The discussion continues....
Mad Professor
Chuck, I really liked your analogy about how using the Recirculation Factor can determine whether a player’s bankroll-doubling efforts are moving along very efficiently in the fast lane, or whether those labors are mired in slow, heavy, stop-and-go traffic.
Chuck D. Bohnes
Yes, it’s quite straight forward.
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.
Spreading wider or re-deploying away from those best wagers only drags down his advantage, 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).
Mad Professor
Okay, so let’s stick with that analogy, and talk about the non-economic (non poor betting) factors that can divert us from the fast lane back into the slow lane of bankroll growth.
Chuck D. Bohnes
We all know better than to fixate on the bumper of the car ahead. To stay in the fast lane we need to keep our head up, eyes out front and be anticipating the development of the traffic flow.
At the craps table that means paying attention to the myriad of factors that could knock one out of the fast lane.
~Are the dice behaving on that specific table?
~Have you been standing too long and need a break?
~Are the new rowdies at the table destroying your concentration?
In other words, eyes up, and anticipate.
Mad Professor
Game-focus seems to be a real sore point with many talented shooters in that their shooting-concentration is easily thrown off or distracted.
So when you see something developing at the table, for good or for bad, many players feel that is an ideal time to resize their bets.
Let’s touch on that urge to re-deploy, redistribute, or resize your bets during a hand. I know this is a subject that many players are always curious about.
What is your take on it?
Chuck D. Bohnes
The anticipation that we just talked about also means not making wild changes in one’s optimal betting strategy. One should watch traffic patterns develop well ahead of a need for emergency action and lead developments with small, smooth adjustments.
In practice, the DI should plan his betting in advance before entering the casino.
The net win or loss on any hand or session should typically not be anywhere close to an amount that triggers a bet re-sizing.
If one feels frequently that intra-session wins or losses require a drastic bet re-sizing then one should consider carefully whether he’s over-betting his bankroll, and courting doom…or severely under-betting his bankroll, and courting chronic win-deficiencies.
For purposes of capturing the fastest, compounded, long-term growth, bankroll is determined by the total available funds during the relevant term.
If someone is willing to add X new dollars to their bankroll every 3 months, for example, then the total bankroll is the sum of today’s bankroll plus the (present value) of the additional funds already earmarked.
Please be careful though.
This definition of bankroll is strictly only applicable to playing with a solid, consistent, validated long-term advantage…and random-betting is always DIS-advantageous to the player.
Like I said, it is very important to base bet-sizing on your total bankroll.
If one tries to calculate bet sizes based on part of the total bankroll, such as a buy-in or trip roll; then one will subject himself to wild fluctuations in his risk of ruin, as I know we’ll talk about in a moment.
Calculating the size of the total bankroll for purposes of determining optimal bets need not conflict with the DI’s session or trip management. It is okay and perfectly consistent to calculate a total bankroll of $Y thousand, but then decide that no more than $Z hundred will be wagered during any individual session, or trip, or that your buy-in per table will be limited to $Q.
When the total craps bankroll is calculated it is clear that the net win on a single hand or session should be a mere fraction of that total, and hence, will seldom trigger the need to re-size the bets.
Seldom-to-never will intra-session, much less intra-hand, re-sizings be necessary.
Mad Professor
Okay, so we know that applying fresh winnings onto new lower-advantage bets simply knocks us back into the slow lane and should best be avoided if we want to maintain optimal bankroll-doubling speed in the fast lane.
What about the idea of immediately re-deploying mid-hand (intra-hand) winnings directly back onto an existing best-advantage wager through a press, power-press or parlay move?
Chuck D. Bohnes
That’s an example of what not to do.
Let’s say I typically bet two numbers, 4 and 10, for a combined 1% of my total bankroll by putting ½% on each number.
For this example, let’s say my total bankroll is $10,000, so that I have $50 on each of the 4 and 10.
If I toss a winner 10 and use the winnings to press that number, while tossing out a couple chips for the vig, I now have $200 on the felt ($50 on the 4 and $150 on the 10).
I have just doubled by bet-size to $200 from $100.
My total bankroll increased by only 1% ($100/$10k) but I raised my bets by 100%. If my assessment of my advantage did not change, then I have roughly doubled my volatility while also more than doubling my risk of ruin.
I know that I have only a percentage-toss (not an always-controlled shot that would allow me to accurately and successfully “call” my throw), and so my edge over the house is relatively small.
This is dice influencing, not total dice control after all. I know equally well that variance plays a huge role in my toss to toss results.
It makes no sense for me to stand at the table increasing and decreasing my risk of ruin by multiples from toss to toss.
I have decided my comfort zone for risk of ruin and I should play within it.
When the edge is constant, never jump bet size, and hence, multiply your risk of ruin out of proportion with changes in the total bankroll.
Mad Professor
How much of a small bankroll-increase increment is too small to resize your bets?
Chuck D. Bohnes
Here’s another example of what not to do.
Let’s say I was obsessed with eking out every last penny of compound advantage while maintaining a constant risk of ruin, and I am eager to deploy my new wealth.
At the table I quickly re-calculate my optimal bet size to account for my newly won wealth.
Old bankroll was $10k and new bankroll is now $10,098 after paying the vig, an increase of 0.98%.
