Regression Avoids Depression Part 16

Today we are taking a behind-the-scenes look at the process by which Steep Regressions work so well for advantage-players.

Effort IN…Profit OUT

If you don’t put the necessary effort INTO calculating your validated in-casino point-cycle SRR, then it makes it much tougher to extract your rightfully deserved profit OUT of it.

Steep Regressions let you take advantage of all but the shortest Point-then-7-Out hands by locking in an early profit on the first paying hit; yet it also lets you stay “in the game” (with multiple active wagers) in the event that you do manage to get a couple more, or even many more paying-hits.

You’ll find that the broader you spread your initial bets, the steeper the regression has to be to accomplish the same goal. For example, if you simply Place-bet the 8 for $12 and regress it to $6 after one hit; then you’d still have an $8 net-profit to show for it, even if the 7 shows up on the very next roll. However, if you make that same bet on both the 6 and the 8, then you’ll only have an in-rack net-profit of $2 (but of course you now have twice the amount of money still in action).

Likewise, as you spread out to $44-Inside ($12 each on the 6 & 8, and $10 each on the 5 & 9); one $14 paying-hit doesn’t leave ANY net-profit to work with while you still have all four Inside Numbers covered even if you regress them down to $22-Inside. 

In this case, you could reduce the breadth of your bets by just wagering on the 6 & 8 for $6 each, or you could increase the initial Inside-Numbers wager to $66-Inside, which would still leave you one-buck short in order to cover the 5, 6, 8, & 9. 

In the alternative, you could start with a steeper ratio $88-Inside for a $28 one-hit payout which generates enough cash-flow to cover a Steep Regression to the $22-Inside level and still guarantee a $6 net-profit after all is said and done even if a 7-Out shows up on the very next roll.

As you can see, the wider you want to spread your bets (to increase your prospects of picking up a “first-hit” payoff), the higher your initial wagers (both individually and collectively) have to be in order for the first hit to pay enough for minimum-bet coverage on just as wide a range of bets once you regress them.

In other words; the wider the range of bets you want to cover; the higher the initial large total bet has to be in order to generate enough revenue to cover the subsequent small wager and still show an overall net-profit…or stated in the alternative; the fewer advantaged-bets that you spread your money over, the lower your initial large ISR bet needs to be.

But again, you have to put the necessary effort INTO calculating your validated point-cycle SRR in order to extract your rightfully deserved maximal-revenue OUT of it.

Several readers have asked about the formulas and calculations that go into the overall ISR validation process, and I’m happy to oblige.  I’ll also quickly note that you can use the same formulas and methods to validate ANY betting-method you are contemplating.

SRR Expectancy-Rate

Calculating your Sevens-to-Rolls Ratio is quite simple.  We know for example that…

The sevens-expectancy-rate for an SRR-6 random-shooter is 16.67% on any given roll (6-out-of-36 possible outcomes).

By dividing those six possible 7’s into the thirty-six possible outcomes, we determine the 7’s expectancy-rate for a random SRR-6 shooter to be 1-in-6 (16.67%) on any given roll.

Likewise, we can do the same for any SRR-rate:

The sevens-expectancy-rate for an SRR-7 shooter is 14.29% on any given roll (5.14-out-of-36 possible outcomes).

The sevens-expectancy-rate for an SRR-8 shooter is 12.50% on any given roll (4.5-out-of-36 possible outcomes).

The sevens-expectancy-rate for an SRR-9 shooter is 11.11% on any given roll (4-out-of-36 possible outcomes).

Even if you have a fractional Sevens-to-Rolls Ratio of let’s say, 1:6.5, you can use the same formula to determine that you’ll see an average sevens-expectancy-rate of 15.39% on any given roll (5.54-out-of-36 possible outcomes).

Though your SRR-rate is NOT the be all and end all of dice-influencing; it is one of the critical factors that you have to keep in mind whenever you are structuring your advantage-play bets simply because a roll-ending 7 wipes out all of your active Rightside wagers at the same time. 

If you ignore your SRR, then you ignore the overall risk your bets are subject to.

