bram1256
bram1256
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November 25th, 2013 at 1:35:58 AM permalink
Hi,

The decision to hit or pass is based on the expected value. But I wonder how is mathmatically the decision made to split and double?
Can anyone show me a link/similar thread where this mathmatically is proven or how it is done by responding?


For further questions please comment.

Thank you.
odiousgambit
odiousgambit
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November 25th, 2013 at 6:41:28 AM permalink
maybe this at WoO will help?

https://wizardofodds.com/games/blackjack/appendix/1/
the next time Dame Fortune toys with your heart, your soul and your wallet, raise your glass and praise her thus: “Thanks for nothing, you cold-hearted, evil, damnable, nefarious, low-life, malicious monster from Hell!”   She is, after all, stone deaf. ... Arnold Snyder
bram1256
bram1256
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November 26th, 2013 at 4:03:19 AM permalink
This is indeed very helpfull. In the example in the link you can see that splitting the 8's is the best decision, because of the lowest expected value.
But how is the expected value calculated for splitting? I would like to see the calculation for expected value for splitting not just the expected value is -0,545 or something. Anyhow thanks for responding.
1BB
1BB
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November 26th, 2013 at 5:07:40 AM permalink
In multi-deck games, if surrender is available, surrender 8,8 vs 10 at TC +2. If playing a H17 game surrender 8,8 vs ace per basic strategy.
Many people, especially ignorant people, want to punish you for speaking the truth. - Mahatma Ghandi
wudged
wudged
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November 26th, 2013 at 5:55:41 AM permalink
The expected values are calculated by finding every possible hand/deck combination that could occur, and how you would make out if you stayed/hit/doubled/split/surrendered.
MangoJ
MangoJ
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November 26th, 2013 at 11:03:11 AM permalink
Quote: bram1256

I would like to see the calculation for expected value for splitting not just the expected value is -0,545 or something.



Exact calculation for splitting is a difficult thing. In essence the calculation is simple: since you only have a limited number of options and cards, you cycle through all possible options and cards to get the EV. For splitting hands, this is not much different, except the number of options and cards "explodes" - as you have now two hands to play.

A basic but pretty accurate method would be: calculate the (exact) EV of the first split hand, and assume that your second split hand has the very same EV. This would be correct if you could not "see" your first hand when playing the second hand. This would be true if you follow, say, a a basic strategy table.
In fact your second hands EV will improve on the knowledge of the first hand consumed cards, so with this basic method you systematically underestimate the EV of the split.

If you are really more into this (in my view interesting topic), you can read on the free article: "Exact Calculation of Expected Values for Splitting Pairs in Blackjack"
http://www.cof.orst.edu/cof/wse/faculty/Nairn/papers/splitting.pdf
anonimuss
anonimuss
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November 26th, 2013 at 11:30:14 AM permalink
Quote: bram1256

Hi,

The decision to hit or pass is based on the expected value. But I wonder how is mathmatically the decision made to split and double?
Can anyone show me a link/similar thread where this mathmatically is proven or how it is done by responding?


For further questions please comment.

Thank you.



Buy Peter Griffins "The Theory of Blackjack" and "Extra Stuff: Gambling Ramblings".
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