CE - Certainty Equivalent, what exactly is it's use?

[bjcount]

After running a cvcx sim to see what my results could be with these parameters,
5/6d, heads up, $50min, 1-12 spread, 1/2kelly, it gives us numbers in the CE column which I don't understand what they represent.

Putting RoR aside, for example:

with a total & trip BR of 10k I get (-270) for CE (for those wondering RoR is 51.7%)

with a 50k total and 10k trip br I get a +52 for CE. (RoR is 3.7%)

What do the values of CE represent and what does it do for us to know them?

Thanks

BJC

 

[nightspirit]

RTFM!

Certainty Equivalent - CE is essentially the value of a wager. This is for math folk and you do not need to understand this concept to use the software.

:laugh::laugh:

No, let's get serious...
When your CE is negative you are overbetting your roll.
I don't know how CVCX comes up with the CE value and I haven't really looked into this but I'm sure SleightofHand or others can provide more help on this topic.

Meanwhile check out the following links:

http://www.gametheory.net/mike/applets/risk/

http://www.bjmath.com/bjmath/kelly/kellyfaq.htm (Archive copy)

http://www.bjmath.com/bjmath/ror/ce.htm (Archive copy)

 

[bjcount]

Just so others are aware, the quote NIGHTSPIRIT posted was the explanation given in CVCX which doesn't explain it's use.

Nightspirit, thanks for the response but "When your CE is negative you are overbetting your roll" that doesn't explain what CE purpose is. RoR provides us with the information to determine if your overbetting your BR.

Thanks for the links, I forgot about checking on bjmath.

If my understanding is correct pertaining to investments CE is the value your willing to pay to take on a certain amount of risk, but how does it apply to BJ.

BJC

Edit: bjmath links were helpful... thanks again. bjc

 

[SleightOfHand]

Ce

Now that NS mentioned me, I feel under pressure to answer this correctly lol.

CE is essentially the value of a wager. While I didn't read any of those articles, I would assume that one would give you something similar to this scenario:

Lets say that you play a game where you flip a coin. If it lands tails, you lose $100. If it lands heads, you win $102. This game has a 1% advantage. However, you have the option of either playing this game, or being paid 75 cents. Which would you choose? This is where CE comes into play. Depending on your risk utility and bankroll size, the CE will be greater or less than the guarunteed 75 cents. If you only have a $100 BR, this is obviously a very risky proposition and the 75 cents is probably the way to go. Conversely, if you have a $10,000,000 BR, a $100 hit is not going to make a big difference and the risk of the game is worth it. Risk is also a factor in CE since if you are willing to risk the $100 BR in the first scenario, then the game may be "worth it" to play.

The basic equation for CE is as follows:

EV-((Bet size*Standard deviation)^2)/(2*k*BR)
where k = kelly factor

As you can see, the CE can never exceed the EV of the game, but can be negative even with a +EV game (I suppose this means that you are willing to pay someone than actually play this game? lol). You can also use CE/WR to calculate if you are exceeding your risk utility or not.

 

[SleightOfHand]

Just so others are aware, the quote NIGHTSPIRIT posted was the explanation given in CVCX which doesn't explain it's use.

Nightspirit, thanks for the response but "When your CE is negative you are overbetting your roll" that doesn't explain what CE purpose is. RoR provides us with the information to determine if your overbetting your BR.

Thanks for the links, I forgot about checking on bjmath.

If my understanding is correct pertaining to investments CE is the value your willing to pay to take on a certain amount of risk, but how does it apply to BJ.

BJC

Edit: bjmath links were helpful... thanks again. bjc

So what use is this in BJ? Its another way to compare games. I prefer this over SCORE because it does not have the limiting factors of a 10k BR and kelly factor of 1. For example: if you are spreading 5-100 in a game vs 10-150 (assuming proper ramping) with a 15k BR, SCORE will tell you that the 5-100 ramp is better because of the bigger spread. However, this is not the better game because the risk is still relatively low with the 10-150 ramp, which would give an improved WR over the 5-100. CE would better reflect the better game.

Although Im not sure, I suppose you can also use it to decide whether to keep your job or to play BJ for a living. If the CE of the game is higher than your salary, then BJ is the way to go. However, notice that if you are indeed living off of BJ, your kelly utility will probably be very low, since you can't afford to lose. Just make sure that your kelly utility properly reflects your risk level.

