we are at keeping the 7 at bay.

In a random outcome game, the 4 and 10 constitute 16.67% of all possible outcomes which is the same occurrence-rate of the 7.

There are:

  1. Three ways to make a 4, and a Place-bet pays 9:5. When the place-bet is "bought", it pays 2:1, less commission.
  2. Three ways to make a 10, and a Place-bet pays 9:5. When the place-bet is "bought", it pays 2:1, less commission.

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
4's & 10's-to-Sevens Ratio
Random SRR 6 SRR 7 SRR 8 SRR 9
4's and 10's to Total Outcomes 6-out-of-36 6.17 6.3 6.4-out- of-36
Per-Roll Probability 16.67% 17.14% 17.5% 17.78%
4's and 10's- to-7's Ratio 1:1 1.2:1 1.4:1 1.6:1

Although the sheer number of 4's and 10'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 4's and 10's than a random-roller does (6.4 versus 6.0). However, since his dice-influencing produces a lower overall sevens-appearance-rate, his actual 4's-and-10's-to-7's ratio improves by 60% (from 1.0 to 1.6).

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

Anatomy Of a 4 & 10 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.

4 & 10 Flat-bet Repayment Rate
4 & 10Hits Total Investment Single Payout Return on Investment Profit
0 $10 $0 0% (-$10.00)
1 - $9.00 90% (-$1.00)
2 - $9.00 180% $8.00

Place-betting the 4 and 10 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 4 and 10 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 4 & 10 Place-bet Expected Flat-bet Win-Rate
Expected Profit/Roll Random SRR 6 SRR 7 SRR 8 SRR 9
4's & 10's-to-7's Ratio 1:1 1.2:1 1.4:1 1.6:1
1 $9.00 $9.00 $9.00 $9.00
2 - $1.80 Weighted payout $3.60 Weighted payout $5.40 Weighted payout
Total Expected Payout $9.00 $10.80 $12.60 $14.40
Remaining Wager $10.00 $10.00 $10.00 $10.00
Net-Profit -$1.00 $0.80 $2.60 $4.40
Return-on-Investment -10% 8% 26% 44%

Your Sevens-to-Rolls Ratio largely determines the average roll-duration of your 4 & 10 Place-bet.

  1. Now we all know that sometimes a random-roller will throw all kinds of 4's and 10's, while at other times they can't produce them to save their life.
  2. On average though, the house wins out on the randomly-wagered 4 and 10 and at the end of the day, it remains a net-detractor to your bankroll.
  3. On the other hand, even a flat-betting SRR-7 shooter can produce a modest net-profit with this wager. Sure, sometimes he'll throw a 7-Out before producing the two required winning hits that it takes to make this bet net-profitable; but over time, even flat betting it will produce a decent profit for this caliber of shooter by providing an average return of 8% profit on each and every hand that he throws. For the SRR-8 shooter, that rate-of-return jumps to nearly 26% R.O.I. per hand.

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.

  1. Your SRR determines the ability for any given wager to survive over multiple Point-cycle rolls.
  2. That survival rate is determined by the ever-present 7.
  3. As your SRR-rate improves over random, your chances of a given bet surviving for additional rolls, increases.
  4. 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 against any given wager has to fight.

  • When we take the survival-rate for a given wager like the Place-bet 4 and 10, and pit it 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 Place-bets into smaller, lower-value ones on the same numbers.

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 4 and 10 Place-bet point-cycle:

4 & 10 Place-Bet Survival-Rate
4 & 10 Hit-rate Random SRR 6 SRR 7 SRR 8 SRR 9
1 16.67% 17.14% 17.50% 17.78%
2 13.89% 14.69% 15.31% 15.80%
3 11.58% 12.59% 13.40% 14.05%
4 9.65% 10.79% 11.72% 12.49%
5 8.04% 9.25% 10.26% 11.10%
6 6.70% 7.93% 8.98% 9.87%
7 5.58% 6.80% 7.85% 8.77%
8 4.65% 5.82% 6.87% 7.80%
9 3.88% 4.99% 6.01% 6.93%
10 3.23% 4.28% 5.26% 6.16%
11 2.69% 3.67% 4.60% 5.48%
12 2.24% 3.14% 4.03% 4.87%

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 rock-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 steady in fact, it increases dramatically. 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.

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. Therefore, a reduced 7's appearance-rate means an increased winning-bet rate.
  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.  As such, your expectancy-chart may look somewhat different than the generic ones here.

As we've discussed before:

  1. If we know how long our hand generally stays in positive-expectation territory; then we can easily determine a way in which to use an initially large "starting-level" wager, and then calculate when the ideal time to regress it down to a still productive Post Regression value is.
  2. As I showed above; even though Kelly-style flat-betting can produce a net-profit, 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. Conversely, 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 chart for the 4 and 10 Place-bet that we just looked at, helps us to correctly factor in the modified sevens-appearance-rate for each SRR; which in turn brings to light 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 but lower-value 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 $25 each on the 4 and 10 versus initially betting $25 each on the 4 and 10 then steeply regressing it to $5 each on the 4 and 10 at the appropriate trigger-point.

