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Regression Avoids Depression: Part 1

A "regression bet" is where you initially start with a large wager on one or more numbers and then reduce it to a lower level. The usual trigger for lowering the initial big bet is if you get a paying outcome or if a winning-hit doesn't appear within a certain number of rolls.

A Quick Example

A simple regression would be if you initially wagered $12 on the Place-6. A paying hit would generate a $14 payout. Upon collecting that, you tell the dealer to reduce your bet to $6, so he returns $7 of your original bet. Since you've collected $14 and you now only have $6 still active on the layout, you've got a guaranteed profit of $8 locked-up for that wager.

There are all kinds of bet-regression permutations, for example:

  1. If you made that same $12 bet on both the 6 and 8, and then regressed both of them down to $6 each after just one hit, you would still have a $2 profit locked up for that series, yet still have $12 in action on the table.
  2. You could bet $88-Inside ($20 each on the 5 and 9, and $24 each on the 6 and 8); then after just one hit which pays $28, you could regress everything down to $22-Inside and still have a $6 profit to show for that series of wagers.

Some players like to keep their "Initial" (large-sized) wager in place for more than one hit and regress them after two or three hits.

  • For instance, starting with $88-Inside and collecting three hits at $28 each would gross $84 in revenue. After regressing that wager to $22-Inside, you would have a net-profit of $62 in your rack while another $22 is still active out on the layout.

The higher your initial bet is compared to what you intend to regress it to; the "steeper" that regression becomes.

Measuring The Steepness of Your Initial Regression

You measure the steepness of your regression by the ratio of the initial bet compared to the subsequent regressed amount.

For example:

  1. A $12 bet regressed to $6 is a 2:1 regression, and so is $44-Inside regressed to $22-Inside.
  2. A $66-Inside initial wager that is reduced to $22-Inside is a 3:1 regression ratio.
  3. However, $66-Inside regressed down to a $6 Six and Eight would represent a 5.5:1 ratio.

Clearly you don't have to strictly stick with Inside or 6 and 8 wagers when you are considering a regression-style wager.

For example:

  1. You could start with a pyramid-shaped bet-weighting like  $25 each on the "bought" 4 and 10, $50 each on the 5 and 9, and $90 each on the 6 and 8, for a total of $330-Across. Depending on which box-number arrives first, you'd be looking at a payout range of $50, $70, or $105. From there you could take one more hit or regress everything down to something like $32-Across, $44-Inside, or $40-Outside.
  2. If you had all the numbers evenly covered with $170-Across ($25 each on the 4, 5, 9, & 10, and $30 each on the 6 & 8); you could consider a regression as shallow as $32-Across to as steep as just $6 each on the 6 and 8.

As you can see, the higher your initial bet is compared to what you intend to regress it to; the "steeper" that regression becomes.

How Regression-betting Fits Into Dice-Influencing

When a skilled player determines and fully validates his dice-influencing ability, he has to support that skill with properly financed and sized wagers.

Using an Initial Steep Regression can actually support and enhance a dice-influencers current skill by what I would call "adaptive betting" or enlightened and rational "affirmative wagering".

When viewed strictly from a math perspective, that doesn't at first appear to make good economic sense. To an advantage-play BJ card-counter; an advantage is an advantage, and therefore they believe that we should never vary our bets when we have an overall proven advantage. That is, to their way of thinking, when we have an advantage, we should never increase our bets when our shooting is doing well, nor ever decrease them when our shooting is doing poorly...and by their logic; since they don't know ahead of time when that will be; then no one should ever use a Steep Regression nor any sort of bet-pressing either.

Unfortunately, the one thing that advantage-play blackjack players fail to understand and acknowledge, is that dice-influencing IS NOT a fixed and stable linear skill; which means that our skill-advantage is NOT the same on each and every throw throughout each and every hand.

Fortunately, as astute dice-influencers, we recognize that we can extend some influence over the dice, while concurrently recognizing that our influence is sometimes fleeting and transient. Therefore by using an Initial Steep Regression (ISR), we bet, strike, and collect a net-profit at the earliest possible moment during each turn we get with the dice.

In reality, the relative advantage we enjoy over the house, especially with novice to intermediate players, is such that our dice-influencing proficiency-level fluctuates. Therefore, using a Steep Regression to lock up an early profit; recognizes, compensates for and ultimately, profitably exploits that variability.

