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Regression Avoids Depression - Part 9

I Shouldn't Be Surprised, but I'm Still Amazed

I'll tell you quite frankly, I find it funny when a player says that he tried using a regression-style bet a time or two, but it didn't work out, so he decided to never try it again.

I wonder to myself if that same player abandoned Passline-wagers, Place-bets, Odds bets, and Come-bets just as quickly when they lost a time or two, but I know better than to ask.

  1. Without doubt, the cost of losing one big initial pre-regression bet can cause a momentary twinge of pain, yet many players will endure countless Place-bet losses and Come-bet losses for many times more money over time, and gladly endure that with a smile.
  2. When asked how much profit their current flat-bet Place-wagering or Come-betting is making for them, they usually reply that it's not yet net-profitable because it usually takes too many hits for those wagers to consistently get over the profit-making hump despite the multiple winning-hits that their dice-influencing skills currently yield.
  3. When I point out that their current SRR justifies the use of an appropriately sized Initial Steep Regression (ISR) that would turn their mediocre break-even bet-results into consistently profitable ones; they simply state that they can't afford to take one big loss; yet they'll continually let the casino slowly chisel and erode their entire bankroll on multi-hit-requirement bets despite their obviously significant dice-influencing edge over the house.

Like I said, some people like to gamble, and some people like to win. In most cases, the difference between winning and losing, regardless of whether you are the world's GREATEST Precision-Shooter or just slightly better than a random-roller; STILL comes down to how you wager your money.

  • If you have an edge, you have to bet it in an exploitable way. For a modestly skilled dice-influencer, Steep Regressions offer a tangible way to turn some of the casinos money into YOUR money.

If you are steadily losing money with flat or pressed-up Place-bets or Come-bets, yet you know that you almost always hit at least one of your normal Place-bet wagers during most hands; then you can afford an ISR that is tailored to suit your skill-level, your SRR-rate, your bankroll limitations, your win-objectives and your personal bet-comfort level.

Winning the most money for the least risk is what this series is all about.

The Iron-Cross

In a random outcome game, the Anything-but-7 Iron Cross wager constitutes 83.33% of all possible outcomes. The Iron Cross (also known as the Umbrella bet) covers all the numbers on the table (2, 3, 4, 5, 6, 8, 9, 10, 11, and 12) except the 7. In this scenario, you would bet one unit each on the 5, 6, 8 and Field.

In the ongoing You Can't Shine A Cow-Patty Or Can You? series, we look at the Iron Cross in a wholly unconventional money-winning way.  Right now though, we are going to investigate whether the Iron Cross can benefit from the use an Initial Steep Regression.

There is:

  1. One way to make the 2, and in most casinos it pays out at 2:1 on the Field.
  2. Two ways to make the 3, and it pays even-money on the Field.
  3. Three ways to make a 4, and it pays even-money on the Field.
  4. Four ways to make a 5, and the Place-bet pays 7:5, but when it hits, your Field-bet loses so it has to be replaced.
  5. Five ways to make a 6, and the Place-bet pays 7:6, but when it hits, your Field-bet also loses so it has to be replaced.
  6. Five ways to make an 8, and the Place-bet pays 7:6, but when it hits, your Field-bet loses so it too has to be replaced.
  7. Four ways to make a 9, and it pays even-money on the Field.
  8. Three ways to make a 10, and it pays even-money on the Field.
  9. Two ways to make the 11, and it pays even-money on the Field.
  10. One way to make the 12, and in most casinos it pays out at either 2:1 or 3:1 on the Field. For this exercise, we'll calculate its winning payouts at 3:1.

Therefore, the Iron Cross wager constitutes 30-out-of-36 (83.33%) of all randomly-expected outcomes, and its average weighted-payout for a $5 ($22 Iron Cross) bettor is $4.10 per hit.

Why is the payout less than even-money when you have so many winning hits?

