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Can You Fool Your Bankroll into THINKING and ACTING Like It Is Bigger? - Part Seven

Arrogance and self-awareness seldom go hand in hand.


Mad Professor

Arrogance and self-awareness seldom go hand in hand.

Beating an ‘unbeatable’ game like craps means
focusing on the things that make it beatable, and staying away from the things that make it unbeatable.

Randomness makes the game unbeatable.

Derandomizing the dice makes it beatable.

Once the dice are de-randomized though, you still have to bet on those now-influenced results in a way that takes the edge you’ve developed, and turn it into tangible profit.

As series of bets are made, a portion of your bankroll is churned, meaning that if you bet let’s say
1% of your total bankroll on a series of wagers; then after one-hundred of those bet-series, you will have churned through your entire gaming bankroll once.

After doing so, how much money can you reasonably expect to have gained or lost?

The answer of course lays primarily in how much of an edge (if any) those bets have over the house. 

The bigger the edge, the more reasonable it is to expect those wagers to produce an overall profit.

The lower that advantage, the lower your expected bankroll growth will be. 

Players tend to get impatient if their bankroll isn’t growing as rapidly as they think it should. If they have a validated edge over the casino, they often feel like they should be making money hand over fist on nearly every hand. 

When that doesn’t happen, they tend to get impatient and frustrated at the lack of rapid progress, which in turn causes them to make high-risk plays that are
not advantageous, but merely temporarily satisfies their urge to “Do SOMETHING” 

The resultant setbacks that they burden their bankroll with because of that, means they'll have more of a hole to dig themselves out of.

That brings us back to the main discussion Chuck D. Bohnes and I are having about applying Recirculation Factors.

Recirculation Factors enable us to actively manage our advantaged wagers with an eye on both their overall positive edge and as well as their volatility . Using the R-F's mean steadier and highly predictive bankroll growth.

For example, I think it’s important to note that the R-F approach leads to much
lower volatility and a substantially lower risk-of-ruin than someone who appears to be betting in a less-aggressive-looking way (like spreading their money over numerous wagers and getting a high hit-rate), yet is experiencing way more radical bankroll gyrations, a substantially higher risk of complete ruin, and practically no real overall bankroll growth whatsoever.

Recirculation Factors direct you to the advantaged-wagers where your money will do the most good and enable you to grow your bankroll the quickest.

Chuck D. Bohnes

Well, it's clear that managing bankroll growth leads to plenty of benefits. Let's play with how we can apply the Recirculation Factors in order to rake in those bennies.

Let's say that our skilled shooter,
Easy Eddie, is currently betting Across (Place-betting the 4, 5, 6, 8, 9, and 10) at a 1% blended edge, but could concentrate his wagers to a 2% blended edge by re-deploying the Outside wagers to increased Odds behind his Passline bet, and wagering Place-bets on the 6 and 8 only.

concentrating his wagers to achieve a higher blended advantage, he has shifted his Recirculation-Factor from 13 to 8, leading to almost halving the amount of time needed to double his bankroll. Easy Eddie has just piled up his bennies by using the R-F concept to identify a more profitable betting strategy. 

He’s using the
same amount of money, but using a more profit-oriented focus.

On the other hand, let's say Easy Eddie has intrinsic potential of a 2% blended edge, but dilutes his betting with marginal center-of-the-table Prop wagers. He is raising his R-F and condemning himself to suffering more time at the crowded, randy-infested, low-min tables.

Mad Professor

You bring up a good point.

Let’s revisit the Recirculation Factor chart to get a better picture of what you are talking about.

Picture 33

The interesting thing about the R-F approach, other than the obvious bankroll-doubling focus that it has, is that it illustrates that complicated betting-schemes are not needed in order for a modestly-skilled dice-influencer to get ahead rapidly…and to stay ahead pretty much of the time.

In the case of
Easy Eddie, it will take him around 203 hands to double a $500 buy-in when he's betting $32-Across; whereas, it will only take 125 hands to double his buy-in if he focused that same money on increased PL-Odds while maintaining Place-bets only on the 6 and 8. It takes Eddie 62% longer to achieve the same buy-in doubling goal even though he had his money on more wagers that offered a higher overall hit-rate.

Chuck D. Bohnes

Exactly! The potential to achieve the most out of our 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 D-I will dramatically slow his bankroll growth-rate if he fails to treat chips won any less strategically than he wagers any chips that were already in his rack.

Mad Professor

Your point is well taken.

By using the lowest possible Recirculation Factors of the bets where we have the highest advantage over the house, we can
double and then keep re-doubling our bankroll growth by using seemingly aggressively-sized wagers that are still actually quite safely within the parameters of Kelly Criterion betting…and obviously still completely safe within risk-of-ruin. 

What continues to amaze me though, even after using the Recirculation Factor chart to guide my best-bet wagering for quite a while now, is how using low-index R-F wagers actually lead to
much-lower-than-expected volatility, as well as drastically lowering my risk-of-ruin over someone who bets much less-aggressively (in terms of lower-valued but wider-spread bets, yet is experiencing bankroll gyrations that are several orders above someone using a lower R-F…all the while enduring a substantially higher risk of complete ruin, and again, realizing practically no overall bankroll growth.

