A frank and candid discussion between Chuck D. Bohnes and the Mad Professor

I want to welcome a co-writer of sorts to this series. Though he hasn’t been involved in dice-influencing as long as many of you; he has been involved in various forms of casino advantage play for many years now.

Chuck D. Bohnes brings a novel perspective and a fresh enthusiasm to our game. While his comments are always thought-provoking; you may find that they’ll also add a new element or two to your money-making efforts. I, for one, always look forward to his unique take on things.

Let’s jump right in.

**Chuck D. Bohnes
**

Mad Professor, your Recirculation Factor articles constitute an excellent series with “money” concepts for D-Is who approach shooting as more than just a recreational game. They shine a fresh light on a topic that should help many dice-influencers better exploit their skill to its fullest potential.

For December 2007, the Borgata reported to the NJ CCC that it had a $4 million win for craps on a handle of just under $21 million, representing a win percentage of 19.6%. Almost 20% earned on individual crap bets that have an average house-edge of only a couple percent each. Without recirculating its bankroll, the Borgata would never achieve a sufficiently high hold and subsequent return on assets to stay in business.

Away from the casinos, many Main Street retail businesses operate on razor thin operating margins that only support sound businesses as a result of the turnover they achieve.

Just like all thin margin businesses that require volume to be profitable, so too does the advantage player who expects to extract more money from the tables than he would make stuffing his bankroll into a money-market fund.

For craps, you have given us the metric, "Recirculation Factor," to cover this critical business concept. You credit Alan Krigman for bringing forward this concept. I am curious which business inspired Mr. Krigman.

**Mad Professor**

Chuck, as you know, Alan Krigman is a highly regarded gaming columnist who has a keen understanding of not only the math of the game, but also a great grasp of the psychology behind how players make their varied and sundry betting decisions.

My sense of it is that Alan wanted the everyday gambler to be aware of how the casinos' recirculation factor impacted their bankrolls. I recognized that a skilled dice-influencer could employ that same business-model in attacking craps to make his bankroll work harder for him.

In fact, the Recirculation Factor of an advantage-player’s bankroll (and especially his smaller session buy-in) is a concept that gets very little attention…but can contribute greatly to either his ultimate success or failure.

**Recirculation Factor as a Proven Business Dynamic**

**Mad Professor**

The average turnover of a bankroll during a session is called the Recirculation Factor.

It’s calculated from house edge, the number of betting-units your bankroll represents, and the "win/drop hold percentage" or "PC" for craps.

Before we can look at how a dice-influencer can fool his bankroll into thinking and acting like it is bigger; we first have to look at how it works in a negative-expectation randomly-rolled game.

To find how many bets you can expect to make in a session, we simply multiply the number of betting-units you have in your bankroll by the Recirculation Factor for the edge at which you are playing.

Here’s a couple of examples of how the recirculation factor works:

~Buy-in for $500.

~Bet $10 on the Pass Line with 1x-Odds.

~Place the 5 or 9 for $5 each.

~Your total 7-exposure is $30.

~Your stake is $500 divided by $30.

~That equals about 17 betting-units.

~The house has an effective edge of 1.9%, and we’ll round it off to 2%.

~Multiply the 17 units by the factor of 8 shown for the 2% house edge shown above.

~We find that 17 x 8 equals 136 bets.

~That means with a $500 buy-in, we can expect to make about 136 of those combined neg-ex bets during a session. On a 14-player table, that equates to about ** ten laps** before the randomly-betting player will usually run out of money.

*What if you Trim the House-Edge for the Same Amount of Money at Risk?*~Bet $10 on Pass Line again, but back it up with 2x-Odds without any other bets.

~Now the house advantage is only 0.6%.

~That gives you a recirculation factor of 20, halfway between 0.5 and 0.75 percent.

~You now have an expected 17 units x 20.

~That equates to 340 bets during the same session, from the same size of bankroll.

~That means with a $500 buy-in, we can expect to make about 340 of those combined neg-ex bets during a session. On a 14-player table, that equates to about

**before we will usually run out of money.**

*twenty-four laps*

*What Happens When 3x/4x/5x-Odds…or 10x…or 20x-Odds are Available?*

While betting more money, you get a lower house-edge on a 3x or higher Odds table.

For example:

~Bet $10 on the Pass Line, then back it up with $30 in Odds (for a total 7-exposure of $40).

~Your buy-in of $500 divided by $40, gives you 12.5 betting units.

~The house-edge against you is now less than 0.5%.

