Negative CE?

[MJ1]

Guys, should I be concerned if the CE of my play is negative? I never really understood the usefulness of this metric. What does geometric CE represent anyway?

I'm playing to a lifetime RoR of 33% and understand the risks. Thanks for any answers.

MJ

[RS]

I'm sure Don or someone else can give a better definition than I can, but with that being said... CE is Certainty Equivalence which basically means "How much guaranteed money would I rather take in lieu of playing this game which contains risk?"

If your EV is $100 and your CE is $45, then getting paid $45/hour guaranteed is essentially the same as playing BJ. If you can get paid more than $45/hour doing something else (say, working a regular job), then you should do that regular job instead of play the BJ game.

Saying that your CE is negative means that it would be BETTER TO THROW AWAY MONEY than to play the BJ game you've simmed.

[Three]

Negative CE means you are better off paying the casino to not let you play rather than playing. You should be extremely alarmed.

If your CE is -$45/100 rounds you are better off paying the casino $44 to not let you play 100 rounds than actually playing 100 rounds.

[Stevie Wonder]

I'm not quite understanding the difference between EV and CE. A game I've got simmed right now shows me an EV of ~$100 per hour, 8% RoR, and a CE of $8. The EV after 100 hours of play is $10,000. The CE would be $800. Is the CE a formula that asses the risk versus reward factor, and says the chance of making the $10,000 is only worth the certainty of making $800?

[RS]

I'm not quite understanding the difference between EV and CE. A game I've got simmed right now shows me an EV of ~$100 per hour, 8% RoR, and a CE of $8. The EV after 100 hours of play is $10,000. The CE would be $800. Is the CE a formula that asses the risk versus reward factor, and says the 92% chance of making the $10,000 is only worth the certainty of making $800?

Let's say there's a coin-flip game (exactly 50/50) where the casino paid you 1.02-to-1 (ie: 1% edge) on heads. Surely you have an advantage and playing would be +EV. Let's say you have a $100k bankroll. The casino only allows bets of $50k. As you can see, this game has high risk, if you were to play it. The CE, however, is going to be a negative number, unless you have an extremely high risk tolerance (ROR).

Now let's say someone else with a gigantic bankroll (Bill Gates) would have a positive CE, because his bankroll is so big (and thus, the game is not as risky).



Try doing this -- in CVCX, lock/freeze the custom bets, then change the ROR figure. Then change the bankroll figure.

[Three]

No stat in your post says you have a 92% chance of winning $10K after 10,000 rounds (You EV is in dollars per 100 rounds. You make an assumption of 100 rounds per hour to get $100/hour. Odds are you aren't playing at that game speed as a BR challenged player due to having to play crowded tables). The 8% RoR is the odds you will bust out after generating that RoR independent of time frame. So 92% of the time you won't bust out if you play the same ramp and game conditions that your sim used forever. The odds of were you will be is a probability cone around your projected EV as rounds are played. A static cross section would bring in Standard Deviation. If your SD/100 rounds is $1200/100 rounds with a expectation of $100/100 rounds then it is a math problem to get your SD and EV as time goes by. SD grows by the square root of rounds played and EV grows linearly as rounds are played. So at 10000 rounds played:
EV = ($100/100 round)*(10,000 rounds/100 rounds) = $10,000/10,000 rounds
SD = ($1300/100 round)*((sqrt 10,000rounds/100rounds) = $13,000/10,000 rounds

Then you consult a bell curve distribution model to get the likelihood of various outcomes for the mean (EV) and SD for that number of rounds:

https://datasciencecareeroptions.com...ve-Chart-2.jpg

The mean is $10K and each SD out is the mean plus or minus the SD for the same number of rounds. EV grows linearly and SD grows by the square root. To go from 100 round to 10K rounds you multiply EV/100 rounds by 100 and SD/100 rounds by the square root of 100.

[Stevie Wonder]

Ok, that makes sense. Thanks for clearing that up for me. Looks like I may have some more aggressive wonging in my future. Its easier to accept a higher than average RoR, but seeing such a low CE is rather disappointing.

[Three]

It seems there might be some confusion. EV doesn't factor in variance. SCORE and N-zero factor in variance as an EV to variance ratio. CE factors in variance by subtracting a relationship between variance, bet size, BR and kelly fraction from EV. This expresses the certainty of BR growth or CE. It is expressed as hourly amount payed to you that would be the equivalent of risking your money playing. IF your CE is $84 then if someone offered you $84/hour to not play it would be better than risking money playing.

[Stevie Wonder]

No stat in your post says you have a 92% chance of winning $10K after 10,000 rounds (You EV is in dollars per 100 rounds. You make an assumption of 100 rounds per hour to get $100/hour. Odds are you aren't playing at that game speed as a BR challenged player due to having to play crowded tables). The 8% RoR is the odds you will bust out after generating that RoR independent of time frame. So 92% of the time you won't bust out if you play the same ramp and game conditions that your sim used forever. The odds of were you will be is a probability cone around your projected EV as rounds are played. A static cross section would bring in Standard Deviation. If your SD/100 rounds is $1200/100 rounds with a expectation of $100/100 rounds then it is a math problem to get your SD and EV as time goes by. SD grows by the square root of rounds played and EV grows linearly as rounds are played. So at 10000 rounds played:
EV = ($100/100 round)*(10,000 rounds/100 rounds) = $10,000/10,000 rounds
SD = ($1300/100 round)*((sqrt 10,000rounds/100rounds) = $13,000/10,000 rounds

Then you consult a bell curve distribution model to get the likelihood of various outcomes for the mean (EV) and SD for that number of rounds:

https://datasciencecareeroptions.com...ve-Chart-2.jpg

The mean is $10K and each SD out is the mean plus or minus the SD for the same number of rounds. EV grows linearly and SD grows by the square root. To go from 100 round to 10K rounds you multiply EV/100 rounds by 100 and SD/100 rounds by the square root of 100.

I pulled the $100 an hour from the win rate per hour at my playing speed. Just rounded my $98 up for simplicity. I play mostly heads up with an ASM, so as fast as they can place 'em, I play 'em. And I sim using the worst possible rule set that I play under. H17 DAS. I was under the impression that RoR was based on doubling a bank roll in an infinite set of time, or going bust whichever came first. Just re-read my earlier post and I didn't word that correct. What I meant was that the CE says the chance of making $10,000 is worth about a certainty of $800. I will correct the post.

[Stevie Wonder]

Sorry for the confusion. I've got it. My response was to RollingStoned as your post didn't populate when I began the reply.

[Gronbog]

I was under the impression that RoR was based on doubling a bank roll in an infinite set of time, or going bust whichever came first.

This is a common misconception when it comes to RoR as discussed in BJA3 and reported by CVCX. RoR in these contexts is the chance of going broke vs playing forever and winning all the money in the world, assuming that you never resize your bets.

The RoR for going broke vs doubling your bankroll would be a lower probability.

[MJ1]

So what does 'geometric' CE mean?

Also, I would much rather take EV of $17 per hour than pay the casino $1 per hour not to play. Why does the CE incorrectly express my risk appetite? What am I missing here?

Is it possible to graph the logarithmic growth rate of my bankroll with respect to time? If so, what is the function?

Thanks,
MJ

[Three]

CE is about certainty of BR growth.

Also, I would much rather take EV of $17 per hour than pay the casino $1 per hour not to play.

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.

Is it possible to graph the logarithmic growth rate of my bankroll with respect to time? If so, what is the function?

Full Kelly play with constant resizing maximizes logarithmic BR growth.