The Source of Your Advantage
The overall goal of dice-influencing is to improve your degree of influence over the dice.
Part of that influence comes from increasing your on-axis tossing while minimizing your double-pitched outcomes; as well, it involves minimizing the number of one-die and both-dice off-axis results.
Considered in the alternative, it involves the exploitation of any correlation that occurs between the two dice.
Simply stated, even though both dice are independent objects; your act of setting them together, gripping them together, throwing them together, and attempting to land them together…has the effect of hopefully having them end up in some sort of correlated outcome together.
DiceTool looks at the results of how you toss the dice regardless of your intentions. It is based on the premise that the dice themselves don't know or care what set you are throwing them in or what your axial intentions are, and therefore neither the dice nor DiceTool makes any pre-suppositions as to your intent.
How the heck can that work?
Well, as you’ve probably figured out by now, the dice only react and respond to the way you throw them, and DiceTool's only concern is how effective you are in actually influencing them.
That is, DiceTool looks at the correlation between the starting-set that you threw them with and the subsequent facial relationship that they ended up with when they stopped moving at the other end of the table.
If you input a reasonable number of roll-samples into DiceTool; then it becomes very indicative of how you generally toss the dice…and therefore quite predictive of what kind of outcomes you can expect while using various dice-sets.
What’s a “Good” Outcome versus What’s a “Bad” Outcome?
If you only consider on-axis outcomes as “good” results, and any one or both-dice-off-axis outcomes as “bad” results; then chances are that you are going to be overlooking all sorts of opportunities.
In other words, if 50% of your outcomes are on-axis while the other 50% are off-axis; but you only look at exploiting the “good” half while concurrently ignoring the “bad” half…then you are likely overlooking about half of all of your money-making opportunities.
That doesn’t make any sense, and it certainly won’t make you very much money.
DiceTool considers ALL of your outcomes on a global basis to determine whether ANY of them are steadily exploitable.
More importantly though, it looks at whether you would produce better results if you used a different dice-set...and it considers the profitable-exploitability of all of your signature-outcomes instead of only considering the on-axis ones.
For example, let’s say that you use the Crossed-Sixes (X-6) dice-set and one of your dice goes off-axis an extraordinary percentage of the time to produce an extraordinary percentage of 4’s and 10’s.
Now if you rigidly follow the axial-based Frequency of Appearance chart, you should only be expecting either an on-axis 4 or on-axis 10 to show up 6.25% of the time (1-out-of-16 on-axis possibilities) instead of their randomly expected rate of 8.33% of the time (3-out-of-36 random possibilities)…in which case it would make betting on the 4 and/or 10 appear to be a “bad” bet.
However with your particular tossing-style and the fact that you produce an inordinate number of one-die-off-axis 4’s and 10’s (way above what both the Frequency of Appearance chart as well as random-expectation indicates); I believe you should be betting on those two numbers especially if they are going to produce a higher edge over the house than some of your conventionally-expected (but non-appearing) on-axis outcomes.
Again, I realize that flies in the face of conventional wisdom and what is generally taught; but to me it makes more sense to bet on the numbers where you have the strongest edge over the house rather than on the numbers that set-theory ‘says’ you can expect but that aren’t showing up as often as set-theory anticipates.
To my mind, you can either take full profitable advantage of what your current skill-set is steadily offering you even if it doesn’t fit into a narrowly-defined axial-set designation; or you can stand there as opportunity continues to pass you by simply because your present dice-set technically ‘shouldn’t’ be producing anywhere near as many of the outcomes that you are currently getting.
Consistency versus Volatility
In one corner we have “Consistency”. He comes from the steady and reliable school of mid to long-term predictability.
In the opposite corner we have “Volatility”. He comes from the changeably inconsistent school of short-term hand-to-hand and session-to-session variance.
On one hand we strive for overall long-term consistency in our dice-influencing performance; but we also know that it is inevitable that we will experience quite a bit of short-term volatility…otherwise, we’d be able to ‘call our shots’…and they’d actually turn out the way we predicted.
Now sometimes we might get it immediately right in inimitable Babe Ruth fashion, but most of the time we are looking to get it right a given percentage of the time.
In other words, each of our roll-outcomes don’t have to be perfectly predictive. Instead, we are looking to exploit some of their overall predictability.
One of the biggest pet-peeves here in the dice-influencing community is that hand-to-hand and session-to-session variance is the most frustrating part of being able to optimally benefit from your advantage.
That is, the annoying volatility that accompanies the win-some/lose-some nature of what we do, is often so exasperating and so infuriating, it drives players to the point where they fail to take anywhere close to full advantage of their edge over the house.
Concurrently, it also often drives modestly-bankrolled players out of the game completely…not because they didn’t have the skill…but because they didn’t have a sufficient bankroll to weather the whip-saw back-and-forth volatility that accompanied their skill.
