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Regression Avoids Depression: Part Four

Reconciling Win-Rate With Roll-Survival Rate

If we look at strictly flat-betting a wager like $22-Inside, we know that it takes several hits to pay for itself before finally emerging with a profit:

$22-Inside Payout Rate
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

For a straight, non-pressed, non-regressed $22-Inside wager, it takes four winning hits before it pays for itself and delivers a profit. Unfortunately, when using that method, a random-roller always stays on the negative side of the equation because the Inside-Numbers-to-Sevens Ratio is 3:1, and it takes more than three hits just to earn your money back.

Likewise, it is important to note that our roll-duration and bet-survival rate is almost opposite to each other.

  1. The longer (the more rolls) it takes for a flat-bet like $22-Inside to pay for itself; the more likely it is to fall short of producing a net-profit.
  2. By the same token, the higher our Sevens-to-Rolls Ratio is, the longer our bets can stay out on the layout to produce a net-profit.
  3. The lower and closer our SRR is to random; then the more condensed our time to harvest a net-profit will be.

Simply stated, a higher SRR gives us more rolls to work with, while a lower SRR reduces our useable number of point-cycle rolls.

The primary way to ascertain the appropriate regression-point in our hand is determined by our Sevens-to-Roll ratio, simply because our SRR is the chief determinant of how long, on average, our point-cycle will last.

This Won't Take Long Did It

Again, when measured on a per-roll basis, our ability to avoid the 7 remains constant.

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
  1. For a random-roller, it remains at 16.67% on each and every toss. However, his chances of having one, two, three, four or more rolls without a 7 decreases simply because of the cumulative nature of the 7-occurrence rate.
  2. For the SRR-7 shooter, the sevens-appearance-rate is 14.29%. As a result, his chances of having one, two, three, four or more rolls without a 7, increases slightly due to the faintly less cumulative nature of his 7-occurrence rate.
  3. Likewise for the skilled SRR-8 shooter, his per-roll sevens-appearance-rate is 12.5%. Therefore, his chances of having one, two, three, four or more rolls without a 7 increases significantly when compared to a SRR-6 random-roller, due to his lower cumulative 7's occurrence-rate.
  4. More over, the SRR-9 Precision-Shooter enjoys an 11.11% sevens-appearance-rate on a per-roll basis. As a result, his chances of having one, two, three, four or more rolls without a 7, increases dramatically when compared to random expectation because of his much lower cumulative 7's occurrence-rate.

When a dice-influencer looks at his skills, he obviously has to include his ability to avoid the 7 into that calculation matrix.

  1. A player's ability to avoid the 7 determines how long, on average, his point-cycle roll will usually last.
  2. Again, we are talking averages here, so that range includes everything from all of his point-then-7-Out hands to his rarer mega and mini-mammoth ones too.
  3. Our SRR determines how frequently the 7 is likely to show up, and by logical extension, it determines how many rolls on average we will have to profitably exploit any of our betting methods.

Knowing this is extremely important when it comes to considering global-type multi-number bets that require numerous hits before becoming net-profitable. Inside-Number wagers fall into this global category. As we will see in a moment, that is whythe use of steep regressions are so important to the net-profitability of skilled dice-influencers.

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

As I pointed out previously, your SRR and the frequency of Inside-Numbers that you produce within that range, will be somewhat different than the even-distribution examples that I've used here; however, these charts will give you a general idea of where some of your biggest profit-making opportunities can be found.

Expected Return-On-Investment for Flat-bet $22-Inside
Random SRR 6 SRR 7 SRR 8 SRR 9
Inside-Numbers-to-7's Ratio 3:1 3.6:1 4.1:1 4.75:1
Inside-Hit Payout/Total Wager $7/$22 $7/$22 $7/$22 $7/$22
Expected Total Payout $21.00 $25.20 $28.70 $33.25
Net-Profit -$1.00 $3.20 $6.70 $11.25
Return-on-Investment -4.54% 14.55% 30.45% 51.14%
  1. If we know how long our hand generally stays in positive-expectation territory for the Inside-Number bets we are making; then we can easily determine the ideal time to regress them from their initially high starting-value.
  2. Once we know where that positive-to-negative transition point is, we can regress our large initial wager down to a lower level and concurrently lock-in a net-profit while still providing us with active bets on the layout in the event that our hand-duration does exceed and survive that transition point, as it often will.

A Practical Comparison

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

Flat-betting $110-Inside Return-on-Investment
Random SRR 6 SRR 7 SRR 8 SRR 9
I-N's-to-7's 3:1 3.6:1 4.1:1 4.75:1
Initial Large Bet $110-Inside $110-Inside $110-Inside $110-Inside
Single-hit Payout $35 $35 $35 $35
Expected Flat-bet Total Payout $105.00 $126.00 $143.50 $166.25
Remaining Exposed Wagers $110.00 $110.00 $110.00 $110.00
Net-Profit -$5.00 $16.00 $33.50 $56.25
Return-on-Investment -4.54% 14.55% 30.45% 51.14%

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-Inside Regressed to $22-Inside Return-on-Investment
SRR 7 SRR 8 SRR 9
I-N's-to-7's 3.6:1 4.1:1 4.75:1
Initial Large Bet $110-Inside $110-Inside $110-Inside
Subsequent Small Bet $22-Inside $22-Inside $22-Inside
1st Hit $35 $35 $35
2nd Hit Post Regression $6.92 Weighted payout $35 $35
3rd Hit - $35 $35
4th Hit - Post Regression $6.69 Weighted payout $35
5th Hit - - Post Regression $6.86 Weighted payout
Total Expected Payout $41.92 $111.69 $146.86
Remaining Exposed Wagers $22.00 $22.00 $22.00
Net-Profit $19.92 $89.69 $124.86
Return-on- Investment 18.11% 81.54% 113.51%

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

$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%

I hope you'll join me for Part Five of this series. 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 4, 2007 3:47 AM.

The previous post in this blog was Ask the Mad Professor - Part 3.

The next post in this blog is Part 6: Putting in the Practice.

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