"Fast" optimal split EVs

[k_c]

This sounds really interesting. I don't fully understand your description yet, will need to read through this some more. In the meantime, I've updated my blackjack_split.exe (the latest release at the previously posted GitHub link) to support the option of forcing resplits at every opportunity, but otherwise making optimal (EV-maximizing) strategy decisions, if it's helpful to check against your potentially much more efficient algorithm.

I would be particularly interested to see what this algorithm computes for the SPL3 case, since I get a different value than Cacarulo's. Following is my output, with inputs if you want to reproduce/experiment yourself:

**Edit: After reviewing what I posted it appears that the conditions in my algorithm can't be met for SPL3 because of running out of cards.**

For 6-6 vs 6 SPL3 dealt from {0,0,0,0,0,11,0,5,0,0} these would be the multipliers:

Pair cards present in shoe: 8   Non-pair cards present in shoe: 5
Number of allowed splits for which to display data (1 - 9): 3
Allowed splits: 3       Expected number of hands: 3.68764568765

P removed       optx(pRem + 2) multiplier    EVPair(pRem) multiplier

0               1.00000000000                -1.23076923077 = -16/13
1               0.82051282051 = 32/39        -1.43589743590 = -56/39
2               0.71794871795 = 28/39        1.17482517483 = 168/143
3               -0.46993006993 = -336/715    -0.19580419580 = -28/143
4               0.06526806527 = 28/429       0.00000000000

Press x to exit, i to reinput p & np, any other key to reinput num splits

In order to compute SPL3, values for optx[] and EVPair[] are needed. I have listed the values that work for SPL2 and added values for EVPair[2] & EVPair[3]. I am missing values for optx[3] (draw to 5 pair cards with 0 splits remaining) and optx[4] (draw to 6 pair cards with 0 splits remaining).
I don't trust myself to get these on an ad hoc basis. Maybe with your experience in dealing with multiple pair cards you might be able to get these without too much trouble. If so after that it is a simple matter of computing the algorithm's SPL3_forcedResplit value to see if it agrees with yours. The 2 missing optx values are denoted with "?".

optx[0] = -0.013986013986014 = -2/143 = EV(draw to 2 pair cards, 0 splits remain)     EVPair[0] = -1/132
optx[1] = -1/33 = EV(draw to 3 pair cards, 0 splits remain)                           EVPair[1] = 1/33
optx[2] = -2/33 = EV(draw to 4 pair cards, 0 splits remain)                           EVPair[2] = 1/12
optx[3] =  ? = EV(draw to 5 pair cards, 0 splits remain)                              EVPair[3] = 10/63
optx[4] =  ? = EV(draw to 6 pair cards, 0 splits remain)

SPL3_forcedResplit = 1*optx[0] + 32/39*optx[1] + 28/39*optx[2] - 336/715*optx[3](?) + 28/429*optx[4](?)
                     -16/13*EVPair[0] - 56/39*EVPair[1] + 168/143*EVPair[2] - 28/143*EVPair[3]

k_c