Now everyone would agree that if you could eliminate all variance and each of your tosses were perfectly predictable and consistent; you could make a killing. However, the reality is that you and I do not have perfect toss-to-toss predictability; yet our overall edge shows us that we can indeed make a killing on our current D-I skill if we maximally-optimize our betting with a sufficient bankroll.
In plain English, that simply means making persuasively-sized bets on our strongest-edge wagers…while ignoring everything else.
The concept couldn’t be simpler, yet most players try to cover too many bets with too little money…and they end up producing too little net-profit. That is because the value of the bets that they make on the numbers where they do have a convincing-edge aren’t big enough to overcome the losses they incur on all the other bets that they make where they either have a marginal-edge...or no edge at all.
What happens then, is that their money is spread so thinly across so many numbers, that their dominant-edged bets don't have enough of a chance to really show their true worth.
It's a sad but true reality that keeps most aspiring dice-influencers in the break-even category despite the fact that their true edge over the house should be producing near-obscene amounts of money.
Consistency does not mean that you are going to be throwing back-to-back-to-back-to-back same-number repeaters; but rather consistency is demonstrated in your overall performance.
Your degree of influence and, dare I say, your degree of consistency as well, is an ever changing thing. DiceTool let's you put your finger on your current degree of influence and your current degree of consistency by pointing out not only your best current betting-opportunities, but also your worst current betting-threats as well…not in general terms, but rather in very specific edge-per-roll and edge-per-hand terms.
Your Edge-per-Roll Accounts for Per-Hand Variance…and Helps Define Your Consistency
A critically important facet of DiceTool's performance, is how it displays your edge-per-ROLL over each wager (in addition to your edge-per-HAND); and in doing so, it automatically accounts for per-HAND variance.
That is, by articulating the player-advantage on a per-roll basis, you don't have to adjust for per-hand or per-session variance...DiceTool does that for you in the form of an edge-per-roll reckoning.
In doing so, it conservatively targets your best-value wagers while concurrently steering you away from lower-valued or negatively-burdened ones...all the while accounting for per-hand hit-rate variance.
By accounting for variance while simultaneously directing you to your strongest-edge plays; the shooter is then encouraged to put the bulk of his geared-to-edge and geared-to-bankroll 7-exposure wagering-weight on the bets where he has the biggest advantage.
The end result is that you make more money, more consistently, and with much less risk...all while the speed at which your bankroll-doubles increase since your net-earnings are no longer impeded and encumbered by low-accomplishment bets or non-performing wagers.
DiceTool rewards consistency by way using your ever-growing set of roll-stats to indicate the bets and sets that would give you the best long-term edge over the house. That is, the more roll-stats you input, the higher the degree of confidence you can have with D-T's indicated set-matched wagers.
Bet-Sizing and the Kelly Criterion
By using the Kelly Criterion to properly size our bets, it allows us to use what I would characterize as a "balanced approach". It's one which recognizes our desire to profitably exploit our edge over the house, and blends it with the need to preserve and grow our bankroll while avoiding risk-of-ruin.
As I explained in my book, your per-ROLL edge on most bets will be about one-quarter to one-third of your edge-per-HAND; or expressed the opposite way, your edge-per-HAND will be three to four times higher than your edge per-ROLL.
As such, your Kelly-based bet-sizing is based on your edge per-ROLL, however as you should know, there are limits as to how much of your TOTAL bankroll (not just your session buy-in unless that buy-in is the entire amount of money you will ever gamble) you should reasonably expose to any given wager, as well as limits on how much of your total bankroll you can reasonably apply across multiple wagers at the same time.
If you have, let's say, a 5% edge-per-HAND; then it probably equates to a per-ROLL edge of between 1.25% and 1.66%; so that lower per-ROLL percentage is the amount of your TOTAL overall bankroll that you can reasonably wager on that bet. However, if your advantage over the house reaches above the 2.5% edge-per-ROLL threshold; then you should restrict your 7-exposure on that one bet to 2.5% of your bankroll.
Likewise, if you have strong advantage over multiple wagers which each exceed 2.5% edge-per-roll; then the maximum cumulative amount that you should reasonably expose to a 7-Out would be capped at about 3.2% of your total gaming bankroll.
In other words, when you have a positive edge over multiple wagers (even if they all individually exceed 2.5% edge-per-roll); then you should still restrict the cumulative multi-wager 7-exposure amount to about 3.2% of your total bankroll in order to maintain that balance between profitably exploiting your edge, against the need to preserve and grow your bankroll...all the while avoiding risk-of-ruin.
There is a complete discussion and explanation of all of this in Chapter 7 of my book.
In Part Five of this series, we’re going to dig down into some actual Foundation Frequency roll-stats to see what kind of profit-making opportunities we can find.
Good Luck and Good Skill at the Tables…and in Life.
The Mad Professor
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