tomchina123
Joined: Aug 26, 2015
• Posts: 282
April 5th, 2019 at 7:10:51 AM permalink
now i can do a lot of ca, but split is very difficult, who can help me?

let's say it is to split 3 times into 4 hands.

i give a concrete example:

hands: 1010 Vs 6

the first hand is 10,
dealer's card 6
10,2, EV*possibility of 2
10,3, EV*possibility of 3
10,4 , EV*possibility of 4
10,5, EV*possibility of 5
10,6 , EV*possibility of 6
10,7 , EV*possibility of 7
10,8 , EV*possibility of 8
10,9 , EV*possibility of 9
10,10, EV*possibility of 10
10, A, EV*possibility of A
total.: sumup
it is first hand EV. my result is the same with others.
second hand, the same way. times 2? shall we consider 2---A removed(first hand)? this is very small difference, i don't really care much.

the difficult is the 3rd hand. we may split 1st hand into the 3 rd hand, or 2nd hand into 3rd. if so, what possibilies to multiply? P of card 10 P*p*card 2-11P?

the most difficult is the 4th hand... i tried lot of ways to caculate it , but the result is a lot different from wizard and bjstrat(the two are different also).
charliepatrick
Joined: Jun 17, 2011
• Posts: 2321
April 5th, 2019 at 8:35:19 AM permalink
There are a numbher of factors to consider - I don't know how others do it.
(i) If you split (even when it's not correct to do so) the assumption is (a) you're going to continue to do so or (b) not.
(ii) Some casinos only allow you to split identical pictures not just any two 10-valued cards.
(iii) Some casinos don't allow you to double 10-A after a split.
(iv) When considering splitting the 3rd hand (i.e. 1st and 2nd aren't 10-10) then you only consider the shoe with three other 10's removed and then a hand starting 10 where it can't split if it receives a 10. This would be based of the EVs as you say. Then iterate backwards based on how many splits you get.

I suspect most people don't look at the cards used within other splits when evaluating hands except for the removal of the split cards. For instance single deck looking at splitting 8s, then one would say that any given hand can't get another 8 after splitting to the max, so you either have two hands starting 8 8, three hands 8 8 8 or four hands 8 8 8 8. Work out the EV of a hand starting with an 8 given one 8 already missing and the second card isn't an 8, etc.)

In some games, e.g. versions of double exposure or similar where it is correct to split 10s and double 10-A, one needs clarifications of the casino local rules as well as the game's rules.
tomchina123
Joined: Aug 26, 2015
• Posts: 282
April 5th, 2019 at 6:47:31 PM permalink
thanks, Charlie, it seems you know a lot.

you are a very successful Ap, aren't u? can i learn from u for real usa experience?
charliepatrick
Joined: Jun 17, 2011
• Posts: 2321
April 6th, 2019 at 12:20:58 AM permalink
I'm not an AP, in fact I don't play so often these days. but I've analysed casino games and treating splits can be interesting - I always use infinite deck analysis as I've never got round to writing the program to analyse BJ for finite decks. There have a been a few variants where splitting 10s was correct so I did discuss this with a casino exactly what their house rules were.
tomchina123
Joined: Aug 26, 2015