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Regression Avoids Depression - Part 15

The main reason I wanted to share the mathematically-based efficacy of Steep Regression exploitability in this series, is so that other players who are still a little skeptical about its use might finally be able to bridge the frustratingly difficult advantage-play chasm between their validated dice-influencing skill and the inconsistency of their redeemable profit.

The concept of regression-betting is nothing new; John Patrick has been writing about it for years. Even in the Precision-Shooting context, consistently profitable ISR's have been widely used by talented players for close to two decades now.

Utilizing the fattest, most frequently occurring part of your roll-duration expectancy-curve allows to you capture your rightfully earned profit much sooner and more often.

It's Your Edge, It's Your Money, and It's Your Opportunity

and what you do with it is entirely up to you.

Let's say that you have a validated Sevens-to-Rolls Ratio of 1:7 (SRR-7), and your properly financed bankroll indicates that either a $110-Inside bet (covering the 5, 6, 8, and 9) or a $110-Even (covering the 4, 6, 8, and 10) would be an appropriately-sized wager to make.

To determine which of those two bet-types will provide the best return on investment, you should do a side-by-side comparison of Initial Steep Regressions (ISR's) versus Flat-betting.

Let's take a comparative look at how each of those bets stack up against each other for a SRR-7 shooter:

Average Net-Profit per-hand ISR-betting versus Flat-betting SRR-7
Bet-Method $110-Inside to $22-Inside vs. $110-Inside Flat-bet $160- Across to $32- Across vs. $160 Across Flat-bet $100-Outside to $20- Outside vs. $100- Outside Flat-bet $110-Even to $22-Even vs. $110-Even Flat-bet $110-Iron Cross to $22-Iron Cross vs. $110-Iron Cross Flat-bet
Initial Steep Regression $19.92 $52.34 $24.38 $25.77 $21.58
Flat-betting $16.00 $24.80 $2.79 $18.80 $13.00
$-Difference $3.92 $27.54 $21.59 $6.97 $8.58
%-Difference 19.68% 52.61% 88.56% 27.04% 39.76%

Although the use of Initial Steep Regressions are clearly superior to comparably-sized Flat-bets, an advantage-player still has to look at the specific bet-type that will provide the best return-on-investment too.

So, not only does the savvy dice-influencer do a side-by-side comparison of Initial Steep Regressions (ISR's) versus Flat-betting, but he also does that same side-by-side comparison between each of those two ISR bet-types as well.

For example, in the SRR-7 chart we see that although the $110-Inside-regressed-to-$22-Inside wager provides a nice average-profit of $19.92 per-hand; the same money wagered on $110-Even-regressed-to-$22-Even provides an even better average-profit of $25.77 per hand. Needless to say, a 29% R.O.I. difference per-hand has a definite way of building session-revenue in a measurably significant way.

Take a look at how SRR-rates not only affect the broad difference between Flat-betting and Steep Regression betting, but also note the difference between each bet-type when the dice are in the hands of an SRR-8 shooter:

Average Net-Profit per-hand ISR-betting versus Flat-betting SRR-8
Bet-Method $110-Inside to $22-Inside vs. $110-Inside Flat-bet $160- Across to $32- Across vs. $160- Across Flat-bet $100-Outside to $20- Outside vs. $100- Outside Flat-bet $110-Even to $22-Even vs. $110-Even Flat-bet $110-Iron Cross to $22-Iron Cross vs. $110-Iron Cross Flat-bet
Initial Steep Regression $89.69 $90.52 $61.24 $105.57 $41.90
Flat-betting $33.50 $55.60 $21.14 $40.13 $33.50
$-Difference $56.19 $34.92 $40.10 $65.44 $8.40
%-Difference 62.65% 38.58% 65.48% 61.98% 20.04%

There is a ton of hidden value in these charts, for example:

Notice what happens (or rather, doesn't happen) when this SRR-8 shooter flat-bets $110-Inside compared to flat-betting a $110 Iron Cross. Both of those bets generate the same average per-hand profit of $33.50 each.

Now compare those same two bet-types in the hands of a similarly skilled ISR-bettor.

Not only does each ISR bet-type now make more money than the flat-bets do, but there is also a dramatic difference between the money that those two bets make in their respective ISR-modes $89.69 in average per-hand net-profit for the $110-Inside-regressed-to-$22-Inside bettor compared to only $41.90 for the $110-Iron-Cross-regressed-to-$22-Iron-Cross bettor.

So although each of the two flat-bets made the same money ($33.50 average net-profit per-hand) on the Inside and Iron Cross wagers; the use of an Initial Steep Regression not only boosted net-profit performance by a significant margin (by over 62% in the case of ISR-Inside vs. Flat-Inside bet, and 20% in the case of ISR-Iron Cross vs. the Flat-Iron Cross); but there was also a dramatic difference between the two ISR wager-types themselves.

The point of all this of course is to illustrate once again that you have to carefully consider not only whether or not ISR-betting is appropriate for you, but also whether one particular bet-type is more suited to your validated skill-level than another.

