Negative CE?

[MJ1]

CE is about certainty of BR growth.

This says that your BR will probably last longer if you pay the casino $1 per hour and not play rather than play with the $17/hour EV and the risk profile you have.

My lifetime RoR is 33%. I would like confirmation of your statement. I've never heard anything even resembling your type of explanation. Not saying your wrong necessarily.

Full Kelly play with constant resizing maximizes logarithmic BR growth.

I already know that. What is the equation for Kelly so I can graph it?

[Three]

https://www.blackjackapprenticeship....dvantage-play/

It explains that CE is the risk adjusted return. If you bust your BR you have a negative hourly in actual play. This gets averaged with the rest of the time you are at EV to get a picture of what you true average hourly should be. EV assumes you can't go broke and therefore will reach the long run. CE attempts to come close to the true average hourly of everyone starting with your BR and playing what you play the way you play it including those that bust out. This is the certainty of BR growth. You are likely to bust your BR with a 33% RoR.

Say you have a $10K BR and you have a RoR of 33%. 3 guys start playing this and 1 is expected to end -$10K by busting out. That reduces the average of the group because he no longer "earns" and he has a lifetime negative $10K deficit. So the 3 guys played with an EV of X but their results reflect 2/3rds of X -$10K when the guy busted out. Did the 3 guys really have an expectation of X dollars for that time given that one was expected to bust out? If none bust out then yes but that is not certain. What if you are the guy that busts out? Certainty equivalent attempts to assign a certainty to BR growth.

If you are betting full kelly CE equals EV.

Perhaps this way of expressing CE will be to your liking:

The certainty equivalent is a guaranteed return that someone would accept rather than taking a chance on a higher, but uncertain, return. To put it another way, the certainty equivalent is the guaranteed amount of cash that would yield the same exact expected utility as a given risky asset with absolute certainty.

[ZeeBabar]

https://www.blackjackapprenticeship....dvantage-play/

It explains that CE is the risk adjusted return. If you bust your BR you have a negative hourly in actual play. This gets averaged with the rest of the time you are at EV to get a picture of what you true average hourly should be. EV assumes you can't go broke and therefore will reach the long run. CE attempts to come close to the true average hourly of everyone starting with your BR and playing what you play the way you play it including those that bust out. This is the certainty of BR growth. You are likely to bust your BR with a 33% RoR.

Say you have a $10K BR and you have a RoR of 33%. 3 guys start playing this and 1 is expected to end -$10K by busting out. That reduces the average of the group because he no longer "earns" and he has a lifetime negative $10K deficit. So the 3 guys played with an EV of X but their results reflect 2/3rds of X -$10K when the guy busted out. Did the 3 guys really have an expectation of X dollars for that time given that one was expected to bust out? If none bust out then yes but that is not certain. What if you are the guy that busts out? Certainty equivalent attempts to assign a certainty to BR growth.

If you are betting full kelly CE equals EV.

Perhaps this way of expressing CE will be to your liking:

The certainty equivalent is a guaranteed return that someone would accept rather than taking a chance on a higher, but uncertain, return. To put it another way, the certainty equivalent is the guaranteed amount of cash that would yield the same exact expected utility as a given risky asset with absolute certainty.

So, T3, what are some of the things you need to calculate CE. BR of course and what? For example, a BR of $40k, a spread of $25-$150 in a DD game, H17, standard rules with pen of 75%. Is that enough to calculate CE?

[Three]

So, T3, what are some of the things you need to calculate CE. BR of course and what? For example, a BR of $40k, a spread of $25-$150 in a DD game, H17, standard rules with pen of 75%. Is that enough to calculate CE?

The link gives you the formula but all the software that you use to sim things does it for you.

[MJ1]

It explains that CE is the risk adjusted return. If you bust your BR you have a negative hourly in actual play.

How does CE compute my negative hourly earnings? How does it know how many hours till you bust out?

This gets averaged with the rest of the time you are at EV to get a picture of what you true average hourly should be. EV assumes you can't go broke and therefore will reach the long run. CE attempts to come close to the true average hourly of everyone starting with your BR and playing what you play the way you play it including those that bust out. This is the certainty of BR growth. You are likely to bust your BR with a 33% RoR.

Seriously this explanation is fascinating. I've never heard of CE being explained this way. So CE averages positive and negative win rates to come up with an 'adjusted' hourly win rate?

Say you have a $10K BR and you have a RoR of 33%. 3 guys start playing this and 1 is expected to end -$10K by busting out. That reduces the average of the group because he no longer "earns" and he has a lifetime negative $10K deficit. So the 3 guys played with an EV of X but their results reflect 2/3rds of X -$10K when the guy busted out.

So does X represent average hourly earnings or net earnings over some period of time? Shouldn't EV be calculated as 2/3 (X-10k) - 1/3 (10k)?

Did the 3 guys really have an expectation of X dollars for that time given that one was expected to bust out? If none bust out then yes but that is not certain. What if you are the guy that busts out? Certainty equivalent attempts to assign a certainty to BR growth.