That's the part that continues to amazes me about the functionality of the R-F approach to advantage-wagering

Chuck D. Bohnes

That’s right. The benefits of a dice-influencer using a lower Recirculation Factor (I like using ‘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.

Mad Professor

Now, if there is one thing that continues to disappoint me (but not surprise me in the least); is the fact that so many skilled players love to play the game too much, and where they put so much money on so many wagers that don’t have an advantage. 

That is, when they have the dice in their hands, they are an
advantage-player who bets with steely determination, discipline, and resolve; but when other non-skilled random-rollers have the dice, they turn back into degenerate gamblers.

Chuck D. Bohnes

One thing to keep in mind though, is if a player is going to be betting on random-rollers; then it is best to stick to the low-vig wagers where the house doesn't take such a big bite out of the randomly-bet portion of your bankroll.

You talked about
random-bet stamina and bankroll staying power in Part One of this series, perhaps it's worth a revisit.

Mad Professor

That's a valid point.

When it comes to random-betting:

WHAT you bet and HOW you bet, will determine your bankroll’s stamina.

SIZE of bankroll is only one consideration of how long you can actually stay at the table. 

Once you understand the laws of house edge and probability, you can get a handle of ways you can fool your bankroll into thinking and acting like it is bigger.

So let’s look at “staying power”.

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.

Picture 34

So for example, if you are going to be betting on random-rollers, where your buy-in is $500.

~You 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 we will usually run out of money.

Chuck D. Bohnes

Okay, that covers random-betting, but the first chart above shows the situation for dice-influencers who are able to create an edge over the house. I think that is the important one from an A-P perspective because it underscores the fact that the lower your Recirculation Factor, the faster your bankroll travels to its “doubled” destination. 

Since lower Recirculation Factors flow from higher advantages, the
conscientious D-I concentrates his wagering on only his highest-edge bets. 

If he is wagering high house-edge bets on
random-rollers; then he's just making things extremely difficult for himself. His advantaged wagers will have an even more difficult time in prevailing too, in terms of producing any overall profit, let alone any thoughts of bankroll doubling. 

Spreading wider or re-deploying away from those best-advantaged wagers only drags down his edge, increases his Recirculation Factor, and lengthens his E.T.A. (estimated time to arrival, measured in number of advantaged hands he’ll have to throw before doubling his bankroll). 

The key concept is that the combination of your skill level, your casino opportunity, and your then-existing preparedness; produces a
very specific optimal betting strategy for you at that time.

If you intentionally avoid
that, then you intentionally avoid profit too.

Mad Professor

Yeah, that’s a good point, but I wonder how many currently-skilled, but not-yet-profitable dice-influencers see it that way. Aren’t they mostly caught up in complicated multi-wager betting-schemes that cover far too many numbers?

Chuck D. Bohnes

Mad Professor, it really comes down to bet-management. Your betting examples in Part II of this series demonstrated that; as a players edge increases, a disciplined dice-influencer can accelerate his bankroll growth through two dynamics:

1) A lower Recirculation Factor; and,

2) A larger wager size for any given risk level. 

I feel the concept you're promoting also speaks to the mirror effect, which is equally important. In particular, having a
lower advantage requires the DI to reduce his bet size to maintain comparable risk levels.

Mad Professor

I agree. When some players see how much their high recirculation-factor bets are costing them, and how much a lower recirculation-factor betting regime could produce…all within their same current D-I skill-set; they quickly realize where they have to make changes if they want to get more money out of those exact same skills.

As you say, the same holds true for players with a more modest set of derandomizing skills. Having a lower advantage requires that player to reduce his bet size to maintain comparable risk levels.

Chuck D. Bohnes

Answering the “How much do I want to make, and how long do I want it to take to make it? question is entirely up to the skilled shooter. It’s based on the advantage he currently has, and the number of advantaged hands he’ll have to play to realize his goals.

He can either exploit his
best opportunity, which will accomplish his goals the fastest; or he can waste most of his efforts (as measured by number of advantaged hands played), by continuing to bet on lesser-advantaged or entirely dis-advantaged wagers. 

Nothing you do can make you go faster than staying with the lowest Recirculation Factor. That identifies the fastest track to bankroll doubling.

Mad Professor

That’s quite a profound and striking statement, Chuck. We’ll pursue that further in Part Eight of this series. I know that part of the discussion holds some very interesting angles by which a dice-influencer can use the Recirculation Factor index for even the most modest of edge, to gain an advantage over the house and over his bankroll doubling and re-doubling efforts.

Until then,

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

The Mad Professor
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This page contains a single entry from the blog posted on February 10, 2009 7:37 AM.

The previous post in this blog was Can You Fool Your Bankroll into THINKING and ACTING Like It Is Bigger? - Part Five

The next post in this blog is Can You Fool Your Bankroll into THINKING and ACTING Like It Is Bigger? - Part Eight.

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