Once again I am joined by our friend, ** Chuck D. Bohnes**, for a lively discussion about what for many is a seemingly dry subject…how to turn more of the casino’s money into

*YOUR*money…and how to fool your bankroll into thinking and acting like it is bigger…thereby turning

**of the casino’s money into**

*even more**YOUR*money.

.

.
I say it *seems *like a dry subject because when you closely study how most dice-influencer’s bet their money; the disconnect between their actual *validated advantage*…and the *wagers *that they definitively bet their money on…the alarmingly wide chasm seems deeper and farther apart than ever before.

Unfortunately though, the opposite can also be said in terms of the amount of money that they bet on their advantaged wagers versus the surprisingly similar amount of money that they bet on *DIS-advantaged* negative-expectation wagers. In that case, the difference between their *advantaged-wagers* versus their negative-expectation *disadvantaged-wagers* is not nearly wide enough.

The idea of employing my previously discussed ** Recirculation Factor **to spur and hasten

*bankroll-growth*on your advantaged wagers…and to minimize

*bankroll-erosion*on your disadvantaged wagers, is probably the least used advantage-play tool by members in our dice-influencing community; yet I can modestly tell you that it is also amongst the top-three most effective advantage-play elements you can employ.

If you don’t know

*why*that is, or just how valuable the

**can be in terms of efficiently extracting every last drop of value from a given session buy-in, and how you can use the Recirc-Factor to consistently**

*Recirculation Factor**double*your session buy-in and then continuously

*re-double*it again and again; then you are not only missing out on expanding your session-to-session wealth, but you are also shortchanging your current D-I abilities by a magnitude that is nearly off the scale.

**Chuck D. Bohnes**

The benefits of a dice-influencer using a lower Recirculation Factor (I’ll use ‘R-F’ for short) on their own best-bet wagers can be extended even beyond the immediate satisfaction and enjoyment of faster bankroll doubling and re-doubling that you just mentioned.

The faster doubling also allows for larger wagers on less crowded tables.

More table time and skill development, producing even higher edges with even lower R-Fs in a self-propelled re-occurring cycle is a very powerful thing. In fact, that self-propelled recurrent doubling can continue pretty much unabated until eventually economic boundaries, such as a high profile or max table-limits kick in.

But until D-I’s reach those economic boundaries, the benefits of bankroll growth can be an accelerating, virtual cycle. We're really talking about the power of investment compounding and exponential growth, which is a topic I believe you've presented elsewhere.

**Mad Professor**

Yeah, I have talked extensively about the power of investment compounding and how even a modestly-talented dice-influencer can use his humble skills to fuel seemingly impossible exponential bankroll growth.

Albert Einstein probably never actually exclaimed, “

*The most powerful force in the universe is compound interest*”, but he is credited with saying so, so whether he did or not, I couldn't agree more with that sentiment.

There is the oft-quoted example of compound-interest, where if the Canarsee Indians of the Lenape tribe that accepted goods worth 60 Guilders (calculated in the 1840’s to be worth about USD $24) from Peter Minuit for the sale of Manhattan in 1626 had invested the money in a Dutch bank at

**interest, compounded annually, then in 2007 their investment would be worth over €700 billion Euros (around**

*6.5%***or 1.58 trillion Guilders), more than the combined current assessed value of ALL of the real estate in ALL five boroughs of New York City.**

*USD $960 billion*However, with a

**interest-rate (that is just a half-point lower), the value of their investment today would have only been €120 billion Euros or**

*6.0%***or 260 billion NL Guilders. That seemingly tiny one-half-of-an-interest-point reduction results in earnings that are**

*USD $160 billion***!**

*6 times lower*Most dice-influencers have no idea whatsoever how powerful their seemingly small edge over the casino really is. Even a half-of-a-percentage-point edge can make all the difference in the world…and it sure makes a huge difference in how quickly they can double and re-double not only their typical session buy-in, but also their entire gambling bankroll. We’re really talking about how a dice-influencer can use his seemingly modest skills to fuel exponential bankroll growth.

Exponential growth occurs when the growth rate of a function is always proportional to the function's current size. An example of this would be where something doubles geometrically like, 1, 2, 4, 8, 16, 32, 64, 128, 256, 512, etc.