The objective of regression-style betting when applied to dice-influencing, is to:

  1. Produce a quick profit on as many hands as possible.
  2. Reduce the volatility and the amount of time (as measured by the number of rolls) over which any given hand reaches net-profitability for our active bets.

Stated another way:

Regression-betting lets dice-influencers achieve a net-profit within a minimal number of rolls.

Regressions Aren't Right For Blackjack, But They Are PERFECT For Craps

In the advantage-play blackjack world where a card-counter can sit back and stoically wait for the mathematical advantage to come to him; an ISR method is meaningless since the non-player influenced deck of cards is the vehicle through which his advantage is gained. The card-counter merely has to react to the variability of the deck-induced count.

Antipodaly, the skilled dice-influencer has to DIRECTLY produce and maintain his own advantage through player-induced physical skill as opposed to having it mathematically-induced by a mechanical-device (through a deck of cards) for him. Now, if the BJ-player was a card-mechanic and the casino let him shuffle and deal; then the comparison to and the ill-based A-P prohibition against dice-influencing ISR's would be valid. Clearly however, that isn't the case.

Regressions let a dice-influencing craps player reach profit much sooner, and with much more certainty than the conventional need to achieve four or five or six paying hits before even reaching the break-even point of a multi-wager hand.

The BJ Math-Crowd View of Regression-Betting

The intelligent Precision-Shooter has to adopt a betting-method that takes his variable physical skill into consideration...instead of ignoring it.

Recent refugees from the ravaged battlefields of BJ advantage-play expect aloof machine-like consistency from their newly developed D-I skills. Sadly, many will be disappointed to discover that even well developed physical skills are not imperturbable nor are they inert like a deck of cards.

Their failure to recognize and address active human involvement in the whole skill-to-profit process, and their entire "it doesn't matter how much your skills vary from your first roll to your eight-millionth roll; your skills will average out and will ultimately be profitable in the long run" credo holds incredible amounts of volatility...but extremely limited amounts of short-hand and medium-hand roll-duration profit.

If you don't mind the volatility where you may endure twenty, thirty, forty, fifty or even more losing sessions in a row despite the fact that you are winning a fair amount of your individual wagers nearly every time you pick up the dice; then you are free to follow that line of thinking. BJ converts appear to love losing hundreds of sessions in a row because they "know" that eventually their advantage will manifest itself for long enough to finally bail out those thousands upon thousands of dollars of short-hand and medium-hand roll-duration loses.

To their way of thinking, collecting "an early profit" on most hands is strictly for fools, while "chasing losses" is what the big boys do…and that you should unflinchingly be willingly to keep on making non-regressed, non-pressed maximum-affordability bets right up until you lose every last cent of your bankroll.

That sure goes a long way to explaining why most talented card-counters go bankrupt long before they are able to profitably exploit their card-counting skills with any degree of consistency.

Unfortunately for them, finding out that Steep Regression betting really is valid and fully applicable to dice-influencing, coming so closely on the heels of "discovering" that dice-influencing really does work and that the world really isn't flat after decades upon decades of impatiently and unwaveringly telling us that Precision-Shooting couldn't possibly work; would just be too much of shock to the system for their delicate constitutions to handle.

Perhaps in another couple of decades or perhaps a century or two, the BJ advantage-play world will finally come around on regression-betting the same way they have on dice-influencing; thereby emerging from their comfortably smug pupae-stage of blissful ignorance…but I wouldn't bet on it.

Comparing Apples to Antelopes

While randomly thrown dice result in a game of independent trials, a dice-influencers skill is advantageously variable from hand to hand and even variable WITHIN any given hand.

  1. We determine that variability by calculating the average number of 7-avoidance throws we are able to make.
  2. When surveyed over a statistically significant number of hands, we can draw some conclusions as to how much influence we are able to exert, on average, over a various number of rolls per hand.
  3. Armed with that knowledge, we should be able to predict the number of Point-then-Out hands we will have versus the average number of three, four, eight, ten or twelve-roll hands we will generally produce…and therefore come up with a validated way to bet on our hands while capitalizing on the fattest part of the roll-occurrence curve.