Well, even though you have single-unit wagers on the 5, 6, and 8; their net-payout (after you replace your Field-bet which loses when the 5, 6, or 8 wins), is a paltry $2 for each non-Field outcome. Since the 5, 6, and 8 constitute fourteen out of your thirty winning Iron Cross outcomes, the steady replacement of Field-bets has a pernicious way of diluting your overall per-hit win-rate. Still though, let's see how that $4.10 average weighted-payout for the Iron Cross fairs in the hands of a dice-influencer.

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
Probability 16.67% 14.29% 12.5% 11.11%
7's-per-36 rolls 6 5.14 4.5 4
Iron Cross-to-Sevens Ratio
Random SRR 6 SRR 7 SRR 8 SRR 9
Iron Cross to Total Outcomes 30 out of 36 30.86 31.5 32 out of 36
Per-Roll Probability 83.33% 85.72% 87.50% 88.89%
Iron Cross to 7's Ratio 5:1 6:1 7:1 8:1

Anatomy Of An Iron-Cross Wager

Iron Cross Flat-bet Repayment Rate
Iron Cross Hits Total Investment Weighted Payout Return on Investment Profit
0 $22 $0 0% (-$22.00)
1 - $4.10 18.64% (-$17.90)
2 - $4.10 32.27% (-$13.80)
3 - $4.10 55.91% (-$9.70)
4 - $4.10 74.55% (-$5.60)
5 - $4.10 93.18% (-$1.50)
6 - $4.10 111.82% $2.60

As with any other bet, a random-roller still has a greater chance of 7'ing-Out than he has of hitting enough Iron Cross bets for it to pay for itself on a consistent basis. That is the nature of ANY randomly-based bets that you make.

As a flat-betting advantage-player, it takes an average of six winning same-bet hits before this $22 Iron Cross wager breaks into profitability. Fortunately, in the hands of a modestly skilled dice-influencer, the Iron Cross can be a steady profit contributor to your bankroll, even if you do decide to strictly adhere to flat-bets. Take a look:

$22Iron Cross Expected Flat-bet Win-Rate
Expected Profit/Roll Random SRR 6 SRR 7 SRR 8 SRR 9
Iron Cross-to-7's Ratio 5:1 6:1 7:1 8:1
1 $4.10 $4.10 $4.10 $4.10
2 $4.10 $4.10 $4.10 $4.10
3 $4.10 $4.10 $4.10 $4.10
4 $4.10 $4.10 $4.10 $4.10
5 $4.10 $4.10 $4.10 $4.10
6 - $4.10 $4.10 $4.10
7 - - $4.10 $4.10
8 - - - $4.10
Total Expected Payout $20.50 $24.60 $28.70 $32.80
Remaining Wager $22.00 $22.00 $22.00 $22.00
Net-Profit -$1.50 $2.60 $6.70 $10.80
Return-on-Investment -6.82% 11.82% 30.45% 49.09%

As with Inside-Numbers, All-Across, Outside, and Even-Number global-type wagers; your Sevens-to-Rolls Ratio largely determines the average roll-duration of your Iron Cross bet too.  Equally, your SRR also determines the bet-survival decay-rate of your validated edge against any given wager and therefore establishes the optimal time to regress your initially large bet into a smaller, lower-value one.

As we've seen in previous chapters, the per-roll decay-rate is different for each SRR-rate as well as for each type of global wager.

Iron Cross Bet Survival-Rate
Iron Cross Hit-rate Random SRR 6 SRR 7 SRR 8 SRR 9
1 83.33% 85.72% 87.50% 88.89%
2 69.44% 73.47% 76.56% 79.01%
3 57.86% 62.97% 66.99% 70.24%
4 48.22% 53.97% 58.62% 62.43%
5 40.18% 46.26% 51.29% 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% 24.97% 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%

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. In the case of the Iron Cross, you get 100% efficiency with that reduced-7's replacement-rate simply because the Iron Cross includes all of the other possible non-7 outcomes.
  2. Therefore, a reduced 7's appearance-rate means an increased winning-bet rate, and that holds especially true for such an all-encompassing wager like the Anything-but-7 Iron Cross.
  3. 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. Since the Iron Cross covers every number except the 7; the beneficial impact of less 7's is much more direct for the I-C than it is for less-encompassing (less-inclusive, fewer covered numbers) types of global bets like the Inside, Across, Outside or Even-Number wagers.
  4. 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.

