"I really appreciate your reply and it is quite an experience for me to be communicating with [you] on a topic. Call it hero worship perhaps, but nevertheless I will always go to the great fonts of BJ knowledge.
"OK let's go a bit deeper with this, I have read his book and I would like to have asked him a number of questions directly but there are no contact details unfortunately.
"His matrix is for European Rules which they are at pains to warn the readers that in some cases the strategy may be different according to the rules of a casino. Their BS refers specifically to BJ with 6D, European No Hole Card (dealers card is dealt last), S17, no DD permitted after a split."
As I suspected. Understand, also, that ENHC isn't just that the dealer doesn't take a hole card, but also that all splits and doubles are lost to a subsequent dealer natural. That's the important part. Otherwise, taking the hole card last wouldn't matter.
"His interpretation is at variance with the more conventional BS matrix that I am using."
For 2,2 v 2, they advise hit with expectation of -0.11 (Split -0.15)
For 2,2 v 3, they advise hit with expectation of -0.08 (Split -0.10)
For 3,3 v 2, they advise hit with expectation of -0.14 (Split -0.20)
For 3,3 v 3, they advise hit with expectation of -0.11 (Split -0.14)
For 4,4 v 5, they advise hit with expectation of -0.07 (Split -0.02)
For 4,4 v 6, they advise hit with expectation of -0.11 (Split -0.02)
For 6,6 v 2, they advise hit with expectation of -0.25 (Split -0.28)
For 8,8 v 10, they advise hit with expectation of -0.58 (Split -0.62)
For 8,8 v ACE, they advise hit with expectation of -0.67(Split -0.89)
"I am agreeing with them for the 8,8 play versus the ACE and against a 10 perhaps a DAS will facilitate that 8,8 v 10 is a split.
No, it isn't. When you can lose all to a dealer natural, you don't split any pair vs. dealer's 10 or ace with the exception of splitting A,A vs. 10.
"Now, maths is maths, and using Markov Chains has allowed them to automate the calculations. Their Basic Strategy has been developed using Probability Theory. They state BJ is completely mechanical and is a game that is resolved by mathematics, and anything else is quite simply wrong."
Well, that's true.
"They advise to split the above if there is DAS and the mathematical expectation are a little better."
Correct for everything but the 8,8. Not correct to split if ENHC.
"However, and a big one. I used to split A, A v Ace but 2 FT Pros (shockingly decent players) told me that for UK don't split them. I simply hit them now So, why is Toffoli advising the split? Maths is maths."
I can never put myself in some other author's shoes and tell you what he/she is thinking. I can only tell you what the right play is. And, for BS vs. ENHC, you can find the correct pair splits at the bottom of p. 490 of BJA3.
"For completeness, I am playing, 6D, ENHC, S17, DAS, Unlimited resplits , DBls on every card. No surrender with a house advantage -0.55%"
I make it -0.51%, from pp. 492-493.
"although in another thread here I have calculated it to be closes to -0.36% due to DBL on every card as opposed to DBL on 9,10 and 11 only."
No. DAS brings -0.54% to -0.40%, but ENHC costs another 0.11%.
"BTW I like your Floating Point Advantage explanation (BJA3)."
Thanks. That was a big project. Glad you enjoyed.
Don