Calculating CE outside of BJ

SleightOfHand

Well-Known Member
#1
From my understanding, an equation to estimate CE when the advantage/disadvantage is less than 10% is

CE = E - V/2kB
E: Expected Winning
V: Variance
k: Kelly fraction
B: Bankroll

What would I do if I wanted to calculate the CE of a MP coupon or a scavenger bet?
 

sagefr0g

Well-Known Member
#2
SleightOfHand said:
From my understanding, an equation to estimate CE when the advantage/disadvantage is less than 10% is

CE = E - V/2kB
E: Expected Winning
V: Variance
k: Kelly fraction
B: Bankroll

What would I do if I wanted to calculate the CE of a MP coupon or a scavenger bet?
just a guess here.
it would seem the trick would be knowing the variance. you could know that by knowing the true count and having ran a sim for the particular game.
thing is MP coupon have various rules that probably didn't apply to the sim so i guess you'd need a way to figure the impact of those rules.
the scavenger bet situation it seems you have some additional information, that you wouldn't have going in on some initial bet at some true count.
but you could know the true count so you could know the variance. the scavenger bet will have some EV associated so i guess that could be added to the EV that the true count represents.
:rolleyes::whip:
 
#3
Half, Perhaps

Let's say you have a $100 free play BJ coupon. Well, the coupon value is cut about in half because we only win about half the hands.
So the CE value is about $50.:joker::whip:
 

SleightOfHand

Well-Known Member
#4
blackjack avenger said:
Let's say you have a $100 free play BJ coupon. Well, the coupon value is cut about in half because we only win about half the hands.
So the CE value is about $50.:joker::whip:
But because of the risk involved, wouldn't the CE would be lower than the WR?
 

SleightOfHand

Well-Known Member
#6
blackjack avenger said:
WR?

In my example you are risking nothing, so I would think it is the ev.:joker::whip:
You are risking $100. You don't win every MP

Edit: Oh I didn't notice that it was Free Play. But what about MPs?
 

moo321

Well-Known Member
#7
blackjack avenger said:
Let's say you have a $100 free play BJ coupon. Well, the coupon value is cut about in half because we only win about half the hands.
So the CE value is about $50.:joker::whip:
No, this would be the EV, assuming no house advantage.

You can get higher EV with lower CE by putting it on a number in roulette.
 
#8
EV for CE

moo321 said:
No, this would be the EV, assuming no house advantage.

You can get higher EV with lower CE by putting it on a number in roulette.
In my example with the $100 bj free play I think the CE and the EV are about the same because:

The ev is about $50.
If I were offered $60 for the free play I would sell it.
If I were offered $40 for the free play I would keep it.
So it seems the CE and the EV are the same.:joker::whip:
 
#9
Play it Quickly

SleightOfHand said:
what about MPs?
I would think you can look at the MP and the cash separately.
The $100 MP in bj is valued a bit less then $50. The money bet would have whatever the CE is at the time you place the bet. If playing positive expectation bj the CE is about 50% of expectation. If you place a $100 bet with a 1% advantage the CE is about 50 cents.

I would think you could wait until you would place a $200 bet and make a $100 bet with the $100 MP.:joker::whip:
 

moo321

Well-Known Member
#10
blackjack avenger said:
In my example with the $100 bj free play I think the CE and the EV are about the same because:

The ev is about $50.
If I were offered $60 for the free play I would sell it.
If I were offered $40 for the free play I would keep it.
So it seems the CE and the EV are the same.:joker::whip:
And I would pay you $60 for the matchplay, and put it on a number in roulette for an EV of over $80.

CE isn't as important of a concept for blackjack as it is for, say, video poker. I would prefer 2.5% cashback on (JOB) video poker to a progressive royal that offered a 2% advantage to the player. Same EV, but I have to hit the royal to get the extra payout in the second example.
 
#11
The Devil is in the Details

moo321 said:
And I would pay you $60 for the matchplay, and put it on a number in roulette for an EV of over $80.

CE isn't as important of a concept for blackjack as it is for, say, video poker. I would prefer 2.5% cashback on (JOB) video poker to a progressive royal that offered a 2% advantage to the player. Same EV, but I have to hit the royal to get the extra payout in the second example.
I was rather specific and said a $100 free bj MP, so you could not use it on roulette.

CE is a rather important consideration if one wants to know the value of a wager.:joker::whip:
 

sagefr0g

Well-Known Member
#12
blackjack avenger said:
......
CE is a rather important consideration if one wants to know the value of a wager.:joker::whip:
how so?
in your words please.
or anyone else who would like to explain.:confused::whip:
 

SleightOfHand

Well-Known Member
#13
sagefr0g said:
how so?
in your words please.
or anyone else who would like to explain.:confused::whip:
CE is a way to analyze whether you would take a risky amount "x" or a guarunteed amount "y." For example, what would you rather take: a $50 MP coupon to play for BJ or $25 right now? What about 24? 23? CE can give a mathematical answer to that, given how risk averse you are.

But let me ask to the mathematically superior out there (as it appears they may not necessarily know the answer to my question): how inaccurate is the equation in the OP for the other kinds of advantage plays?
 

