It took me years to get the splitting pairs correct myself. Cindy of Gambling Tools was very helpful. Peter Griffin also addresses this topic in chapter 11 of the The Theory of Blackjack Let’s say I want to determine the expected value of splitting eights against a dealer 2. Resplitting up to four hands is allowed. Here is how I did it. Take a 2 and two 8’s out of the shoe. Determine the probability that the player will not get a third eight on either hand. Go through all ranks, except 8, subtract that card from the deck, play out a hand with that card and an 8, determine the expected value, and multiply by 2. For each rank determine the probability of that rank, given that the probability of another 8 is zero. Take the dot product of the probability and expected value over each rank. Multiply this dot product by the probability from step 2. Determine the probability that the player will resplit to 3 hands. Take another 8 out of the deck. Repeat step 3 but multiply by 3 instead of 2. Multiply dot product from step 7 by probability in step 5. Determine the probability that the player will resplit to 4 hands. Take two more 8’s out of the shoe. Repeat step 3 but multiply by 4 instead of 2, and this time consider getting an 8 as a third card, corresponding to the situation where the player is forced to stop resplitting. Multiply dot product from step 11 by probability in step 9. Add values from steps 4, 8, and 12. The hardest part of all this is step 3. I have a very ugly subroutine full of long formulas I determine using probability trees. It gets especially ugly when the dealer has a 10 or ace up.