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Regression Avoids Depression: Part Three

As a dice-influencer, your task is to de-randomize the dice to a point where you have an exploitable edge over the casino.  Thereafter, your primary task is to determine which wagers your shooting proficiency gives you the biggest advantage over, and then to wager your money in such a way so as to produce the most profit.

In Part Two of this series I showed you in very clear detail:

  1. How your own validated Sevens-to-Rolls Ratio (SRR) reconfigures the outcome-probabilities chart, and how that resultant 7's appearance-rate determines the length of your average hand.
  2. How to calculate your Inside-Numbers-to-Sevens ratio, and why it is critically important for you to do so, especially if you are considering making any global, multi-number Inside or Across wagers.
  3. Finally, we looked at how long you have (as measured by the number of point-cycle rolls) in which to profitably exploit a regression-style wager.

Today, we are going to delve much further into regression-style wagering to figure out how much profit-per-hand we can reasonably expect to make off of an Inside-Number wager.

As dice-influencers, we know that the further we move our shooting away from the randomly-expected Sevens-to-Rolls Ratio of 1:6, the better we are at keeping the 7 at bay.

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/Roll 16.67% 14.29% 12.5% 11.11%
7's-per-36 rolls 6 5.14 4.5 4

How SRR Affects Average Roll-Duration

Why is it so hard to get consistently long hands even when we have a validated edge over the casino?

The answer is two fold.

  1. Though our SKILL may be fairly consistent throughout an entire hand, our EDGE over the bets that we make is not.

Let me explain:

  1. When looked at in total isolation on a per-roll basis, our dice-influencing skill determines the edge that we have over a certain bet.
  2. However, when viewed over the entirety of a hand and in relation to our Sevens-to-Rolls Ratio, a gap starts to form.

That gap is the chasm that is formed between our skill and the relative declining-value edge that we have over the house when our SRR is considered and reconciled with the expected number of rolls of our average-duration hand.

If our skill remains the same, and our edge, when considered against a single roll remains the same; then how does our overall edge decline?

Well, the same thing that makes long random rolls exceptional, is exactly the same thing that makes long dice-influenced rolls exceptional too.

  1. The likelihood of a long duration random hand declines with each and every subsequent toss that is made during any given hand.
  2. The random occurrence-rate of the 7 remains constant at 16.67%, but the chance of a 7 not appearing over an extended period becomes increasingly less likely.
  3. This has nothing to do with "due number theory", but everything to do with the mathematical expectancy of random outcomes.  The ratio of 7's to all the other numbers remains constant at 1-in-6 (16.67%), but the longer a 7 doesn't appear, the less likely it will continue to stay away.

The math-guys have already calculated how that applies to random SRR-6 shooters; and in the chart below, I simply applied the same formulas to calculate point-cycle duration for SRR-7, SRR-8, and SRR-9 dice-influencers too.

Point-cycle Rolls
Random SRR 6 SRR 7 SRR 8 SRR 9
1 83.33% 85.71% 87.50% 88.89%
2 69.44% 73.46% 76.56% 79.01%
3 57.86% 62.96% 66.99% 70.24%
4 48.22% 53.97% 58.62% 62.43%
5 40.18% 46.26% 51.30% 55.50%
6 33.48% 39.65% 44.88% 49.33%
7 27.90% 33.98% 39.27% 43.85%
8 23.25% 29.13% 34.36% 38.98%
9 19.37% 24.96% 30.07% 34.65%
10 16.14% 21.40% 26.31% 30.80%
11 13.45% 18.34% 23.02% 27.38%
12 11.21% 15.72% 20.14% 24.34%
  1. If we know the SRR rate of a shooter; then we can predict how long his average point-cycle will last.
  2. Based on his current ability to generate non-7 outcomes, we can then structure a betting-method that best satisfies his profit motive.

Anatomy Of An Inside-Wager

To understand why we have to look at using an Initial Steep Regression (ISR) to achieve a net-profit much sooner and on a much more consistent basis; we can take a look at the anatomy of an Inside-Number wager.

If, for example, you flat-bet $22-Inside (neither increasing nor decreasing your wager at any point during the point-cycle of your hand); then you need to make four successful Inside-Number hits before reaching net-profitability.

$22-Inside Return-on-Investment
Inside-Number Hits Total Investment Payout Return on Investment Profit
0 $22 $0 0% (-$22)
1 - $7 31.8% (-$15)
2 - $7 63.6% (-$8)
3 - $7 95.4% (-$1)
4 - $7 127.2% $6

Though you could consider taking your $22-Inside wager down after one, two or three hits, thereby locking up a profit; a hand that lasts beyond that "bets-off/bets-down" point could see a situation where Inside-Numbers continue to roll, but you no longer have any active Inside-Number wagers to take advantage of your ongoing hand.

One way to contend with this issue is to use an Initial Steep Regression (ISR) where you start out with a higher wager at the beginning of your point-cycle; and then after one or more hits, you reduce that initial large wager down to a lower amount thereby locking in a profit while still leaving active Inside-Number wagers out on the table.

What the ISR does is to recognize the fact that your dice-influencing skills are much more likely to produce at least one paying Inside-Number hit than they are to produce two or three or four or more of them; but in the event that your hand does continue unabated, then the ISR has already locked in a quick and guaranteed profit while still affording you even more upside profit potential as your hand continues.

Inside-Bet Survival-Rate

Your Sevens-to-Rolls Ratio (SRR) pretty much determines the survival-rate of your Inside-Number bet.