 

[nightspirit]

Now that NS mentioned me, I feel under pressure to answer this correctly lol.

I didn't want to put you under pressure! lol Thanks for stopping by, you mentioned it somewhere before that you are rather using CE than SCORE, that's why I thought of you.
Good job!

 

[blackjack avenger]

CE = Certainty Equivalent

The definition is in the name. Yes, it is essentially the value of a wager. In BJ it is about half or a little less. It can be used to compare a job to BJ. If the CE of BJ is higher then that can be considered superior to the jobs wage. However, if one is considering quitting a job for BJ one needs to be very concerned with ROR, expenses, real world playing conditions and short/long term variance.:joker::whip:

 

[Nynefingers]

As you can see, the CE can never exceed the EV of the game, but can be negative even with a +EV game (I suppose this means that you are willing to pay someone than actually play this game? lol).

I can think of (made up, extreme) examples where this would be the case. For example, if your only choices were to either flip a coin to either lose your entire bankroll or triple up, or to pay a fixed amount to avoid that bet, you'd probably be willing to pay a good amount to avoid that bet even though it is pretty hugely +EV. In less extreme cases, if you are overbetting your bankroll and have an excessive RoR, you'd be better off to pay a small fixed amount to stop betting vs. to continue to place your bankroll at risk. Not that you would actually need to pay for the privilege of not betting, but the point is there are times when it would be the better choice.

 

[SleightOfHand]

I can think of (made up, extreme) examples where this would be the case. For example, if your only choices were to either flip a coin to either lose your entire bankroll or triple up, or to pay a fixed amount to avoid that bet, you'd probably be willing to pay a good amount to avoid that bet even though it is pretty hugely +EV. In less extreme cases, if you are overbetting your bankroll and have an excessive RoR, you'd be better off to pay a small fixed amount to stop betting vs. to continue to place your bankroll at risk. Not that you would actually need to pay for the privilege of not betting, but the point is there are times when it would be the better choice.

Ah yes, good example.

 

[QFIT]

SCORE is defined as $10K bankroll and 1.0 KF, but SCORE is the same at any bankroll or Kelly factor, which in my mind makes it more useful as a standard for BJ situation comparison. Assuming optimal betting, at a Kelly factor of 1 and bankroll of $10,000, CE is always SCORE/2.

At any bankroll and Kelly factor, CE should be one-half win rate. When your CE is less than one-half your win rate, you are over-betting.

 

[SleightOfHand]

SCORE is defined as $10K bankroll and 1.0 KF, but SCORE is the same at any bankroll or Kelly factor, which in my mind makes it more useful as a standard for BJ situation comparison. Assuming optimal betting, at a Kelly factor of 1 and bankroll of $10,000, CE is always SCORE/2.

At any bankroll and Kelly factor, CE should be one-half win rate. When your CE is less than one-half your win rate, you are over-betting.

Not that I want to argue with you, but while SCORE is fine to compare games in general (as is done in bj21), it's not as useful in for individuals. A game with, say, 100 SCORE but $100 minim bet is not going to be a good game for someone with a 10k roll (assuming Kelly betting is too much variance for this player). I feel CE better reflects the game's value right now

 

[QFIT]

No need to argue. It's why I supply both.

 

[sagefr0g]

maybe i'm jumping the gun asking this question (as I haven't read up on CE much) but anyway I was reading some on CE in BJA page 371.
looking at the equation CE = E - (f/2)*V , where E represents expected value, V represents variance and f is the size of the wager, expressed as a fraction of the Kelly-equivalent (optimal) bankroll, I was wondering (in the midst of my confusion) why is the fraction of the Kelly-equivalent bankroll divided by two?
i'm guessing it came about as a result of the derivation. just curious.

 

[DSchles]

So what use is this in BJ? Its another way to compare games. I prefer this over SCORE because it does not have the limiting factors of a 10k BR and kelly factor of 1. For example: if you are spreading 5-100 in a game vs 10-150 (assuming proper ramping) with a 15k BR, SCORE will tell you that the 5-100 ramp is better because of the bigger spread. However, this is not the better game because the risk is still relatively low with the 10-150 ramp, which would give an improved WR over the 5-100. CE would better reflect the better game.

