Compute Probabilities

B

bruceB

Member
#1
#1
Does anyone know how to compute the probabilities when you know the dealer up card and your 2 cards. I can compute the probabilities for the dealer up card and my value, but I don't know how to use this to hit or stand.
In Thorp's book Beat the dealer he gives a chart which shows the players gain by Drawing over Standing. How did he compute this:
Thanks
 
KenSmith

KenSmith

Administrator
Staff member
#4
#4
To do these calculations, you'll need to do combinatorial analysis of all the possible outcomes.

That is, you look at each possible next card, weight it by the appropriate probability, and play out the hand from there, again weighting each branch of the probability tree.

Why are you asking? We might can save you the trouble.
 
jack.jackson

jack.jackson

Well-Known Member
#6
#6
bruceB said:
Does anyone know how to compute the probabilities when you know the dealer up card and your 2 cards. I can compute the probabilities for the dealer up card and my value, but I don't know how to use this to hit or stand.
In Thorp's book Beat the dealer he gives a chart which shows the players gain by Drawing over Standing. How did he compute this:
Thanks
Click to expand...
You might want ask KC. He has some pretty good software that does these sort of things.
 
Sonny

Sonny

Well-Known Member
#8
#8
bj bob said:
Great English, Ken! You either got to return to your nap or have a couple more cups of JO.
Click to expand...
That's how they talk down south. Don't be hatin' just cause you ain't down with the local colloquialisms :grin:

-Sonny-
 
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bj bob

bj bob

Well-Known Member
#9
#9
Sonny said:
That's how they talk down south. Don't be hatin' just cause you ain't down with the local colloquialisms :grin:

-Sonny-
Click to expand...
Weeeee doggie! I guess I should oughta known that more better.:laugh: And about them colloquialisms...I just had my checked out this week at the Doc's.
 
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jack.jackson

jack.jackson

Well-Known Member
#14
#14
Canceler said:
I've been on this board almost forever and I'm dying to know...

Who is KC?
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KC is the bright individual that first introduced himself and his free demo software, in Alternative betting P1 about 4 months ago. Curious myself, I searched the members list. And the reason you cant find his name is because for some reason is the last one under K?

Ive PM a couple times and hes responded with some really good advice!
He usually sneaks on here in the early morning hours. Hopefully he'll see this thread and give us a pointer or two:)
 
K

k_c

Well-Known Member
#16
#16
Canceler said:
You mean k_c.
Click to expand...
I would've been kc except that a minimum of 3 characters were required.

In any event, the demo of my program that works for single deck can be downloaded (Dead link: http://www.bjstrat.net/cdca_demo_download.htm) _here_. I was hoping to get some feedback on it.

The program in Ken's link is by Eric Farmer. It is a very fine program and like mine computes composition dependent EVs. My program, however computes EVs vs up cards of ten or ace assuming player loses to dealer's blackjack, whereas Eric's computes the EV assuming dealer has already checked for blackjack and doesn't have it. The proper strategy can be derived from either set of EVs. In order to convert use the formula -
Code: 
EV(dealer has checked for BJ) = [EV(player loses to DBJ) + pBJ]/(1-pbj)
     where pBJ = probability of dealer blackjack
One of the reasons I used the unconditional, rather than the conditional EVs is that my program can compute early surrender and no peek (ENHC) and in those cases condtional EVs don't make much sense. Additionally, it displays the overall EVs for a hand or partial hand and those are unconditional. Most reliable sources, however, usually quote the conditional EVs for up cards of ten and ace. I am working on another program that can compute a few other things and in that one I plan on giving the user the option to choose to display the conditional EVs (where they make sense) or the unconditional. Also, I could add that option to the existing program relatively easily.

Anyway, I'd be happy to address any questions about running the program.

k_c
 
B

bruceB

Member
#17
#17
pROBABILITIES

k_c said:
I would've been kc except that a minimum of 3 characters were required.

In any event, the demo of my program that works for single deck can be downloaded (Dead link: http://www.bjstrat.net/cdca_demo_download.htm) _here_. I was hoping to get some feedback on it.

The program in Ken's link is by Eric Farmer. It is a very fine program and like mine computes composition dependent EVs. My program, however computes EVs vs up cards of ten or ace assuming player loses to dealer's blackjack, whereas Eric's computes the EV assuming dealer has already checked for blackjack and doesn't have it. The proper strategy can be derived from either set of EVs. In order to convert use the formula -
Code: 
EV(dealer has checked for BJ) = [EV(player loses to DBJ) + pBJ]/(1-pbj)
     where pBJ = probability of dealer blackjack
One of the reasons I used the unconditional, rather than the conditional EVs is that my program can compute early surrender and no peek (ENHC) and in those cases condtional EVs don't make much sense. Additionally, it displays the overall EVs for a hand or partial hand and those are unconditional. Most reliable sources, however, usually quote the conditional EVs for up cards of ten and ace. I am working on another program that can compute a few other things and in that one I plan on giving the user the option to choose to display the conditional EVs (where they make sense) or the unconditional. Also, I could add that option to the existing program relatively easily.

Anyway, I'd be happy to address any questions about running the program.

k_c
Click to expand...
What algothrym do you use to compute whether to hit or stand? I can compute the probabilities for the dealer and for your hand, but how do know whether to hit or stand?
 
B

bruceB

Member
#18
#18
Probabilities

I can compute the probabilities for the dealer and for your hand, but how do you compute the probabilities to hit, stand,or double down.
 
Sonny

Sonny

Well-Known Member
#19
#19
bruceB said:
I can compute the probabilities for the dealer and for your hand, but how do you compute the probabilities to hit, stand,or double down.
Click to expand...
Just weigh the probability of being dealt every possible card. It would actually be much easier to just compare the EVs for each play since the probabilities have already been calculated (and can be very difficult in some cases). You can either calculate them yourself:

EV = p(Win) * Winning Payout + p(Loss) * Losing Payout

or you can look at the EV charts I mentioned earlier:

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

-Sonny-
 
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C

Canceler

Well-Known Member
#20
#20
Sometimes things that go without saying go even better if you do say them! :)

The correct play for the hand is the one that has the highest EV.
 
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