Although your Sevens-to-Rolls ratio is not the only dice-influencing metric that matters, many dice-influencers often underutilize it when it comes to shaping and structuring betting-methods and their related same-bet, press or regress trigger-points.

If you ignore or dismiss your SRR-rate; you are not only overlooking your best indicator of average hand-duration, but you are also rejecting the best gauge by which to successfully structure a consistently productive multi-number betting-method.

Intelligent advantage-players aren't so quick to turn their backs on such an important profit-patterning benchmark.

If you ignore what your skill-based sevens-appearance-rate is trying to tell you; then don't be surprised if consistently produceable profit ignores you too.

As we've discussed before:

  1. If we know how long our hand generally stays in positive-expectation territory for the Iron Cross wager; 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. Even though advantage-play Kelly-style flat-betting can produce a net-profit for us; in most cases, 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; and obviously 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 for the Iron Cross correctly factors in the modified sevens-appearance-rate for any given SRR; which in turn then produces 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 $110 on the Iron Cross versus the use of an initial $110 Iron Cross wager that is steeply regressed to a $22 Iron Cross at the appropriate trigger-point. For greater clarity, a $110 Iron Cross is spread out as follows:

  1. $25 on the Field.
  2. $25 on the Place-bet 5.
  3. $30 on the Place-bet 6.
  4. $30 on the Place-bet 6.

A $22 Iron Cross is spread out as follows:

  1. $5 on the Field.
  2. $5 on the Place-bet 5.
  3. $6 on the Place-bet 6.
  4. $6 on the Place-bet 6.
Flat-betting $110 Iron Cross Return-on-Investment
Random SRR 6 SRR 7 SRR 8 SRR 9
Iron Cross-to-7's Ratio 5:1 6:1 7:1 8:1
Flat Bet $110.00 $110.00 $110.00 $110.00
Single-hit Weighted-Payout $20.50 $20.50 $20.50 $20.50
Expected Total Payout $102.50 $123.00 $143.50 $164.00
Remaining Exposed Wagers $110.00 $110.00 $110.00 $110.00
Net-Profit -$7.50 $13.00 $33.50 $54.00
Return-on-Investment -6.8% 11.8% 30.5% 49.1%

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 should take place.

Initial Steep Regression $110 Iron Cross Regressed at Optimal Trigger-Point to $22 Iron Cross Return-on-Investment
SRR 7 SRR 8 SRR 9
Iron Cross-to-7's Ratio 6:1 7:1 8:1
Initial Large Bet $110.00 $110.00 $110.00
Subsequent Small Bet $22.00 $22.00 $22.00
1st Hit $20.50 $20.50 $20.50
2nd Hit $20.50 $20.50 $20.50
3rd Hit Post Regression $2.58 Weighted payout $20.50 $20.50
4th Hit - Post Regression $2.40 Weighted payout $20.50
5th Hit - - Post Regression $2.28 Weighted payout
Total Expected Payout $43.58 $63.90 $84.28
Remaining Exposed Wagers $22.00 $22.00 $22.00
Net-Profit per-Hand $21.58 $41.90 $62.28
Return-on- Investment 19.62% 38.09% 56.62%

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

$110 Iron Cross Flat-bet vs. $110 Iron Cross Regressed to $22 Iron Cross
SRR 7 SRR 8 SRR 9
$110 Iron Cross Flat-bet Net-Profit/Hand $13.00 $33.50 $54.00
$110 Iron Cross Regressed to $22 Iron Cross Profit/Hand $21.58 $41.90 $62.28
$-Difference $8.58 $8.40 $8.28
Increased Return-on-Investment 37.8% 20% 13.3%

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.