Your dice-influencing skill is variable, and that has a bearing on your 7-avoidance outcomes because your ability to preserve and sustain your influence mathematically declines with each and every subsequent roll that you make within a given hand. If it didn't, hands of several hundred rolls each would be a common everyday casino occurrence for dice-influencers. Since that is not the case, we want to arrange our bets so we can sustainably profit from as many of them as possible.

While the house-edge against a bet remains constant in a game of randomly-thrown independent trials, the savvy dice-influencer has to look at his skill-based variability over a number of hands and determine how many will last for one point-cycle roll, how many will last for two point-cycle rolls, how many will last for three point-cycle rolls…and so on. That is how we determine where the fattest part of our roll-occurrence curve is.

Trying to draw worthless non-connective associations between blackjack wagering and the enlightened D-I skill-based adaptive method of using an Initial Steep Regression is beyond an apples-to-oranges comparison. Rather, the use of rationally affirmative roll-duration-based ISR wagering versus traditional BJ-betting is like comparing apples to antelopes. What isn't even germane or relevant in their world, works with perfect utility and practical function in ours.

We'll be taking a close look at the math and science behind dice-influencing roll-duration variability in Part Two of this series.

In the meantime…

C'mon Back Into the Real World of Profit-Making

Using an Initial Steep Regression to lock up an early profit doesn't mean that everything stays static once your bets are fully paid for.

  1. Once you are past the point of net-profit for this hand, your wagering flexibility actually increases substantially.
  2. Though that doesn't mean you can go crazy and start betting on everything in sight; it does mean that you can vary your bets to reflect the now-extended profit-expanding potential of your hand if and when it continues past your average hand-duration point.

Since we aren't perfect automaton-shooters with unwavering skills; we need to adapt our bets to suit our current average roll-production rate.

Determining Average-Roll Duration

While you can't consistently predict how long each particular hand will last; intelligent dice-influencers have to look at how well they generally perform and how long their average hand will last.

You have to honestly and accurately calculate, reason out and "cipher" your relative skill-level and its corresponding likely roll-duration (by way of number-of-rolls per hand) like a savvy sports handicapper or derivatives trader might.

That analysis includes, but is not limited to:

  1. Determining how quickly you hit at least ONE Inside-Number before 7'ing-Out; and then determining how often you hit two of them and then three of them…and four of them as well, and so on.
  2. Determining, on average, the duration (as measured by total number of rolls) of your hand as well as your point-cycle Sevens-to-Rolls Ratio (SRR).

I personally like to look at three sets of numbers in this category:

  1. Determining how many Point-then-Out hands you throw, on average.
  2. The difference in average when non-Inside-Number hands are both included and excluded in the Point-then-Out roll-duration calculation.
  3. The difference in average, when long rolls (the mega hands and mini-mammoth ones) are both included and excluded in that roll-duration calculation.
  4. The difference in profit-generation when various Steep Regressions ratios (ie. 3:1, 5:1, 6:1, 10:1, and their natural multiples, ie. 10:2 or 12:3) are applied and compared to multiple-hit rates (ie. 1, 2, or 3 or more hits at the initial big-bet level) before regressing it when a hand is nearing its weighted-average roll-duration.

The amount of risk on our bets is reflective of our ability to influence the dice. For a random-roller, that risk remains constant from one roll to the next. For the dice-influencer, that is definitely NOT the case.

A properly structured regression-style wagering approach truly reflects our current dice-influencing skills when they are affirmatively matched to our average roll-duration.

A thorough and clear-headed examination of our skill-level in context with how long, on weighted-average, each hand will last; is a common sense approach that hasn't yet caught on, but that doesn't mean that it isn't valid.

Precision-Shooters have endured more than 45 years of the math-guys telling us that dice-influencing couldn't, shouldn't or wouldn't work; so I think it's appropriate that we cut them some slack in terms of letting them get up to speed on the efficacy of Steep Regressions too. Hopefully they won't needlessly waste another half century telling us that regressions can't work before finally wising up and "discovering" that ISR's really are validly and profitably applicable to dice-influencing.

Is Regression Betting Applicable to YOUR Dice-Influencing Skills

The ISR is intended to get your "at-risk" money off the table as quickly as possible, while maintaining action in the ensuing hand.

To make ANY betting-method work consistently enough for the long-run, you have to have an advantage...although the required player-advantage to actually do that can be absolutely miniscule in size.

