Question for Don - Geometric CE

[MJ1]

Don, can you please explain what it means to optimize the geometric CE of your bankroll? I know it has something to do with logs but the math is over my head. Maybe you can state it in layman terms such that you explain the math but not too intensively? I think a lot of members on these board could benefit.

On another note, you advocate SC0RE but this metric only considers games under very strict conditions. What if two games have different table minimums and maximums? What if you can generate substantially more EV in one game but a higher SC0RE in the other game? In your opinion, between CE and SC0RE, is one metric a better indicator of long-term bankroll growth than the other?

Thanks, MJ

[DSchles]

"Don, can you please explain what it means to optimize the geometric CE of your bankroll? I know it has something to do with logs but the math is over my head. Maybe you can state it in layman terms such that you explain the math but not too intensively? I think a lot of members on these board could benefit."

Kelly wagering has several important qualities, among them optimal geometric growth of the bankroll. What this means is that: a) If someone else with the same bankroll uses a different money management scheme for the same game, your bank will grow faster than his. In fact, if you play "forever," your bank will exceed his by any predetermined multiple; b) You tend to reach a specified level of winnings in the least average time. That is, the number of hands you will have to play, on average, to reach any predetermined goal will be the minimum possible, compared to any other wagering system.

On another note, you advocate SC0RE but this metric only considers games under very strict conditions. What if two games have different table minimums and maximums? What if you can generate substantially more EV in one game but a higher SC0RE in the other game? In your opinion, between CE and SC0RE, is one metric a better indicator of long-term bankroll growth than the other?"

"What if you can generate substantially more EV in one game but a higher SC0RE in the other game?"

A rational investor should prefer the investment with the higher Sharpe ratio, and a rational player should prefer the game with the higher SCORE. One blackjack expert used to say, "EV isn't everything." The point is, you have to consider the risk you take in attaining that EV. Maximizing EV blindly, without referencing the risk you take is foolish.

Don

Don

[MJ1]

Thanks Don. Based on how you defined geometric CE, does that mean CE is better than SCORE for optimizing long term bankroll growth? If that is indeed the case why bother with SCORE?

Regarding the Sharpe ratio it would seem for blackjack it would be calculated as (Hourly EV - Hourly CE)/Hourly SD. Correct?

Thanks,
MJ

[DSchles]

"Thanks Don. Based on how you defined geometric CE, does that mean CE is better than SCORE for optimizing long term bankroll growth? If that is indeed the case why bother with SCORE?"

I don't tend to think of them as different concepts. If you bet optimally, you maximize SCORE; they go together. Similarly, if you bet optimally for blackjack, CE is, normally, 50% of your EV. You don't have to do anything else to attain that. It simply falls out of the equations or math.

"Regarding the Sharpe ratio it would seem for blackjack it would be calculated as (Hourly EV - Hourly CE)/Hourly SD. Correct?"

Interesting comment, but, no, I don't think so. In finance, to compute the Sharpe ratio, you subtract the risk-free rate (RFR) from what you're earning, because, well, anyone can achieve the RFR with no effort at all. But CE is different. CE indicates an amount you'd be willing to accept to forgo playing the risky game, simply to have that amount of money, with certainty. But, no one says that you can actually receive that money without any effort whatsoever in real life. Let me give you an example:

In a theoretical game, I give you a chance to flip a coin. Heads, you win $1 million, tails, you get nothing. Alternatively, I ask you, "What amount of money would you be willing to receive with certainty, to NOT play the game?" Now, different people give different answers, thereby creating different CEs. But, in all cases, you aren't going to get that money (around $500,000 or less) in real life! And, if you're playing blackjack with an EV of, say, $500 an hour and a CE of $250, that does NOT mean that you can readily find a job that pays $250 an hour with certainty ($500,000 a year)!

Do you see my point? To me, the CE in BJ is not the same as the RFR. The latter is a real, attainable concept. The former may very well NOT be.