Flat-betting $25 Place-bet each on 4 and 10 Return-on-Investment
Random SRR 6 SRR 7 SRR 8 SRR 9
4's and 10's-to-7's Ratio 1:1 1.2:1 1.4:1 1.6:1
Flat Bet each $25.00 $25.00 $25.00 $25.00
Per-hit Payout $49.00 $49.00 $49.00 $49.00
Expected Total Payout $49.00 $58.80 $68.60 $78.40
Remaining Exposed Wagers $50.00 $50.00 $50.00 $50.00
Net-Profit -$1.00 $8.80 $18.60 $28.40
Return-on-Investment -2% 17.6% 37.2% 56.8%

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 4 and 10 Regressed at Optimal Trigger-Point to $5 each Place-bet on 4 and 10 Return-on-Investment
4's and 10's-to-7's Ratio 1.2:1 1.4:1 1.6:1
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 $49.00 $49.00 $49.00
2nd Hit Post Regression $8.45 Weighted payout $49.00 $49.00
3rd Hit - Post Regression $8.80 Weighted payout $49.00
4th Hit - $49.00
5th Hit - - Post Regression $8.45 Weighted payout
Total Expected Payout $57.45 $106.80 $204.45
Remaining Exposed Wagers $10.00 $10.00 $10.00
Net-Profit per-Hand $47.45 $96.80 $194.45
Return-on- Investment 94.9% 193.6% 388.9%

Here's a summarized comparison between flat-betting the 4 and 10 Place-bet versus the use of an Initial Steep Regression:

$25 each Place-bet on 4 and 10 Flat-bet vs. $25 each Place-bet on 4 and 10 Regressed to $5 each Place-bet on 4 and 10
$25 each Flat-bet Net-Profit/Hand $8.80 $18.60 $28.40
$25 each Regressed to $5 each Profit/Hand $47.45 $96.80 $194.45
$-Difference $38.65 $78.20 $166.05
Increased Return-on-Investment 81% 81% 85%
  1. A $8 per-hand profit for a SRR-7 flat-bettor is fairly meager when compared to the $47 per-hand profit from the same guy using a Steep Regression.
  2. Each scenario starts off with the same bet, $25 each on the 4 and 10. 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.

Now the argument could be made that the guy who never regresses his bets will make more money in the event that this hand turns out to be THE hand of the century. That assumption of course is correct for long hands; however, we are talking about your average-hand and your average-session shooting where your skills should be producing a profit for you but they currently aren't.

No one in their right mind is saying that you can't press-up your regressed bets with ongoing winning-wager revenue if your longer-duration hand does continue to produce money; however the fact remains that MOST of your barely-better-than-random hands don't get to that point; yet they can STILL be net-profitable if you bet them properly.

Anyone can make money off of 20, 30, 50 and 70-roll hands, but it takes an acute sense of skills-awareness and betting-efficiency to take advantage of the short and mediocre ones too.

SRR-based ISR's help you accomplish that.

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.

Place-bet on 4 and 10 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 $18.00 $27.00 $39.00 $49.00 $98.00
2nd Hit Post Regression $8.45 Weighted payout Post Regression $8.45 Weighted payout Post Regression $8.45 Weighted payout Post Regression $8.45 Weighted payout Post Regression $8.45 Weighted payout
Total Expected Payout $26.45 $35.45 $47.45 $57.45 $106.45
Remaining Exposed Wagers $10.00 $10.00 $10.00 $10.00 $10.00
Net-Profit $16.45 $25.45 $37.45 $47.45 $96.45
Return-on- Investment 82% 85% 94% 95% 96%

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

Place-bet on 4 and 10 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 $18.00 $27.00 $39.00 $49.00 $98.00
2nd Hit $18.00 $27.00 $39.00 $49.00 $98.00
3rd Hit Post Regression $8.80 Weighted payout Post Regression $8.80 Weighted payout Post Regression $8.80 Weighted payout Post Regression $8.80 Weighted payout Post Regression $8.80 Weighted payout
Total Expected Payout $44.80 $62.80 $86.80 $106.80 $204.80
Remaining Exposed Wagers $10.00 $10.00 $10.00 $10.00 $10.00
Net-Profit $34.80 $52.80 $76.80 $96.80 $194.80
Return-on- Investment 174% 176% 192% 194% 195%

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 two point-cycle rolls before needing to steeply regress them. In the case of a SRR-9 shooter using the 4 and 10 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 4 and 10 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 $18.00 $27.00 $39.00 $49.00 $98.00
2nd Hit $18.00 $27.00 $39.00 $49.00 $98.00
3rd Hit $18.00 $27.00 $39.00 $49.00 $98.00
4th Hit $18.00 $27.00 $39.00 $49.00 $98.00
5th Hit Post Regression $8.45 Weighted payout Post Regression $8.45 Weighted payout Post Regression $8.45 Weighted payout Post Regression $8.45 Weighted payout Post Regression $8.45 Weighted payout
Total Expected Payout $80.45 $116.45 $164.45 $204.45 $400.45
Remaining Exposed Wagers $10.00 $10.00 $10.00 $10.00 $10.00
Net-Profit $70.45 $106.45 $154.45 $194.45 $390.45
Return-on- Investment 352% 355% 386% 389% 390%
  1. The fewer advantaged-bets that you spread your money over, the fewer winning-hits you will need in order to produce a net-profit.
  2. By limiting your wagers to just two Place-bets like the 4 and 10; the required number of winning-hits to break through to net-profit is minimal.
  3. When you add in the use of an Initial Steep Regression, you enable your dice-influencing skills to get to that profit breakthrough point much faster and with much more consistency.

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


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!


This page contains a single entry from the blog posted on January 13, 2007 3:35 AM.

The previous post in this blog was Long Tables = Po$$ibilitie$ - Part 3.

The next post in this blog is Mad Professor's Mini-Table Craps Tour with the Vegas Ghost - Part 15.

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