Global-Bet Expectancy-Rates

I refer to multi-number wagers like Inside (5, 6, 8, and 9), Across (4, 5, 6, 8, 9, and 10), Outside (4, 5, 9, and 10), Even (4, 6, 8, and 10), Iron Cross (5, 6, 8, and Field) and similar, as “global bets”, because they are semi or fully-encompassing wagers that cover several numbers at the same time.

In the hands of a random-roller, NONE of those bets hold ANY merit whatsoever, and frankly NONE of your money should be ventured on ANY of them if you want your advantage-play bankroll to stay in positive-expectation territory. 

Conversely, each one of those bets holds their own special place in the world of dice-influencing.  Your task as an advantage-player, is to figure out how good your own shooting ability is; and then determine which bets are best suited to those talents.

Part of that process is to figure out how often you can expect one of the numbers covered by any of those wagers will show up and then compare it to your 7’s expectancy-rate.

For example…

In the random world, the Across-numbers (4, 5, 6, 8, 9, and 10), account for 24-out-of-36 possible outcomes. That equates to an appearance-rate of 66.67% and an Across-Numbers-to-7’s Ratio of 4.00:1

For the SRR-8 shooter, the Across-Numbers will account for about 25.20-out-of-36 possible outcomes and a slightly improved appearance-rate of 70.00%.

Although the 1.2 additional appearances of Across-numbers over random (24 versus 25.2) may not seem like much; when it is combined with the lower appearance-rate of the 7 (4.5 for SRR-8 versus 6.0 for random); then all of a sudden the Across-Numbers-to-7’s Ratio improves dramatically to 5.6:1 instead of 4:1 for random (a whopping 40% improvement).

Here’s a chart that shows those rates for the All-Across wager:

Now obviously those respective appearance-rates change as we change the type of bet that we make.  For example, the appearance-rates for a broader bet like the Iron Cross (Anything-but-7) increases…

…while the paying-hits appearance-rate for a less-encompassing bet like the 4 and 10 Place-bet drops substantially…

The fewer 7’s that a shooter throws, the more its place will be taken by non-7 outcomes.  For simplicity, I spread those 7-replacement outcomes evenly across all the other non-7 numbers (favoring none).  Your own shooting may produce a different, less even distribution pattern, so it may be best to calculate your own expectancy-charts for the bets you are contemplating.

In any event, each SRR-rate change not only alters the ratio of 7’s-to-non-7’s, but also the appearance-rate (expected hit-rate) of each bet-type.  As a result, the average payout from each of these global-type bets changes too.

Weighted Bet Payout

When we look at the potential payout for any multi-number wager, we have to look at how often each number within that wager will pay off relative to any of the other wagers. 

For a bet like the Place-bet 6 and 8 it is easy because both the 6 and 8 appear the same number of times and they both have the same Place-bet payout-rate of 7:6. 

On the other hand, the Across-wager takes a little more time to figure out because it covers six different numbers with three different occurrence-rates and three different payout-rates.

To determine the weighted (average) bet-payout for a given multi-number wager like the Across-bet, we calculate the payout and the occurrence-rate for each of the individual Place-bets within the global-wager itself.

For example with $32-Across…

The wagers are spread out with $5 each on the 4 and 10, $5 each on the 5 and 9, and $6 each on the 6 and 8.

To accurately assess what the average weighted payout will be, we have to multiply the occurrence-rate with its respective payout.

Therefore we multiply the 4 and 10 payout of $9 by six because there are three ways each to roll the 4 and 10.

We do the same for the 5 and 9, but in this case we multiply the $7 per-hit payout by eight to reflect those two numbers appearance-rate of four times each.

We also do that for the 6’s and 8’s $7 payout and then multiply it by ten to reflect the five ways each that we can make the 6 and the five ways each that we can make an 8.

All of that equates to $54 for the 4 and 10, $56 for the 5 and 9, and $70 for the 6 and 8. That equals $180, which we then divide by the 24-ways we multiplied their respective individual payouts by.