Pro21

Well-Known Member
#14
The television show Deal or No Deal is nothing more than measuring people's CE, although most people don't realize what they are actually giving up.
 
#15
Solve for CE

SleightOfHand said:
From my understanding, an equation to estimate CE when the advantage/disadvantage is less than 10% is

CE = E - V/2kB
E: Expected Winning
V: Variance
k: Kelly fraction
B: Bankroll

What would I do if I wanted to calculate the CE of a MP coupon or a scavenger bet?
Wouldn't you just plug in the variables and solve the equation?:joker::whip:
 

Sonny

Well-Known Member
#16
SleightOfHand said:
But because of the risk involved, wouldn't the CE would be lower than the WR?
It might be, or it could be higher. Lots of people play the lottery even though the EV is lower than their CE. Insurance policies are the same way. It all depends on what your personal utility function looks like and where it intersects with the EV function. Some people are willing to make a few bad bets if it could bring them some form of happiness or security. Other people are more willing to take a smaller payoff that involves less effort.

blackjack avenger said:
The ev is about $50.
If I were offered $60 for the free play I would sell it.
If I were offered $40 for the free play I would keep it.
So it seems the CE and the EV are the same.:joker::whip:
In your case they are. Your personal utility is directly proportionate to the EV of the game because the risk has been neutralized and the opportunity to use the "free play" coupon is available to you. Your utility function might change under different circumstances (e.g. you must match the coupon with live money, you are unable to play the coupon yourself, you want to avoid attention at that casino, you must give up your identity to receive the coupon, etc.), but in this case the EV and CE are the same for you. The game is risk-free from the outset so there are no risk-less alternatives to compare it to.

For a scavenger bet you are required to risk some of your money so things will be different. Now you have to have a better idea of your personal risk aversion utility.

SleightOfHand said:
But let me ask to the mathematically superior out there (as it appears they may not necessarily know the answer to my question): how inaccurate is the equation in the OP for the other kinds of advantage plays?
It’s fine as long as your personal risk utility is equal to the Kelly utility. If you are concerned about factors other than optimal growth than it might not be correct in all cases. It's a very personal thing.

-Sonny-
 

SleightOfHand

Well-Known Member
#17
Sonny said:
It’s fine as long as your personal risk utility is equal to the Kelly utility. If you are concerned about factors other than optimal growth than it might not be correct in all cases. It's a very personal thing.
Lets just say that given all the factors, my personal risk utility is equal to that of .6 Kelly. Would the equation give an answer that is relatively close to the true CE?

Just for example: I have a $25 MP and 10k BR. So my CE would be approximately

12.5-1.33/(2(.6)(10000))

which is pretty much ~12.5. I suppose this could make sense due to the huge advantage given by the coupon. However, could this be the problem warned by the 10% advantage/disadvantage?

Also, is there a resource for the standard deviations of the scavenged doubles (as I am assuming they are not the same as the SD of BJ).
 

sagefr0g

Well-Known Member
#18
SleightOfHand said:
....

Also, is there a resource for the standard deviations of the scavenged doubles (as I am assuming they are not the same as the SD of BJ).
here is a link that has a lot of stats for possible scavenged hands. (a whole bunch of expected value tables has probabilities as well)
http://www.bjmath.com/search/search.htm (Archive copy)
just put in expected value table in the search field.
or if you have k_c's tdca you could crank these sort of figures out.

i'm not sure about the associated standard deviation, i think you'd get that from a sim where you'd have standard deviation associated with a given true count for which the scavenge hand presents or you also have from a sim standard deviation per round in units sort of thing.

but again i'm guessing you'd add the ev for the scavenged hand to the expected value at a given true count.
 
#19
To Be or Not To Be Concerned About

SleightOfHand said:
Lets just say that given all the factors, my personal risk utility is equal to that of .6 Kelly. Would the equation give an answer that is relatively close to the true CE?

Just for example: I have a $25 MP and 10k BR. So my CE would be approximately

12.5-1.33/(2(.6)(10000))

which is pretty much ~12.5. I suppose this could make sense due to the huge advantage given by the coupon. However, could this be the problem warned by the 10% advantage/disadvantage?

Also, is there a resource for the standard deviations of the scavenged doubles (as I am assuming they are not the same as the SD of BJ).
Think you are missing something.
If you bet $25 and a $25 MP when you should bet $50 then the CE for the combined $25 and MP is probably higher then any other bet you will make for the trip.:joker::whip:

or

$25 bet with a $25 MP has a higher CE then a $50 bet.
 

SleightOfHand

Well-Known Member
#20
blackjack avenger said:
Think you are missing something.
If you have 25 cash and a $25 mp but play it when you should bet $50 then the CE is lower then any other bet
you will make for the trip.:joker::whip:
What are you talking about? From that CE equation, this bet gives a CE of ~$12.5. Other bets of $50 (lets say placed at an advantage of 1.5%) gives a CE of 0.75-1.33/(2(.6)(10000)) or ~$0.75.

Edit: Oops I put in unit variance instead of $ variance

CE of MP ~=$12.43
CE of $50 ~= $0.48
 
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