~You have 12.5 units x a recirculation-rate of 25, or about 312 bets during the session.

*So How is the Re-Circulation Rate Applicable to Your Bankroll?*Using the recirculation factor when making bet-decisions; helps you determine the optimum size and placement of your wagers.

Now in a randomly-thrown game that only means being able to stay at the tables

*substantially longer*while using the same bankroll.

However, if you are an advantage-player, then it changes not only your

**, but also your**

*STAYING-power***as well.**

*EARNING-power*To my mind, it is important to be able to stay in the game long enough to get into a shooting groove. For many players, this may take one, two, or even three trips around the table.

If you don’t have the staying power or “bankroll stamina”, you may never be able to fully capitalize on your own shooting skills.

Fooling your bankroll into thinking and acting like it is bigger lets you stay in a randomly-thrown game longer; but more importantly, it lets you better capitalize on your own dice-influencing talents when the dice come around to you.

**Unlocking Bankroll Potential**

**Chuck D. Bohnes**

The potential to achieve the most out of their bankroll has always existed. DIs simply need to apply discipline and simple tools, such as your Recirculation Factor, to “unlock” that potential.

One of those disciplines is to recognize that every chip won immediately adds to the DI's bankroll. If you win the bet, the payoff is yours, not the casino's.

A DI will dramatically slow his bankroll growth-rate if he fails to treat chips won any less strategically than he wagers chips from his rack.

**Mad Professor**

I agree, the idea of thinking of freshly won money as "found money" or “playing with the casino’s money” is a false premise; and it certainly leads to bet-making carelessness and bankroll negligence.

The thrust behind the concept of determining the Recirculation Factor for random-rollers, is so that skilled shooters will focus whatever money they feel compelled to wager on random-rollers, on bets that will give them the highest recirculation-rate, and therefore, the most likely bankroll-survival option.

Concurrent with that, if they use one of the lower-ranked Recirculation-rates for their own shooting on their most advantaged wagers; then the quicker their bankroll-doubling will be.

I think in many ways, the concept of ‘unlocking’ one’s bankroll potential, is closely tied to how a player thinks about, respects, and utilizes his money.

Even when a skilled player doesn’t say something along the lines of “I’m playing with the casino’s money now, so I can be a little more carefree with it”; you can see it in the way they bet on subsequent negative-expectation wagers.

You can also see it in the blithe way they increase the breadth and risk-factor of the bets they are making when they get the dice back in their own hands. Instead of putting the bulk of their money on the wagers that actually brought in most of that new-found profit; they’ll spread it out over less positively-advantaged wagers or even onto negatively dis-advantaged ones.

Their (usual) subsequent losses almost make it seem like they don’t want to keep their newly-won profit and they don’t feel deserving of its bankroll-expanding benefits; but I’ll leave that discussion for another day.

**How Many Pos-Ex Hands Will I Throw Before Likely Doubling My Buy-In?**

If you’ve read Regression Avoids Depression - Part 21; you already know approximately how many ISR-based hands it will take to double a given TOTAL gaming bankroll depending on your SRR-rate and the triggering of the Steep Regression at the optimal point in your hand.

Today though, we are looking at how long, on average, it will take to double your typical Session Buy-In based on the blended positive-edge your dice-influenced wagers have over the house.

Now obviously I am only talking about your own advantaged shooting. If you piss away twice as much money on random-rollers as you make on your own shooting; well you’re very rarely going to double anything except your frustration and aggravation.

As we did in

*Part One*of this article, let’s look at a typical $500 session buy-in.

To find how many bets you can expect to make in a session, we multiply the number of combined betting-units you have in your session buy-in by the positive-expectation Recirculation Factor for the edge at which you have over the house.

Here’s a couple of examples of how the re-circulation factor works for an advantage-play dice-influencer:

~Buy-in for $500.

~Bet $10 on the Pass Line with 1x-Odds.

~Place the 5 or 9 for $5 each.

~Your total 7-exposure is $30.

~Your stake is $500 divided by $30.

~That equals about 17 betting-units.

~Let’s say that your pos-ex overall blended-advantage for these wagers gives you an effective edge of 1.9%; so we’ll round that off to 2%.

~Multiply the 17 units by the factor of 8 for the 2% player-edge shown above.

~We find that 17 x 8 equals 136 hands.

~That means with a $500 buy-in, you can expect to throw about 136 of those combined pos-ex hands before doubling your $500 buy-in.

**What if You Decrease the Player-Edge for the Same Amount of Money at Risk?**

Let’s say that your shooting-edge is quite a bit lower than 2%.

