Methodology behind exact Basic Strategy calculation (Splits & computational complexity)

Hello,
I am currently researching the mathematical modeling of Blackjack and how the Basic Strategy is derived. Michael Shackleford often mentions that his results are exactly calculated rather than simulated. Especially his results of the house edge calculator makes me ask, how exact these numbers are. My question is:
What methodology is used to compute the Basic Strategy exactly?
Is it based on complete recursive expected value calculations?
In particular, how are the computational challenges of splitting handled? John Nairn (2019) (Exact Calculation of Expected Values for Splitting Pairs in Blackjack) describes overcoming this problem using dealer-caching and pre-enumeration to reduce the state space — is a similar or different approach applied here?
Any insights or references would be greatly appreciated.

Exact calculation? Probably does not exist. It’s all about how you define it.

What do you mean exactly? Because technically it can exist. So you think Shackleford used only approximating numbers?

Wizard has solved infinity deck assuming one split. Two and three splits have been solved too.

So what are those probabilities based on of his Blackjack house edge calculator?

I have a math problem. In an infinite deck blackjack game where a player may split times, what is the expected value?

What are you even trying to say?

Consider an infinite deck blackjack game. Use this hand, 8,8 vs. 6 as an example. Find the expected value of this hand if a player may split infinite times.

Im not talking about infinite times. I am talking for example how the expected value is calculated for 6 decks with the ability to split 4 times.

If you solve my puzzle, I’ll read into yours.

It was a mistake asking it here... Your question is unsolvable. Someone thinks he's funny huh

If you haven't seen it yet, this video may be informative.

https://youtu.be/jCF-Btu5ZCk

The infinite deck approach is somewhat simpler than a finite deck approach. In general, I believe one would define an array containing an element for each card in the source deck, remove dealt cards from consideration, and then iteratively calculate what would happen for each possible hit card.

Basically, the easy way to calculate uses a program that handles each special case (like splitting).

Simulation does the basically the same thing, but for a random sampling of possible cases. Calculation evaluates all cases.

There are serious shortcuts available if you don't care about suits, and don't mind grouping all the ten-value ranks.

The infinite deck approach is not the hard problem that OP is asking about.

OP is asking about how gaming mathematicians calculate the composition-dependent probabilities for split hands (with re-split up to n times).

For example
In the Composition Dependent Combinatorial Analyzer (cdca) at bjstrat.net the EVs for splitting and resplitting 88 versus 7 with 6 decks are:

First split hand, SPL1: 0.1711
2nd split hand,SPL2: 0.2509
3rd split hand, SPL3: 0.2604

More impressively the EVs for splitting and resplitting 22 versus 4 with 6 decks, S17, are:

First split hand, SPL1: 0.3762
2nd split hand,SPL2: 0.3634
3rd split hand, SPL3: 0.3615

Not only are these fresh deck composition-dependent calculations reported but if you remove cards from the composition of the deck the CDCA calculates different results.

The OP's question is an excellent one: How does this get calculated? And, how does the Wizard calculate his House Advantage results for resplit one, two and three times?

There are two questions here.

1. For an infinite deck game, what are the respective numbers for 8, 8 vs. 7?

SPL1: 0.1711;
SPL2: 0.2509;
SPL3: 0.2604;
SPL4: ?
SPL5: ?
…
SPL Infinite: ?

2. These SPL EV numbers assume you must split 5 times whenever available in SPL5. They are not split-up-to-5-times numbers.