BJ, splitting pairs expected value.

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.

maybe this at WoO will help?

https://wizardofodds.com/games/blackjack/appendix/1/

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.

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.

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.

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

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".