That gives us an average weighted All-Across payout of $7.50 per winning hit.  When your wager on the 4 and 10 reaches $20, then it’s a good idea to “buy” it.  By paying a vig (commission) of 5%, you receive a 2:1 payout which lowers the house-edge substantially.  Therefore, you’ll also want to adjust for that on the average weighted-payout for your pre-regression large-bet.  For example, the weighted payout for a $160-Across wager is $38.50 (net of vig).

Here’s a summary of the basic weighted payouts for each of the global-bets we’ve been discussing in this series:

The weighted-payouts will be used when calculating how much each winning-hit will pay and therefore how well each global-bet will stack up against the 7.  To do that, we have to take a detailed look at the expected roll-duration/bet-survival rate for each SRR and for each of these global-bets.

Determining Bet-Specific Roll-Duration Decay-Rates

We’ve long talked about the critical importance of exploiting the fattest, most frequently occurring portion of the roll-duration expectancy-curve.

“Roll-duration” simply means how long, on average, your point-cycle will last, and how likely a particular bet is to hit before the 7 appears.

For an SRR-8 shooter, there’s a 87.50% chance that he’ll get past his first point-cycle roll; a 76.56% chance that he’ll get past the second one; a 66.99% chance on the third; and a 58.62% chance that he’ll survive the fourth p-c roll.

Though that tells us how likely he is to throw a “non-7”, it doesn’t help us in terms of addressing any specific bets that he might make (other than the Anything-but-7 Iron Cross wager which perfectly mirrors non-7 roll-duration, as it should).

For other methods that are less-encompassing than the Iron Cross, we have to look at their specific occurrence-rate and figure out the decay-rate as it pertains to that wager.

Once we know what the per-roll probability of that bet is, we can take the cumulative roll-duration decay-rate to figure out where and for how long that bet stays in positive-expectation territory.

Again, the PER-ROLL expectancy of the 7 remains rock-steady for the SRR-8 shooter at 12.5% on any given roll (16.67% for an SRR-6 random-roller, 14.29% for an SRR-7 shooter, and 11.11% for an SRR-9 shooter); however the cumulative odds of making MORE than one non-7 roll in a row actually deteriorates quite rapidly…and for some types of bets, that deterioration is more pronounced due to their low initial appearance-rate.

For example:

The Across-bet starts off at an expected appearance-rate of 70.00% on the first point-cycle roll, but declines to 61.25% on the second one, 53.59% on the third one, and only 46.89% on the fourth one. That is due to the decay-rate of non-7 outcomes in a row as it relates to the Across-bet…or stated in the alternative; the cumulative-odds of the 7 appearing after two, three, or four, etc. non-7’s in a row.

I have charted the roll-duration hit-probability decay-rate for each of the bet-types that we’ve covered in this series:

Roll-Duration Hit-Probability Decay-Rate

SRR-7

So how do we reconcile the roll-duration decay-rate for any given bet-type with regression-betting, and most importantly, how do we determine the optimal regression point?

Determining Optimal Regression Trigger-Point

Once we know what the per-roll probability of a bet is, we take the cumulative roll-duration hit-probability decay-rate (as seen above) to figure out where and for how long that bet stays in positive-expectation territory. 

Calculating how long that bet stays in positive-expectation territory and where the Optimal Trigger-Point is (in which to do the large-to-small regression) for each particular type of bet is critical in terms of extracting as much profit from as many hands as possible.

The process is fairly simple:

First we look at the “7-exposure” value of the bet. That is the total amount of money you would lose if a 7 shows up. For $22-Inside it is $22, and for $160-Across, it is $160.

Each SRR-rate has it’s own per-roll risk associated with it. For a random SRR-6 shooter it is 16.67%; for SRR-7 it is 14.29%, for SRR-8 it is 12.50% and for a SRR-9 shooter it is 11.11%.

We use those figures to calculate the proportional-risk threshold that any wager has to overcome to be in positive-expectation territory.

For example, an SRR-7 shooter who is betting $5 each on the Place-bet 5 and 9 has a minimum $1.43 proportional-risk threshold to overcome. That number is derived from the $10.00 7-exposure value of his two $5 Place-bets ($10.00 7-exposure x 14.29% per-roll 7’s-expectancy = $1.43 proportional-risk threshold).

