Checking out Wizard's tables

I have been playing with the numbers from Appendix 1 on wizardofodds (not to look for errors, but to see if I can calculate those returns myself), and there is still something that I can't get - namely, the expected returns by splitting - I am getting different values for (I think) all of the cases, that makes me think I am doing something wrong, but I can't figure out what it is.
For example, take the case of splitting 10s against a 2. I tried to take a 10, add another card to it, one by one (you won't want to resplit or double, so there is no complication here), and sum the expected returns, weighed by their probability (1/13 for A-9, and 4/13 for 10 - this is an infinite number of decks). All the EV values match the respective Wizard's tables, but the result doesn't for some reason:

A(21): 0.8820
10(20): 0.6400 * 4 = 2.56
9(19): 0.3863
8(18): 0.1217
7(17): -0.1530
6-3(16-13): -0.2928*4 = -1.1712
2(12): -0.2534

If I sum up all the numbers in the second column, and divide by 13, I get 0.1825.
Multiplying this by 2 to take two hands into account, the expected value ends up being 0.3645, while the corresponding value from Wizard's table is 0.1348

I have been pulling my hair out all day over this, but cannot figure out what I am missing. Could some kind soul please look at this an point out where my mistake is? I'll greatly appreciate any help!

The problem is probably due to resplitting. In my appendix 1 I state I assume the player can resplit to up to four hands. It is complicated determining how many hands on average that will lead to. At the bottom of my appendix 1 I have a link to my spreadsheet at Google docs, which shows all my work. That document is based on infinite resplitting. In the case of splitting tens, the first split will on average lead to 3.6 final hands.

Oh, so you are saying that the value in that table is calculated under an assumption that the player will keep splitting until the limit is reached, not play the best strategy on each of the hands? Is this it?

Sorry, for bugging you again, but I still don't get it :(
The return from hitting 10 points against a 2 is 0.1825. I can't see how the EV of splitting two tens can be any lower than twice that. I mean, after all the resplitting, you will end up playing at least two ten-point hands against the dealer's two, how can the return from that be less than from playing exactly two hands?

Quote: weaselman

Oh, so you are saying that the value in that table is calculated under an assumption that the player will keep splitting until the limit is reached, not play the best strategy on each of the hands? Is this it?

Yes. If it was right to split the first time, it will always be right to keep resplitting.

Right, I got that already. But still, since you play two or more hands with expected value of 0.1825, shouldn't the overall return be more than 0.1825*2?

Ok, I misspoke that. The figure in question is not 0.1825, but the conditional return value on a ten-point hand, provided that the second card is not the same as the first (still could be ten value though) - (0.1825*13 - 0.64)/12 = 0.1444.
This is the minimum you'll make on each hand, and you'll play the minimum of two of them.

This was bugging me so much, that I gave up on the formulas, and just wrote a little simulation program, running a 10-10 hand against a 2, under the rules that it must always split 10s up to four hands, hit below 14 points and stand otherwise.
After about 30 million experiments, the number I am getting is about 0.3173, that matches exactly what I am getting from my formula (after the correction, that you have to split tens if you can - thanks for pointing that out to me!).

It seems that your table is wrong after all (although, I could not find any case when it would actually affect the strategy).