Blackjack Hand Combinations and Probabilities

Hi all,

I've been looking through the math the Wizard used to construct his basic strategy solver:
https://docs.google.com/spreadsheets/d/1D5-YtpwtCGsTRig7WmOGw9r2uxKXHwq4XWiIYzIGLrU/edit#gid=1073235289

I had a question on how he's getting his hand combination numbers in column B of the "probability" tab.

Hands 5 through 11 make sense to me.
5 can be made with a 2,3 or a 3,2 (2 combinations)
6 is a 2,4 or 4,2 with the 3,3 falling into the "split" category (2 combinations)

This continues through 11, however the 12 through 19 combinations don't add up for me. Is he calculating these using >2 card combinations or is it a function of having more 10s in the deck than other cards?

Also, why does cell L41 not = 1? Wheres the missing 4.8%?

Any help would be great.

Answered my own question - the combinations on 12+ that I couldn't figure out are due to the additional 10s in the deck.

I'm still not sure why cell L41 doesn't add up to 1 though. Anyone have any ideas?

The missing 4.8% is for dealer blackjacks.

Thanks just found that in cell b43 on the "er" tab. Makes sense.

One other question - why is the wizard deviating from his normal formula in cells B1:K7 on the "double" tab? It looks like he's saying the probability of doubling and receiving a 10 card is 3/13 instead of 3/14.

Here's one of the formulas: "=sum(stand!K10:K19)+3*stand!K18"

3 of the 10s are accounted for in 3*stand!k18, and the other is included as one of the terms in the =sum(stand!K10:K19). So, he just used a shorter formula instead of using the "=sum(stand!K10:K17)+stand!K19 + 4*stand!K18"

Thanks for your help!