The general principle behind exponential growth is that the larger a number gets, the faster it grows. Any exponentially growing number will eventually grow larger than any other number which grows at only a constant rate for the same amount of time.

A constant growth-rate example would be where it grows by one unit at a time such as 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 etc.

The difference between the two types of growth is demonstrated by the classic riddle in which a child is offered two choices for an increasing weekly allowance.

**~**The first option begins at 1-cent and doubles each week.

**~**The second option begins at $1 and increases by $1 each week.

Although the second option which grows at a constant rate of $1 per week pays more in the

*short run*; the 1-cent option eventually grows much, much larger than the $1 option does.

For example, by the twelfth week the

**option pays a**

*1-cent***allowance, while the**

*$20.48***option pays just**

*$1***. By the time we hit the six-month mark, the**

*$12***option pays**

*1-cent***while the**

*$335,544.32***option pays just**

*$1***.**

*$26*Most players look at what the early seemingly paltry returns would be if they re-invested some of their profit into their

*NEXT*hand or their

*NEXT*session (instead of pressing-up their bets during their

*CURRENT*hand), and decide that

*immediate gains*trump

*long-term growth*.

Unfortunately they couldn’t be more wrong…which underscores and gives voice to the reason why most skilled players find it so hard to grow their bankroll from their advantaged dice-rolling (instead of constantly having to add money to it from other non-gaming sources); even though on the face of it, self-fueled bankroll-growth from skilled shooting shouldn’t be difficult at all.

**Chuck D. Bohnes**

Your example illustrates a couple of excellent points:

1) Even small increases in advantage generate large profits when compounded, as demonstrated by the Manhattan example. D-Is, thus, should fully exploit even small boosts in edge.

2) The power of compounding is easily overlooked, as demonstrated by the allowance example. D-Is, thus, should deliberately plan to harness that power.

3) Compounding's value "builds steam" as new tosses are added to lifetime play. The more frequently a DI tosses and the longer his DI career, the more important compounding becomes to his overall profitability.

4) A casual shooter on a

*rare*craps playing excursion is not making a large mistake by ignoring compounding, however a

*frequent*shooter is making a huge mistake to ignore it. Similarly, a recreational shooter who anticipates playing for many years to come, is also making a huge mistake to ignore it.

**Mad Professor**

An important point about exponential growth is that even when its growth

*seems*slow in the short run; it becomes impressively fast in the long run. In many ways it’s a matter of being mature and patient.

Most dice-influencers (especially those whose leanings and expectations are based on a gambler’s mindset), look at each hand or each session as a barometer of how they are doing. In many ways that is way too small of a sampling to give you a realistic view of your

*overall*talents. As a result, many players will start making all kinds of changes to an already-validated derandomized toss that gives them an overall advantage but is momentarily performing on the negative side of the standard deviation curve.

Instead of staying the course on what will provide them with long-term exponential growth, they start messing with the thing that has been giving them generally good results, but is experiencing some short-term negative variance. That is, at the first sign of a temporarily bad result, they start making all kinds of wholesale changes to what is otherwise a good solid bet-strategy. Instead of sticking with what generally works, they 'throw out the baby with the bath water' in hopes of getting a greater level of

*instant gratification*.

A bad hand or even a bad session should not see you completely abandon a statistically validated betting-strategy (especially if it has been verified by your own in-casino derived roll-stats, which I

*strongly*recommend).

Instead, the mature dice-influencer has to stay the betting-course on a small, select number of advantage-validated wagers where he has the strongest edge, and where he can and should be using a predominant portion of his per-hand 7-exposure betting-weight.

From a dice-influencing perspective, the advantage-player’s main objective is to hurry along the “long run” and make his skills pay a major dividend now and for the forseeable future.

*How does he do that?*

Well that brings us right back to my advantage-play

*Recirculation Factor***and "**

**How to hurry along the long run**".

Chuck and I will be discussing that at length in

*Part Five*of this series.

Until then,

**Good Luck and Good Skill at the Tables…and in Life.**

*The Mad Professor*Copyright © 2007