More Optimal Split EVs

k_c

Well-Known Member
#1
I wrote an algorithm with the goal of computing split EVs that are a little better at approximating optimal split EVs. In computing splits there are 3 types of hands that come from drawing to a one or more single pair cards. When splits remain there are 2 types - N when a non-pair card is drawn and P when a pair card is drawn. A special case exists when exactly 1 pair card remains since no matter how many splits remain if an N card is drawn then that particular drawing sequence is finished. When no splits remain there is 1 type of hand - x hands. A card of any rank, including a pair card, can be drawn on an x hand since no more splitting can be done.

I think maybe the reason CDP is not necessarily more optimal than CDP1 even though it considers more information has something to do with the way it considers N hands on the condition that a non-pair card has already been removed. In that case the EV is figured as the conditional probability involving differing numbers of pair cards removed. The EV is right but each non-pair card needs to be specifically removed to be included in computing subsequent playing strategy. So my algorithm does this. Up to 2 specific non-pair cards can be removed.

For x hands when a fixed strategy is used it turns out the EV is the same for each x hand even though different drawing sequences are possible. I guess the reason is because the chance of each hand being played versus each possible dealer composition turns out to be the same. For SPL1 there are 2 x hands. If the first hand is played optimally without any consideration of the second then the EV for the first hand is simply the optimal EV for burning one pair card and drawing to one pair card. If the second hand is played with the same strategy as the first then the EV of the second hand is the same EV as well and SPL1 EV = 2*(hand 1 EV). In order to consider more information for x hands my algorithm specifically considers the first card drawn to the first hand in computing a strategy for the second hand. For SPL2 there are up to 3 x hands and for SPL3 there are up to 4 x hands. What my algorithm does is to specifically remove all combinations of 0, 1, 2, or 3 ranks progressively depending upon the current number of x hands being computed.

Broadly speaking the algorithm removes the rank of the first card drawn to each hand so it can be considered for subsequent hands. It doesn't consider each and every card drawn though. Considering more than the first card drawn to each pair card would require considering separate compositions for each up card since strategy for each up card is potentially different. It assumes EV for the current calculation is the computed EV for whatever is presently known so no possible covariability between split hands is considered.

The algorithm is not fast. It seems to get reasonable values but I don't know if it correctly does what in theory I'm trying to do, but hopefully it does.
I named the algorithm CDPnnxxx since it's supposed to specifically remove up to 2 N cards and/or 3 x cards.

Link is showing sample hand of 2-2, single deck, s17, DAS.

2-2, single deck, s17, DAS
 

MGP

Well-Known Member
#2
CDPN in my CA accounts for however many N cards are removed as well as the P cards. I'd probably name yours CDPN1x :)
 
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