Although Im not sure, I suppose you can also use it to decide whether to keep your job or to play BJ for a living. If the CE of the game is higher than your salary, then BJ is the way to go. However, notice that if you are indeed living off of BJ, your kelly utility will probably be very low, since you can't afford to lose. Just make sure that your kelly utility properly reflects your risk level.

You misunderstand SCORE. Your example above can't possibly reflect the "goodness" of the games, because you're mixing and matching concepts.

Don

 

[sagefr0g]

..., so about dividing the fraction of the Kelly-equivalent (optimal) bankroll, by two (https://www.blackjackinfo.com/commu...nt-what-exactly-is-its-use.16357/#post-496335).
is that maybe that half Kelly betting was taken into consideration?

 

[DSchles]

..., so about dividing the fraction of the Kelly-equivalent (optimal) bankroll, by two (https://www.blackjackinfo.com/commu...nt-what-exactly-is-its-use.16357/#post-496335).
is that maybe that half Kelly betting was taken into consideration?

No.

Don

 

[sagefr0g]

No.

Don

I know it's beyond me, lol.
did find this http://canjarrm.faculty.udmercy.edu/InsurancePaper.pdf , where derivation of CE is described.
so far unable to find Friedman's paper.
anyway, still reading BJA pages with respect to CE.
reason being, it appears I've found a game where sometimes even though one has (what appears to be a 'significant') positive expected value, well paradoxically (it seems), one might just not want to make the bet, sorta thing. on the other hand there can be a 'spectrum' (sort of like various TC's and the question of risk averse indices) of bets, some of which one would doubtless want to make the bet.
not sure, so am reading up on that sort of thing.

 

[sagefr0g]

I have trouble interpreting the meaning of the concept of net odds. hopefully someone can enlighten me.
please consider the following:

f* = (bp-q)/b = [p(b+1) – 1]/b

where:

• f * is the fraction of the current bankroll to wager, i.e. how much to bet;
• b is the net odds received on the wager ("b to 1"); that is, you could win $b (on top of getting back your $1 wagered) for a $1 bet
• p is the probability of winning;
• q is the probability of losing, which is 1 − p.

can anyone help me properly interpret the parameter b ? say, specifically for the following example:

bet = $50

ev = $9.99 note: one’s expectation is to get the $50 bet back in addition to the expected value of $9.99 .

question being, what is the proper value of the parameter b ?

is it b = $9.99 or is it b = $9.99/$50, or maybe even b = $59.99/$50 ?

edit: the above formula is written about in Thorp's paper on The Kelly Criterion in Blackjack, Sports Betting and the Stock Market.
also in the link:
https://en.wikipedia.org/wiki/Kelly_criterion
end edit

 

[DSchles]

I have trouble interpreting the meaning of the concept of net odds. hopefully someone can enlighten me.
please consider the following:

f* = (bp-q)/b = [p(b+1) – 1]/b

where:

• f * is the fraction of the current bankroll to wager, i.e. how much to bet;
• b is the net odds received on the wager ("b to 1"); that is, you could win $b (on top of getting back your $1 wagered) for a $1 bet
• p is the probability of winning;
• q is the probability of losing, which is 1 − p.

can anyone help me properly interpret the parameter b ? say, specifically for the following example:

bet = $50

ev = $9.99 note: one’s expectation is to get the $50 bet back in addition to the expected value of $9.99 .

question being, what is the proper value of the parameter b ?

is it b = $9.99 or is it b = $9.99/$50, or maybe even b = $59.99/$50 ?

edit: the above formula is written about in Thorp's paper on The Kelly Criterion in Blackjack, Sports Betting and the Stock Market.
also in the link:
https://en.wikipedia.org/wiki/Kelly_criterion
end edit

F is the correct Kelly wager to make for a proposition where, you bet 1 unit, with probability q of losing, and you get b units (plus your original wager) when you win, with probability p, and p + q = 1. B is the "odds to one" for a winning wager.

Don

 

[sagefr0g]

F is the correct Kelly wager to make for a proposition where, you bet 1 unit, with probability q of losing, and you get b units (plus your original wager) when you win, with probability p, and p + q = 1. B is the "odds to one" for a winning wager.

Don

got it!
thank you once again Don.