Iron Cross Profit Projections using various Steepness Ratios SRR-7
Ratio 2:1 3:1 4:1 5:1 10:1
Initial Large Bet $44 $66 $88 $110 $220
Subsequent Small Bet $22 $22 $22 $22 $22
1st Hit Weighted Value $8.20 Weighted Value $12.30 Weighted Value $16.40 Weighted Value $20.50 Weighted Value $41.00
2nd Hit $8.20 $12.30 $16.40 $20.50 $41.00
3rd Hit Post Regression $2.58 Weighted payout Post Regression $2.58 Weighted payout Post Regression $2.58 Weighted payout Post Regression $2.58 Weighted payout Post Regression $2.58 Weighted payout
Total Expected Payout $18.98 $27.18 $35.85 $43.58 $84.58
Remaining Exposed Wagers $22.00 $22.00 $22.00 $22.00 $22.00
Net-Profit -$3.02 $5.18 $13.38 $21.58 $62.58
Return-on- Investment -6.86% 7.85% 15.20% 19.62% 28.45%

The risk of using too shallow of a regression demonstrates itself with the SRR-7 shooter who uses an initial $44 Iron Cross that gets regressed down to a $22 I-C. However, by simply increasing his ISR steepness-ratio from 2:1 to 3:1, he immediately regains profitability. Once again, we see how critically important it is to structure our bets properly.

"Better that random" does not automatically mean better profit.

Having an edge over the house does NOT mean that money will start to automatically flow in our direction. We have to intentionally divert it that way through the use of properly structured wagers.

As your SRR-rate improves, so too does your return on investment, even when you are using a shallow 2:1 regression ratio.

Iron Cross Profit Projections using various Steepness Ratios SRR-8
Ratio 2:1 3:1 4:1 5:1 10:1
Initial Large Bet $44 $66 $88 $110 $220
Subsequent Small Bet $22 $22 $22 $22 $22
1st Hit Weighted Value $8.20 Weighted Value $12.30 Weighted Value $16.40 Weighted Value $20.50 Weighted Value $41.00
2nd Hit $8.20 $12.30 $16.40 $20.50 $41.00
3rd Hit $8.20 $12.30 $16.40 $20.50 $41.00
4th Hit Post Regression $2.40 Weighted payout Post Regression $2.40 Weighted payout Post Regression $2.40 Weighted payout Post Regression $2.40 Weighted payout Post Regression $2.40 Weighted payout
Total Expected Payout $27.00 $39.30 $51.60 $63.90 $125.40
Remaining Exposed Wagers $22.00 $22.00 $22.00 $22.00 $22.00
Net-Profit $5.00 $17.30 $29.60 $41.90 $103.40
Return-on- Investment 11.36% 26.21% 33.37% 38.09% 47.00%

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 two hits; the SRR-8 dice-influencer can reasonably keep them up at their initial large size for the first three point-cycle rolls before needing to steeply regress them. In the case of a SRR-9 shooter using the Iron Cross bet that we've been discussing today, he'll generally get the benefit of four pre-regression hits before optimally reducing his bet-exposure.

Iron Cross Profit Projections using various Steepness Ratio SRR-9
Ratio 2:1 3:1 4:1 5:1 10:1
Initial Large Bet $44 $66 $88 $110 $220
Subsequent Small Bet $22 $22 $22 $22 $22
1st Hit Weighted Value $8.20 Weighted Value $12.30 Weighted Value $16.40 Weighted Value $20.50 Weighted Value $41.00
2nd Hit $8.20 $12.30 $16.40 $20.50 $41.00
3rd Hit $8.20 $12.30 $16.40 $20.50 $41.00
4th Hit $8.20 $12.30 $16.40 $20.50 $41.00
5th Hit Post Regression $2.28 Weighted payout Post Regression $2.28 Weighted payout Post Regression $2.28 Weighted payout Post Regression $2.28 Weighted payout Post Regression $2.28 Weighted payout
Total Expected Payout $35.08 $51.48 $67.88 $84.28 $166.28
Remaining Exposed Wagers $22.00 $22.00 $22.00 $22.00 $22.00
Net-Profit $13.08 $29.48 $45.88 $62.28 $144.28
Return-on- Investment 29.73% 44.67% 52.14% 56.62% 65.58%

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 9, 2007 3:29 AM.

The previous post in this blog was Mad Professor’s Mini-Table Craps Tour with the Vegas Ghost - Part 8.

The next post in this blog is Ask the Mad Professor - Part 9.

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