Inside-Bet Survival-Rate
Inside-Number Hit-rate Random SRR 6 SRR 7 SRR 8 SRR 9
1 50.00% 51.19% 52.08% 52.78%
2 41.67% 43.87% 45.57% 46.92%
3 34.72% 37.61% 39.87% 41.70%
4 28.93% 32.23% 34.89% 37.07%
5 24.11% 27.63% 30.53% 32.95%
6 20.09% 23.68% 26.71% 29.29%
7 16.74% 20.29% 23.37% 26.04%
8 13.95% 17.39% 20.45% 23.14%
9 11.62% 14.91% 17.89% 20.57%
10 9.69% 12.78% 15.66% 18.29%
11 8.07% 10.95% 13.70% 16.25%
12 6.73% 9.39% 11.99% 14.45%

Your Sevens-to-Rolls Ratio (SRR) establishes the survival-rate of your Inside-Number bet simply because it determines, on average, how likely your hand will be able to stay alive on a roll-to-roll basis.

Expected Win-Rate

If we know the survival-rate for an Inside-bet based on a shooters Sevens-to-Rolls ratio; then we can calculate his expected average win-rate on a roll-by-roll basis too.

For example:

  • The SRR-6 random-shooter will always be in a negative-expectation position, as we already knew; and no matter what he does with that wager, it will always remain on the negative side of the profit-expectancy curve.
Expected Win-Rate $22-Inside
Expected Profit/Roll Random SRR 6 SRR 7 SRR 8 SRR 9
1 (-$0.17) $0.44 $0.89 $1.25
2 (-$0.08) $0.44 $0.84
3 $0.04 $0.48
4 (-$0.31) $0.16
5 (-$0.14)

On the other hand

  1. The SRR-7 shooter actually has a strong and positive expectation on his first point-cycle roll. Unfortunately, if he doesn't hit an Inside-Number payer on that first post Come-Out roll; then things start to look fairly bad for him or at least for his money. In this case, a strong argument could be made, that it is in his best interests to use a very quick and steep regression for his Inside-Number wager. For example, since his shooting only puts him in positive-expectation territory on the first point-cycle roll of this particular $22-Inside bet; then an Initial Steep Regression that secures a quick and early profit is called for.
  2. The SRR-8 dice-influencer fairs better, and for a longer period of time (as measured by the number of point-cycle rolls) than his SRR-6 or SRR-7 counterparts. His skilled shooting keeps him in positive territory for his first three point-cycle rolls. Therefore, this shooter could reasonably consider taking two or possibly even three winning hits at the initial large-bet portion of his Inside-Number wager before regressing it down to a lower amount.
  3. The SRR-9 precision-shooter clearly enjoys an even greater amount of bet-making flexibility. Since his first four point-cycle rolls are in strong positive-expectation territory for this particular bet, he should obviously consider leaving his initial large Inside-Number wager up for those first four rolls before regressing them.

Show Me The Money

So how do we figure out how much our initial large-bet Inside-Number wager will make for us, and how do we figure out the best time to regress?

We simply multiply the amount of money we want to use as our initial large-bet Inside-Number wager by the Expected profit-per-roll Win-Rate.

Inside-Bet Win-Rate Expected Profit-per-Dollar Wagered
Expected Profit / Roll Random SRR 6 SRR 7 SRR 8 SRR 9
1 (-0.8¢) 2.0¢ 4.0¢ 5.7¢
2 (-0.4¢) 2.0¢ 3.8¢
3 0.2¢ 2.2¢
4 (-1.4¢) 0.7¢
5 (-0.6¢)

That chart tells us, on average, how much money we can reasonably expect to make:

  1. For each point-cycle roll that we throw.
  2. For each Inside-Bet dollar that we wager.
  3. How long our wager stays in positive-expectation territory.

Please note that all figures in these charts were rounded off.

Expected Profit-per-Roll SRR-7
Expected Profit/Roll $22-Inside $44-Inside $88-Inside $110-Inside
1 $0.44 $0.88 $1.76 $2.20
2 (-$0.08) (-$0.17) (-$0.35) (-$0.44)
Expected Profit-per-Roll SRR-8
Expected Profit/Roll $22-Inside $44-Inside $88-Inside $110-Inside
1 $0.88 $1.76 $3.52 $4.40
2 $0.44 $0.88 $1.76 $2.20
3 $0.04 $0.08 $0.16 $0.20
4 (-$0.31) (-$0.62) (-$1.24) (-$1.55)
Expected Profit-per-Roll SRR-9
Expected Profit/Roll $22-Inside $44-Inside $88-Inside $110-Inside
1 $1.25 $2.50 $5.00 $6.25
2 $0.84 $1.68 $3.36 $4.20
3 $0.48 $0.96 $1.92 $2.40
4 $0.16 $0.32 $0.64 $0.80
5 (-$0.13) (-$0.27) (-$0.56) (-$0.68)

Part Four of this series looks at how all of this applies to practical real-world casino betting, and how best to apply what you've learned when it comes to putting your advantage-play money into action. I hope you'll join me for that.

Until then,

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


The Mad Professor

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This page contains a single entry from the blog posted on January 3, 2007 2:46 AM.

The previous post in this blog was Ask the Mad Professor - Part 2.

The next post in this blog is Part 7: Not a Puppy Anymore, the Hunt Gets Serious.

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

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