We then look at the SRR-7 point-cycle roll-duration expectancy for this particular wager. In this case, he has a 22.85% chance of hitting either a 5 or 9 on his first point-cycle roll. That equates to $1.60 in expected-earnings on a $7 payout. On his second p-c roll, it declines to $1.37 (which is below his $1.43 proportional-risk threshold), so he is best advised to keep his large pre-regression 5 and 9 wager out there for only one hit before regressing it.

On the other hand, an SRR-8 player only has a $1.25 proportional-risk threshold to overcome on the same five-dollar 5 and 9 Place-bet, so his expected-earnings are $1.63, $1.42 and $1.25 on his respective first, second, and third p-c positive-expectation rolls. In that case, he can afford to take three winning-hits before optimally regressing his bets.

The reason you’ll often see the Optimal ISR Trigger-Point extend beyond that particular global-bets “7’s-to-winning-hits” ratio is due to the better-than-even-money payout that Place-bets generate (7:6 for 6 and 8; 7:5 for 5 and 9, and 9:5 or 2:1-buy for the 4 and 10).

Let’s take a look at a typical multi-number bet to see how this optimal regression trigger-point process works in real life:

The first thing we have to do is figure out what our per-roll loss-expectancy is for a given set of wagers.

To do that we take the TOTAL 7’s exposure of the bets we are appraising and multiply that by the per-roll expectancy of the 7 for that particular SRR-rate.

For a SRR-8 shooter, the 7’s expectancy is 12.5% on any given roll.

On a simple $32-Across wager, our 7’s exposure risk is $32.

For a SRR-8 shooter the proportionally expected “cost” per-roll on that $32-Across bet is $4.00. That is the 7’s expectancy hurdle that this bet has to overcome on each roll for it to remain in positive-expectation territory…so any expected revenue-per-roll below that amount puts it into negative-expectation territory.

To figure out where that positive-to-negative transition point is during the point-cycle, we take the weighted payout-per-hit and multiply it by the roll-duration occurrence-rate.

In this case the first point-cycle roll carries an Across-bet expectancy-rate of 70.00%.  We then multiply the $32-Across expected per-hit weighted-payout of $7.50 by the 70.00% first point-cycle roll expectancy-rate. That equates to $5.25 in expected revenue from the first p-c roll which is more than the expected $4.00 “cost”.

This expected revenue figure also takes NON-Across-number outcomes into consideration too (as is seen in the disparity between expected weighted-payout, the 7’s-expectancy cost, and non-Across-occurrences); which account for 17.50% of the first p-c roll outcomes).

The second p-c roll carries an Across-bet expectancy-rate of 61.25%, which equates to $4.59, so it is still in positive-expectation territory (above the $4.00 expected proportional risk cost of this wager).

The third p-c roll carries an Across-bet expectancy-rate of 53.59%, which equates to $4.02, and although it is still in positive-expectation territory by 2 cents, it is clearly right on the positive-to-negative transitional cusp.

As you can see, pre-regression 7-Out losses are accounted for in the Across-numbers appearance-rate minus the expected 7’s appearance-rate, so losses of pre-regression bets are fully built into the equation.

The fourth p-c roll carries an Across-bet expectancy-rate of 46.89%, which equates to $3.52 which obviously puts this wager into negative-expectation territory. Now that does not mean that the 7 is automatically going to show up on the very next roll. Instead, it means that the SRR-8 shooter can generally take three positive-expectation hits at the large-pre-regression bet-level before reducing his wagers to the lower post-regression amount when the roll-duration decay-rate transitions into negative-expectation territory.

I have charted out exactly where the Optimal Regression Trigger-Point is for each of the bets and each of the SRR-rates that are covered in this series:

The SRR-7 shooter does not stay in positive-expectation territory for very long during his point-cycle roll and should therefore optimally regress his bets after just one or two hits (depending on which global bet-type he has wagered on).

As your SRR-rate improves, so does the flexibility of your betting-methods.  In most cases, an SRR-8 shooter can take two or three winning hits before reducing his initially large wager.

Likewise, a SRR-9 shooter has the luxury of having all of his global-type bets stay in positive-expectation territory for four winning hits before optimally regressing them.