To figure out whether regression-betting is right for you and your current dice-influencing skills; simply figure out how many Point-then-7-Out hands you throw versus how many you throw that includes at least ONE of the box-numbers that you plan to include in your Initial Regression wager. For example;

  1. Let's say that you generally throw three Point-then-Out hands out of every 20 turns with the dice. That equates to 15% of all the hands you throw.
  2. For this exercise, a "Point-then-Out" hand also includes any hands where your intended ISR (Initial Steep Regression) bets are not hit.
  3. If, let's say, you plan to only bet on the Inside numbers (5, 6, 8 and 9) for your ISR, then even if you throw a 4 and/or a 10 (or any other non Inside-number) before you throw a 7-Out, but you don't hit any ONE of your planned ISR numbers; then that hand is also included in the Point-then-Out count.
  4. The reason we need to know what our Point-then-Out rate is, is because we need to know, on average, how frequently that will be happening and how much our short hands will be losing BEFORE we figure out the ideal regression-rate (the steepness of the ISR).
  5. Our early-7-Out loss-rate dictates whether or not our dice-influencing skills are good enough to justify the risk of having large ISR bets out on the layout in the first place.
  6. Let's say we were planning to start with $110-Inside and then regress to $22-Inside after our first Inside-number hit.
  7. In this example, we know that, on average, we will throw three Point-then-Out hands where none of our Inside-numbers hit before our hand ends. That means we'll have $330 of expected losses to overcome before we even begin to talk about any kind of profit.
  8. We know that one winning hit on any of our $110-Inside bets generates $35.
  9. We plan to leave $22-Inside on the layout. That means that we have $13 to the good for each of our remaining 17-out-of-20 average hands. That, in and of itself generates $221. Obviously that isn't enough to cover the $330 in expected losses from those 3-out-of-20 Point-then-out hands.

That means we have some more work to do.

  1. We can and should look at how many hands we throw where we get TWO or THREE Inside-number hits before 7'ing Out. That may tip the scales in our advantage. We can also look at an even STEEPER ISR like $220-Inside regressed down to $22-Inside.
  2. Additionally, we should calculate how many hits that we would generally get AFTER triggering our Initial Steep Regression, and figure out if the $7 that each one of those Inside-bets generates at their new lower base-level is enough to put us into a profit position.
  3. In the above example, we would need at least sixteen more Inside-number hits at $7 each to overcome the balance of the deficit of those three ISR's that DIDN'T hit.

That isn't as daunting a task as it may first appear. The sixteen required hits at the regressed $7 payout value, works out to just one additional paying-hit per hand.

We can also go back and consider the number of hits that we could viably keep our ISR at its original $110-Inside level before regressing it, or like I just mentioned, we could look at starting with a larger ISR like $220-Inside.

  1. Let's say that upon further review, we find that, on average, we actually get THREE Inside-Number hits on 16-out-of-20 hands.
  2. Though that means we'll now have a $440 deficit to overcome (four non-Inside Point-then-Out hands out of the twenty hands that we throw); but it also means that we'll be able to generate MORE money at the higher $110-Inside ISR rate before we drop down to the $22-Inside level.
  3. The math tells us that a three hits-per-hand average at $35/hit multiplied by sixteen hands, will generate $1680.
  4. We then subtract the $440 expense of those four Point-then-Out non-Inside-hit hands where we lost $110-Inside each time, and we are left with $1240.
  5. We still have to pay for the $22-Inside money that we intend to leave on the table once we do our Steep Regression after collecting our first three Inside-hits. That will cost us $352.
  6. Therefore our three-hits-at-$110-Inside-before-regressing-to-$22-Inside bet-sequence over twenty average hands will generate a net-profit of $888 over twenty hands. That equates to an average profit of $44 per hand.
  7. Obviously that doesn't include any additional money that our $22-Inside bets continue to generate on the medium to long hands either, so our profit-per-hand average will likely climb substantially.

For those who haven't seen it, I highly recommend the original Can Frequency Compensate For Shortness? study where we look at this subject in even more detail.

Further, in Part Two of this series we'll be looking a number of typical "what if" scenarios, and determining the appropriate steepness-ratio, as well as the most rational bet-spreads to use in each case. I hope you'll join me for that.

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 1, 2007 12:06 AM.

The previous post in this blog was Streaks, Trends and Opportunity Part 7.

The next post in this blog is Ask the Mad Professor - Part 1.

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