~Bet $10 on Pass Line again, but back it up with 2x-Odds without any other bets.

~Now the player-advantage is only 0.6%.

~That gives you a re-circulation factor of 20, halfway between 0.5 and 0.75 percent.

~You now have 17 expected betting-units x a re-circulation factor of 20.

~That equates to 340 hands before you will likely double the size of the same session buy-in.

~In other words, with a $500 buy-in, you can expect it to take about 340 of those combined pos-ex hands before doubling your base buy-in.

**If You Have a Greater Than 2% Blended-Advantage**

I’ll use this example to illustrate how an increased edge affects how rapidly you cn double your buy-in.

~Buy-in for $500.

~Bet $10 on the Pass Line with 3x-Odds.

~Place-bet the 6 and 8 for $24 each if they are your top two, best-performing box-numbers.

~Your total 7-exposure is $88.

~Your stake is $500 divided by $88.

~That equals about 5.7 betting-units.

~Let’s say that your pos-ex overall blended-advantage for these wagers gives you an effective edge of 5.0%.

~Multiply the 5.7 betting-units by the re-circulation factor of 3 for the 5% player-edge shown above.

~We find that 5.7 x 3 equals 17 hands.

~That means with a $500 buy-in, you can expect to make about 17 of those combined pos-ex hands before doubling your $500 buy-in.

**Benefits
**

**Chuck D. Bohnes**

Advantage players seem to like nothing better than to count their bennies (benefits), whether they be hundred-dollar bills or comp benefits. Let's count down some of the bennies of deploying strategies grounded by your Recirculation Factors.

**Mad Professor**

Let me preface that count-down by noting that the common denominator of the many benefits, is that they all follow from targeting lower Recirculation Factors to achieve faster bankroll growth.

**Long Run Bennie**

**Chuck D. Bohnes**

Until an advantage crapster reaches the "long run" his profitability and his confidence in his ability is highly subject to volatility. A primary objective of any profit-oriented player should be to reach the long run as quickly as possible where results more clearly reflect validated skill and where skill can be distinguished from the noise of natural variance.

**Mad Professor**

That’s a very good point.

I like the idea of getting profit-results that are more closely tied to one's shooting ability than the feast-of-a-long-hand variance that most shooters count on to make most of their money. When you subtract the famine-inducing variance that a short Point-then-7-Out hand induces; you are often left with a negative bankroll balance.

Now don’t get me wrong, I know that variance is part of the game, and I have actually grown to embrace it as part of the ebb and flow of winning; but what I like about the Re-circulation Factor is that it defines the horizon over which you can expect to double your buy-in (including all of those P-S-O’s that seem to turn-off a shooter’s confidence even when he should hold the course). I think that sort of near-immediate gratification is important to shooters from the Dr. Spock era.

Important too, is the idea of forcing the “Long Run” to show up sooner, and the Recirculation Factor is the tool that can show exactly how, why, and when that can happen.

So How is the Re-Circulation Rate Applicable to Your Own Advantage-Play Bankroll?

Using the re-circulation factor when making bet-decisions, helps you determine the optimum size and placement of your wagers.

In a randomly-thrown game, using the re-circulation factor and betting as little money on the lowest house-edge bets means that you will be able to stay at the tables substantially longer while using the same bankroll.

However, as an advantage-player who is validly able to influence the dice; then it changes not only your STAYING-power, but also your EARNING-power as well.

In that case, the more you bet (within the confines of your session buy-in) on your highest-advantage positively-influenced wagers; the quicker you will double that buy-in.

In other words, it will take less hands to double your bankroll if you stick with your absolute best, highest-edge bets than it would if you spread your money more thinly across additional lower-edge numbers…thereby diluting your overall blended-advantage and stretching out the number of hands it will take before you double-up your session buy-in.

To my mind, the quicker you can double your session buy-in (as measured by the number of advantaged hands you will have to throw in order to do so); the better.

To my mind, the quicker you can double your session buy-in (as measured by the number of advantaged hands you will have to throw in order to do so); the better.

Fooling your bankroll into thinking and acting like it is bigger, not only lets you stay in a randomly-thrown game longer; but more importantly, it lets you better capitalize on your own dice-influencing talents when the dice come around to you.

**Chuck D. Bohnes**

Those are some important points, MP. I would like to discuss them further in Part Four of this series.

**Mad Professor**

You’ve got a deal.

Until then,

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

*The Mad Professor*

**Copyright © 2007**