Let’s Start With an Example
Let’s say that you use the Crossed-Sixes (X-6) dice-set for your Point-cycle, and you get a lot of single-die off-axis Hard 8’s and 10’s (just like Heavy and I do when we use that particular set); then despite the fact that those outcomes are OFF-axis doesn’t mean that we shouldn’t take advantage of them, especially if they are showing up as frequently (or even more frequently) than some of our ON-axis outcomes.
We call those kind of results: Off-axis Dominants.
They are OFF-Axis, yet they are DOMINANT in a given Foundation Frequency category…and to my mind, if their outcomes give you an edge over the house; then you should be betting on them despite the fact that they don’t neatly fall into the ON-Axis category.
Let me use another facile example:
If a single-die off-axis Hard-4 or Hard-10 shows up when I’m using the 3-V dice-set during my point-cycle; I immediately throw in a bet on both the H-4 and H-10.
Because for me, either one of those outcomes is a strong predictive signal that more of the same results are about to occur (although not always immediately on the next roll; then almost certainly before I Seven-Out).
Sure I could ignore them; but when they occur in such closely-spaced clumps as they most often do; then I see that as a money-making opportunity that shouldn’t be ignored much in the same way that our friend Heavy doesn’t often ignore the ‘See a Horn…Bet a Horn’ approach of taking advantage of his tightly-grouped clumps of Horn-numbers.
If you take a look at your Foundation Frequencies (by way of primary-faced hits, single-pitched hits, double-pitched hits, single-die off-axis hits, and both-dice off-axis hits); you can not only quickly determine what your OFF-axis Dominant-numbers are likely to be for a given dice-set; but you can also determine approximately how often they are likely to hit during a given hand or over a given session of play.
That’s how you determine whether it is a viable betting-opportunity or if it falls into the category of superstitious ‘hopeful-but-nearly-hopeless’ gambling.
To my mind, determining whether or not your current tossing-style produces any Off-Axis Dominants and deciding whether or not they are profitably exploitable, is an area where most modestly-skilled shooters can mine substantial dice-influencing gold…but it takes some honest appraisal on your part.
So let’s look at this concept a little bit further.
Off-Axis Dominants…a Definition
Off-axis Dominants are found in the outcomes where one or both dice do not maintain their axis.
Now obviously not all off-axis outcomes are dominant numbers.
Rather, you are looking at perhaps one or two numbers that produce or contribute to an overall positive-expectation edge over the casino.
In other words, you’ll often notice that even when the dice DON’T stay on-axis, they DO tend to end up on a small selection of the alternative outcomes.
For example, when one or the other die goes off-axis, there are 16 possible outcomes. All things being equal, all sixteen possible outcomes would each have an equal 6.25% chance of showing up within that grouping (and a 2.77% overall chance of showing up within the total 36 possible outcome grouping).
However when you study your roll-stats (or let BoneTracker do it for you); you will often notice that a couple of those one-die off-axis outcomes dominate and outperform their expected appearance-rate, while some of the others fall far below it.
It is in those outperformers that we often find profitably exploitable Off-Axis Dominants.
Many times the preponderant appearance-rate of those better-than-expected off-axis outcomes either add to an advantage that you already have over an ON-axis outcome…or the Off-Axis Dominant will create a positive-edge over a given number all by itself where that particular number isn't even part of our on-axis pos-ex mix.
Under 50% On-Axis…Dice-Correlation… Off-Axis Dominants…and Your Profit
Many players have a hard time breaking through and maintaining an on-axis consistency above 50%.
Though it may be frustrating, there is nothing to say that they don’t currently have a substantial edge over the house.
A careful review of sub-50% on-axis stats will often reveal a strong player-advantage that is comprised by a combination of on-axis results as well as off-axis dominants.
It is in those sub-50% O/A outcomes where Stanford Wong’s dice-correlation concept takes on new meaning, significant gravity…and plenty of profit-making potential.
Off-axis dominants (where you still have a high degree of facial correlation but without a high degree of on-axis integrity) holds some very consistent money-making opportunities and should not be overlooked or dismissed out-of-hand simply because one or both of your dice go off-axis more often than they stay on-axis.