As your dice-influencing skill improves, that bet-type/average-profit disparity reveals itself more and more. Take a look

Average Net-Profit per-hand ISR-betting versus Flat-betting SRR-9
Bet-Method $110-Inside to $22-Inside vs. $110-Inside Flat-bet $160- Across to $32- Across vs. $160- Across Flat-bet $100-Outside to $20- Outside vs. $100- Outside Flat-bet $110-Even to $22-Even vs. $110-Even Flat-bet $110-Iron Cross to $22-Iron Cross vs. $110-Iron Cross Flat-bet
Initial Steep Regression $124.86 $129.27 $134.53 $146.27 $62.28
Flat-betting $56.25 $86.40 $35.83 $61.87 $54.00
$-Difference $68.61 $42.87 $98.70 $84.40 $8.28
%-Difference 54.94% 33.16% 73.37% 57.70% 13.29%

Each of these charts clearly illustrate how superior an ISR Steepness Ratio of 5:1 compares when matched up against a similarly sized flat-bet; so let's look at how the steepness of any given regression-bet can also affect each bet-type's overall profitability.

Defining Steepness Ratios

When we talk about ISR Steepness Ratios, we are really talking about the difference of size between the initial pre-regression LARGE wager and the subsequent Post Regression SMALL wager.

For example, if you wagered $12 each on the 6 and 8 Place-bet, and then after one paying-hit regressed both of them down to $6 each, then you have used a 2:1 ISR Steepness Ratio.

If you started with $18 each on the 6 and 8 and then regressed them to $6 each then you have employed a 3:1 ISR Steepness Ratio.

Some players even use a two or three-stage regression. For example, if you started off with $220-Inside and regressed it down to $110-Inside after one hit, and then further regressed it down to $44-Inside after the next hit; then you have used a 10:5:2 regression.

For simplicity of understanding I always use the basic $5-or-$6-per-number-wagered amount to signify the ":1" of the ratio. For example the standard $22-Inside wager constitutes the ":1" when we are talking about that bet-type, so a 5:1 ratio would indicate a $110-Inside-to-$22-Inside regression. Likewise, a $330-Inside-to-$66-Inside regression still represents a 5:1 ratio.

Steepness Ratio Comparison

As you can see on this first chart for SRR-7 shooters, a shallow steepness ratio of 2:1 for both the Inside-ISR and the Iron-Cross ISR leaves this player in a negative position even though he has a substantial edge over the casino. By simply sharpening the steepness-ratio to 3:1 or higher, the SRR-7 shooter regains per-hand profitability.

Steepness Ratio Comparison of Profit per-hand SRR-7
Steepness Ratio Inside Across Outside Even Iron Cross
2:1 -$1.08 $5.34 $3.39 $1.02 -$3.02
3:1 $5.92 $20.34 $11.25 $8.77 $5.18
4:1 $12.92 $36.84 $20.38 $17.65 $13.38
5:1 $19.92 $52.34 $24.38 $25.77 $21.58
10:1 $54.92 $129.34 $61.09 $66.02 $62.58

The steeper the regression-ratio is; the higher, earlier and more often a net-profit will be secured.

The shallower the regression-ratio is; the less frequent and lower your net-profit will be.

When you take that concept to the extreme and don't use ANY regression at all (theoretically a 1:1 steepness ratio); then your comparable shooting-skill profit takes a lot longer to get, and the chase certainly becomes less consistent and more volatile.

Steepness Ratio Comparison of Profit per-hand SRR-8
Steepness Ratio Inside Across Outside Even Iron Cross
2:1 $26.69 $20.02 $19.26 $31.32 $5.00
3:1 $47.69 $42.54 $34.98 $54.57 $17.30
4:1 $68.69 $67.27 $53.24 $81.21 $29.60
5:1 $89.69 $90.52 $61.24 $105.57 $41.90
10:1 $194.69 $206.02 $134.66 $226.32 $103.40

Again, the higher your SRR improves over random, the higher your rate-of-return on each of your validated-edge wagers 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.

Steepness Ratio Comparison of Profit per-hand SRR-9
Steepness Ratio Inside Across Outside Even Iron Cross
2:1 $40.86 $35.27 $50.57 $47.27 $13.08
3:1 $68.86 $65.27 $82.01 $78.27 $29.48
4:1 $96.86 $98.27 $118.53 $113.79 $45.88
5:1 $124.86 $129.27 $134.53 $146.27 $62.28
10:1 $264.86 $283.27 $281.37 $307.27 $144.28

How ISR's Offer Better Profit Dependability

If a player has a fairly good dice-tossing consistency, yet he has a hard time getting to any level of revenue-consistency; then chances are, he hasn't properly matched his shooting prowess with his betting prowess.

ISR's are especially useful to players who have developed a modest ability to influence the dice, but haven't yet been able to turn their skills into steady earnings.

With the use of Initial Steep Regressions, a novice player can reap a larger degree of the rewards that his de-randomized throws are offering; while an advanced player can extract even more income from his current skill-set on a much more predictable basis...with each player accomplishing his profit-objectives more often and with less overall risk than flat Kelly-style wagering does.

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 15, 2007 3:40 AM.

The previous post in this blog was FAQ’s About The Choppy-Table/Short-Leash Method - Part 3.

The next post in this blog is The Match-Play Coupon Circuit - Part 3.

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

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