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Regression Avoids Depression: Part Two

For the longest time now, immigrants from the advantage-play blackjack community have been saying that regression-style wagering is not applicable to craps (or any other form of gambling) even if you have an edge over the casino. They reason that your edge is steady from one roll to the next, and therefore your bets should remain steady as well; so that precludes any wagering ideas that involve any form of bet-decreasing or bet-increasing.

As I've been saying all along, regression-betting IS validly applicable to dice-influencing. Just as they were wrong about the entire notion that dice-influencing couldn't, wouldn't or shouldn't work; they are wrong now about the prohibition against regression-betting too.

You Wanted Proof You've Got It

The randomly-expected 6-out-of-36 appearance-rate for the "7" produces an overall Sevens-to-Rolls Ratio (SRR) of 1:6.

  1. That equates to a 7's expectancy-rate of 16.67% on any given roll.
  2. Expressed another way; that means the expectancy-rate of not rolling a seven is 83.33%.

As dicesetters, we have come to recognize that we can influence the dice to the point where we actually affect the randomly-expected distribution of those outcomes. One of the ways to measure that influence is through our Sevens-to-Rolls Ratio (SRR).

The more we can avoid the 7, the more we can exploit the other numbers that are appearing in its stead.

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

The less 7's we have to contend with in our personally reconfigured outcome distribution chart; the more we are able to exploit the dice results we actually produce. Though our SRR is not the be-all and end-all of our dice-influencing skills; it does give us a strong foundation upon which we can configure fundamental betting strategies.

That is, if we know how many rolls per point-cycle we have to deal with, and for example, how many Inside-numbers we will generally hit before 7'ing-Out; the better prepared we are to utilize our dice-influencing abilities to their fullest.

Let's do a side-by side comparison between a random SRR-6 roller and a modestly-skilled SRR-7 dice-influencer, an SRR-8 guy and a SRR-9 precision-shooter, to see how far each can confidently get in their respective expected roll-durations.

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%

A "point-cycle roll" is one that occurs after you first establish the Passline-Point but before you either repeat your PL-Point or you 7-Out. If let's say, you establish the 6 as your PL-Point, and you subsequently roll a 5, an 11, a 9, a 10, and a 7; then the 5 was your first point-cycle roll, while the 11 was your second point-cycle roll, and the 9 was your third. The 7-Out occurred on the fifth point-cycle roll.

As you can see from the chart above, the random-roller will get in at least one point-cycle roll before 7'ing-Out, about 83% of the time; while the chances of him getting to his second, third and fourth roll drops precipitously.

By skillfully avoiding the 7, the ascending-order dice-influencers enjoy an increasingly wider margin over the random-expectancy of a short-lived hand. However, it is obvious that each skill-level of shooter still has a limited time (as measured by the number of point-cycle rolls) in which to have his bets fully pay for themselves and ultimately produce a net-profit regardless of (or rather, in full recognition of) his respective SRR-rate.

Now to be clear, a random-rollers chance of throwing a 7 remains rock-steady on a per-roll basis at 1-in-6 (16.67%). The problem however is with the cumulative effect of such a high-percentage occurrence. That means that the snowballing effect of roll-after-roll-after-roll 7-avoidance mathematically gangs up and ultimately conspires against the likelihood of frequent long hands. Although long, randomly-tossed mega-rolls sometimes do occur; they are noteworthy because of their unusual length and infrequent appearance, and that is why even regression-style betting cannot overcome the house-edge in a randomly-thrown game.

In a random outcome game, Inside-Numbers constitute 50% of all possible outcomes:

  1. Four way to make a 5
  2. Five ways to make a 6
  3. Five ways to make an 8
  4. Four ways to make a 9

Therefore, Inside-numbers constitute 18-out-of-36 (50%) of all randomly-expected outcomes.

With eighteen Inside-number outcomes for every six 7-Out results, that 3:1 Inside-numbers-to-Sevens ratio at first blush seems like a pretty good hit-rate. Take a look at how a dice-influencers skill-set improves upon that ratio and ultimately puts him into the drivers seat.

Inside-Numbers to Sevens
Random SRR 6 SRR 7 SRR 8 SRR 9
Inside-Numbers 18-of-36 18.43 18.75 19-of-36
Per-Roll Probability 50.00% 51.19% 52.08% 52.78%
Inside-Numbers-to-7's Ratio 3:1 3.6:1 4.1:1 4.75:1

Based on this, we can make some general observations about how many Inside-numbers each player will hit based upon his skill-level. From there we can determine how often an Inside-number might occur for each of these SRR-rates, and how far each player can be expected to go during an average hand.

Now clearly you should be looking at your SPECIFIC Foundation Frequency and Signature Number outcomes to personalize this chart, but here is how it looks if you have an even distribution across all of the other non-7 outcomes.

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%

As you can see for the SRR-6 shooter, the Inside-Numbers expectancy-rate declines precipitously on each and every subsequent point-cycle toss, which explains just why it is so hard from a random-roller to get anywhere with any type of betting. On the other hand, as a dice-influencers skill improves, so does the average duration and Inside-Number hit-rate of his rolls.

Since the 7 is the most dominant of the eleven possible two-die outcomes, we know that long rolls are possible, but they are far outnumbered by many more short ones. The savvy advantage-player recognizes this and can ultimately exploit it through the use of an Initial Steep Regression.

By utilizing the exact same proven methodology that the math-guys do to figure out random-expectancy roll-duration; we can use that very same process to figure out the average duration of a dice-influenced 7-avoidance hand, thereby giving us a basis upon which to properly structure a geared-to-skill Initial Steep Regression too.

In Part Three of this series, I'm going to show you a number of innovative ways to profitably utilize what we have covered today.

Until then,

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 2, 2007 12:27 AM.

The previous post in this blog was Part 9: Give That Dog A Bone.

The next post in this blog is Part 8: Taking a Class.

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

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