Rather, if your off-axis dominants produce a nearly-identical number of bettable-outcomes as your on-axis results do (and ESPECIALLY if some of those off-axis dominant numbers mirror the same on-axis Signature Numbers where you are currently showing a positive-expectation advantage); then you should treat those off-axis outcomes with the same value, respect and betting-weight as you would if they were among your ON-axis Signature-Numbers.
Obviously then, face-control correlation (even when one or both dice go off-axis, but do so in a fairly predictable percentage-toss sort of way) is directly related to our prime dice-influencing objective of producing exploitable de-randomized outcomes.
In other words, you may not be able to keep the dice on-axis more than 50% of the time; but through the act of sifting through your off-axis results, you may find some facially-correlated outcomes that keep showing up time and time again. Those are your set-specific Off-Axis Dominants.
As you switch dice-sets or set-permutations, you can often tailor your outcomes to perfectly match your current toss-dynamics. So even though your toss may not be a thing of on-axis beauty; it can be set-tailored to deliver up a powerful combination of both on-axis and off-axis outcomes that compliment and support each other in terms of producing an even higher positive-expecation edge over certain numbers.
As such, it becomes patently clear as to why the transpositional relationship that each die has to the other is based on the dice-set that you start with (your “starting-set”); is also directly related to your ability (or at least the ability of excellent roll-tracking software like Maddog's BoneTracker w/DiceTool) to figure out the ideal starting-set that you should be using in order to achieve a higher percentage of the "desired" outcomes you are looking for.
Regardless of whether you sort and sift through your roll-stats manually or you let BoneTracker do it for you; it is important to note that a significant portion of your edge over the house is likely produced by OFF-axis Dominants as much as it is produced by ON-axis outcomes...but it is through the sorting and analysis process that you can find the precise set-permutation that will give you the highest edge over a given set of box-numbers.
Understanding Your Evolving Advantage
As we emerge from the primordial ooze of the random-roller swamp, and set foot on the dry land of dice-influencing; how we bet our most dominant outcomes determine whether we will walk upright, directly into the profit-zone; or if we’ll endlessly crawl around blindly sniffing and grubbing for a few edible crumbs as the reward for all of our evolutionary “advancement”.
Just as in evolution, there are natural occurrences that bend, shape, interrupt, change and redirect our progress. Likewise, our dice-setting evolution is not a straight-line progression. Rather, it is organic in its development, and the growth-curve often meanders way off course.
As dice-influencers, we are always trying to improve the various advantage-play aspects of our game, and to keep our forward progress on-track.
We do that by trying to determine what our most-dominant power-numbers are, and how much better they are over “random”. Then, based on our evolving skills, those Signature-Numbers are used to largely determine the strength and validity of the bets that we SHOULD be making, instead of the hunch, superstition, and premonition betting that often pervades the thought-process behind the bets that we are currently making.
Focusing the lion's share of our betting-weight on our highest-edged box-numbers helps us to make the shift from being mere gamblers...into being bona-fide advantage-players.
In a nutshell, the whole idea behind all of this is to determine which box-numbers are most dominant, and then fully exploit them through betting-methods that are carefully tailored to our current toss-dynamics.
As our shooting evolves, so does our edge over the house.
As such, some of the most-dominant power-numbers that we may have had a strong edge over just a few months ago, may no longer be where our most dominant edge is now.
In fact, some box-numbers that appeared to be undeserving of our betting-dollars mere months ago…may be among some of our strongest-edged, most-dominant numbers now.
In the alternative, some of the box-numbers that are indeed currently undeserving of our betting-dollars…can be converted into some of our strongest-edged, most-dominant numbers by simply switching dice-sets or slightly altering our current set.
Understanding your evolving advantage comes from a comprehensive examination of our BoneTracker/DiceTool results…and when you do that, don’t be surprised if a significant portion of your advantage over your stoutest-edged, most-domineering numbers come from your OFF-Axis Dominants. From there it becomes a simple matter of tailoring your dice-set permutation to take even better advantage of your current toss-dynamics.
Good Luck and Good Skill at the Tables…and in Life.
The Mad Professor
Copyright © 2007-2008