But what if I'm comfortable with a lifetime 33% RoR? Should I disregard the negative CE? On the double barrier RoR calculator my RoR is 11%. This is far more realistic as real world play has time and goal constraints.

If you are betting full kelly CE equals EV.

Isn't it CE = 0.5 EV?

Thanks for your help.

MJ

[DSchles]

"Isn't it CE = 0.5 EV?"

Yes.

Don

[Three]

"Isn't it CE = 0.5 EV?"

Yes.

Don

Thanks for the correction both of you.

[Three]

How does CE compute my negative hourly earnings? How does it know how many hours till you bust out?

There is no hours until you bust out. It is probability distributions.

Seriously this explanation is fascinating. I've never heard of CE being explained this way. So CE averages positive and negative win rates to come up with an 'adjusted' hourly win rate?

That is just a way of understanding it. CE is not actually calculated that way. CE is used a lot in investing in order to maximize growth.

So does X represent average hourly earnings or net earnings over some period of time? Shouldn't EV be calculated as 2/3 (X-10k) - 1/3 (10k)?

Again I just tried to lay it out in a way you would understand. CE maximizes the utility of money "invested".

But what if I'm comfortable with a lifetime 33% RoR?

If you maintain a constant 33% RoR you are all but guaranteed to bust out. RoR assumes you will never resize your bets. If you make money the RoR from that point will be smaller but the RoR from the original point is still 33%. You are just less likely to be in that 33%. Like Don said RoR tends to catch you quick because if it doesn't your BR should be growing and that would mean a current RoR would be smaller.

If you are comfortable with suboptimal growth at extreme risk then go ahead at your own peril. 13.5% RoR would give optimal growth. I am assuming you are severely underfunded and have no choice but to play at such a high RoR. Many have been in that situation and some survived to build a big BR. You should attempt to get your RoR down to 13.5% RoR or less as soon as you can but we all understand that with a limited BR doing that now may not be practical.

On the double barrier RoR calculator my RoR is 11%. This is far more realistic as real world play has time and goal constraints.

I assume you mean the odds of busting out before you double your BR. That is a great statistic if you are going to quit when you double your BR or for a team that will break their bank when they double their BR but is pretty meaningless unless you intend on resizing bets at that point. If nothing changes when you reach your upper barrier the stat is pretty useless.

[MJ1]

There is no hours until you bust out. It is probability distributions.

If you maintain a constant 33% RoR you are all but guaranteed to bust out. RoR assumes you will never resize your bets. If you make money the RoR from that point will be smaller but the RoR from the original point is still 33%. You are just less likely to be in that 33%. Like Don said RoR tends to catch you quick because if it doesn't your BR should be growing and that would mean a current RoR would be smaller.

Once I double my bankroll I would resize my unit so RoR gradually scales backward. I would not increase unit in proportion to bankroll growth.

If you are comfortable with suboptimal growth at extreme risk then go ahead at your own peril. 13.5% RoR would give optimal growth. I am assuming you are severely underfunded and have no choice but to play at such a high RoR.

I am severely underfunded, would be playing off a 5k bankroll.

You are talking about kelly betting. I don't plan on resizing my unit until I double my bankroll. I don't think pure kelly is practical.

Assuming no resizing shouldn't playing 33% RoR grow the bankroll faster than 13.53%?

I assume you mean the odds of busting out before you double your BR. That is a great statistic if you are going to quit when you double your BR or for a team that will break their bank when they double their BR but is pretty meaningless unless you intend on resizing bets at that point. If nothing changes when you reach your upper barrier the stat is pretty useless.

I mean the odds of busting out before reaching an N0 of 240 hours or 12000 rounds. This is how much play I can get in a year. If I'm ahead I would rseize the unit such that RoR is less than 33% RoR. Does that make sense?

Thanks,
MJ

[Three]

Assuming no resizing shouldn't playing 33% RoR grow the bankroll faster than 13.53%?

No. 13,5% is optimal BR growth. Any more is suboptimal due to likelihood of busting out. Any less is safer from a busting out perspective but suboptimal.

[MJ1]

No. 13,5% is optimal BR growth. Any more is suboptimal due to likelihood of busting out. Any less is safer from a busting out perspective but suboptimal.

EV is greater with 33% RoR than 13.5% RoR so how can you say the latter will grow your bankroll faster? How do you define what is 'optimal'? EV and RoR are mutually exclusive, no?

[DSchles]

EV is greater with 33% RoR than 13.5% RoR so how can you say the latter will grow your bankroll faster? How do you define what is 'optimal'? EV and RoR are mutually exclusive, no?

Instead of arguing, you would do well to read about the Kelly criterion and optimal bankroll management. It isn't like there isn't a wealth of material on the subject on the internet.
EV might be greater with 100% ROR also, no? Don't you understand that your bankroll grows as a function of TWO simultaneous concepts -- both e.v. and variance -- and not just one of those functions?

Don

[Three]

Thanks Don. I was about to suggest the same thing.