Don

[Freightman]

Norm. Comparing in CV Data. DI is Sharpe Ratio? The higher the SCORE the better and the lower the DI the better. Correct?

DI^2 = SCORE. Higher the SCORE, higher us the Desirability Index.

SCORE is a bit easier.

[MJ1]

"Thanks Don. Based on how you defined geometric CE, does that mean CE is better than SCORE for optimizing long term bankroll growth? If that is indeed the case why bother with SCORE?"

I don't tend to think of them as different concepts. If you bet optimally, you maximize SCORE; they go together. Similarly, if you bet optimally for blackjack, CE is, normally, 50% of your EV. You don't have to do anything else to attain that. It simply falls out of the equations or math.

But what happens when you can't bet optimally due to being severely underfunded so RoR is around 30% to 40%? Now CE is no longer 50% of EV. In fact the ratio is around 5%.. In this case should the counter choose the game with higher SCORE or CE? The problem with C-Score is it doesn't factor in the size of the bankroll. So long as the bet spread is large C-Score is acceptable. CE on the other hand is practically around 0!

Given the constraints of the game when CE is maximized SCORE is in the 20s and hourly EV is low. Should I just try and find a happy medium between hourly EV and RoR?

Thanks,
MJ

[ZenMaster_Flash]

"DI is Sharpe Ratio?"

Not exactly, but the Kelly Criterion was a
direct outgrowth of the Sharpe Ratio.

Try reading "Fortune's Formula"

Remember, many BJ questions are not
mathematical in nature, nearly as much

as they are economic issues. Economists
use mathematics as their tool.

I have had full-blown (real live) arguments
with a prolific poster on this forum as he is
not capable of understanding this crucial
distinction when discussing casino-related
issues for an A.P., much to the amusement
of another very sharp A.P. No pun intended
when referring to Sharp(e) L.O.L.

[ZenMaster_Flash]

Book Sent.

Excellent Summer Reading!

[DSchles]

"But what happens when you can't bet optimally due to being severely underfunded so RoR is around 30% to 40%? Now CE is no longer 50% of EV. In fact the ratio is around 5%.. In this case should the counter choose the game with higher SCORE or CE?"

This is what you're not understanding. A game has no SCORE if you aren't betting optimally. It may have an hourly win rate, but that can't be a SCORE. So, there's no such thing as a game with a ROR of 30% having a SCORE. By definition of SCORE, the two concepts are incompatible.

"The problem with C-Score is it doesn't factor in the size of the bankroll. So long as the bet spread is large C-Score is acceptable. CE on the other hand is practically around 0!

"Given the constraints of the game when CE is maximized SCORE is in the 20s and hourly EV is low. Should I just try and find a happy medium between hourly EV and RoR?"

Yes, I suppose. I'm not trying to be evasive. I just think that playing with such large RORs is such a bad idea that I haven't devoted a lot of time to thinking about it.

Don

[MJ1]

If the goal is to grow the bankroll as quickly as possible wouldn't it make sense to take the game with the highest geometric mean, aka CE, regardless of how tiny it might be?

I want to try and double the bankroll as quickly as possible while optimizing the expected growth rate given the parameters of the game.

MJ

[MJ1]

Any thoughts?

[Norm]

The max CE for a specified game and desired RoR is 50% of the win rate.

But, I'm not sure what you're getting at. There are a lot of variables.

[MJ1]

The max CE for a specified game and desired RoR is 50% of the win rate.

This is only true when playing to 13.53% RoR. But what about when a counter is underfunded and consequently playing to 33% RoR with a fixed unit? Now CE/WR ratio is well below 0.5.

What I was asking is under such circumstances should one use CE or C-SCORE for game selection? C-Score doesn't factor in the size of a small bankroll whereas CE does. It would seem C-Score can be increased indefinitely just by increasing bet spread. But then CE drifts toward 0. So which metric should you use in this underfunded scenario?

Thanks
MJ