At a constant risk of ruin, the new bet size could be $10,098 X 1% = $100.98, but the dealer refuses to book bets of $50.49 each 4 and 10.
Practical considerations leave me with the choices of racking the profit or dramatically increasing my risk of ruin - neither ideal, but one far worse than the other.
In the real world, it only makes sense to re-size my bets when I can afford to raise the bet by some practical incremental size. Fortunately, I lose very little in expected bankroll growth even with very wide bands, such as double my $10,000 to $20,000…or halving it to $5000.
Mad Professor
Okay then, in your opinion, how often should one re-size their bets?
Chuck D. Bohnes
It’s a matter of personal preference. Some of the considerations include:
- What are the next larger and smaller practical bet sizes for my best advantage wagers?
- What is my patience for running numbers? At the table? Between sessions? Once each morning? Before each new trip? Only when I absolutely must?
- How often do I play?
- How close is my risk of ruin to an over-bet? The easier it is for losses to result in an over-bet, the more frequently one should re-calculate.
- Do I use only one simple advantage all the time or do I have complex assumptions of my advantage based on varying conditions, such as position, toss-type, table size, table surfaces? And hence, do I need to remember many more numbers each time I re-size?
Mad Professor
I generally increase my base bet-values by a substantial amount when my overall bankroll increases by 50%. I also re-appraise and re-size my bet-values incrementally on a monthly basis even if my bankroll hasn’t increased by that amount. For example, if it has grown by 15%; then I might increase my basic bet-values by around 10% until my BR has reached the full 50% growth-mark.
Chuck D. Bohnes
There are two practical re-sizing methods.
Absolute boundaries. One practical method is to define absolute boundaries to re-size. They can be stated as percentages or dollar amounts.
For example, double or halve bankroll, or +/- $5000.
For this method, you simply calculate three bet sizes:
Bet size for your starting bank roll, bet size for a bankroll that has doubled and bet size for a bankroll that has halved. Knowing these three sizes you play at the tables using whichever of the three is appropriate.
For example, my starting bankroll is $10,000.
My bet is $50 each 4 and 10.
When my bankroll is equal or greater than $20,000 I will bet $100 each 4 and 10.
When my bankroll is $5,000 or less I will bet $25 each 4 and 10.
Following a session/trip that the upper (e.g., double) or lower (e.g., halve) threshold is breached I will need to recalculate my bet sizes.
For example, let’s say during my last session my bankroll increased from $18,150 to $22,450.
I now need to recalculate my bet size based on a bankroll of $20,000.
So my new upper and lower bankroll boundaries are $40,000 (double $20k) and $10,000 (half of $20k).
My new bets are $100 each 4 and 10, bumped to $200 each 4 and 10 to the upside (above $40,000) and $50 each 4 and 10 to the downside (below
$10,000).
This approach is most useful when the game rules or number of variations is complex. For example, if I use differing advantage assumptions for 3 table sizes, 4 positions and 2 surfaces.
Away from craps I have re-sized bets when my bankroll increases one-third (+1/3rd) or declines by one-quarter (-1/4).
These numbers represent a compromise between re-sizing regularly and spending excessive time re-calculating numbers.
The +1/3 and -1/4 also creates symmetry in the re-sizing.
For example, if I start with $10,000 and increase it by +1/3 to $13,333 and then decline by -1/4, I am back to my original $10,000. Hence my bet size when the bankroll is between $7,500 and $13,333 is always the same size no matter how I get there.
This symmetry is lost if you re-size say + or - $5,000. Re-sizing at double or half does display a similar symmetry that occurs with the +1/3 and -1/4 resizing.
Mad Professor
How about using a time-interval (like a monthly re-appraisal) to re-size your bets instead of waiting for an actual milestone-percentage bankroll increase?
Chuck D. Bohnes
That raises the second practical method whereby you regularly re-size your bets, perhaps once a week or before each trip. Teams often employ this method since having several people playing concurrently can sometimes lead to dramatic bankroll swings over very short periods.
With regular re-sizing one simply re-sizes more frequently than $-boundaries are breached, and hence, $-boundaries become mostly irrelevant. Nonetheless, it always helps to designate safety levels at which new numbers should be run just in case of those very rare, extreme swings.
The simplicity of craps betting makes regular re-sizing quite reasonable for anyone with the patience to regularly run their own numbers. Regular re-sizing also has the advantage of maintaining a near-constant risk of ruin.
Mad Professor
That’s an interesting approach. I think I’m going to incorporate some of your suggestions into my own game-plan. Any final words on this portion of the discussion before we move on to Part Seven of this series?
Chuck D. Bohnes
Yes, the risk-conscious dice-influencer grows his bankroll most quickly by focusing on his few best-advantaged wagers and gradually “stair-stepping” his bet sizes in accordance with bankroll fluctuations across sessions, not intra-session nor intra-hand.
And for those who are wondering … yes, this approach is 100% consistent with fractional Kelly betting, but one need not be a Kelly adherent to employ it successfully.
Mad Professor
I’ll say this, Chuck. If fellow board-members are only deriving even one-tenth of the bankroll-growing nuggets of wisdom out of your ideas here, as I am; then they are well on their way to substantially increasing their advantage-play earning.
I, for one, truly appreciate your fine contributions.
Until Part Seven of this series,
Good Luck and Good Skill at the Tables…and in Life.
The Mad Professor
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