I'm surveying whatever literature I can find on optimal total-dependent basic strategy generation before I start to build a generator of my own. I can't find anything that spells out the state-of-the-art methodology, so I'm trying to absorb and infer as best as I can from what I can find here, in the discussion of Appendix A of BJA3, and elsewhere.

One issue I haven't seen addressed is that truly accurate strategy generation has to be recursive(as best as I can tell). For example, it's fairly obvious that in order to determine whether to double 9 v 2, we must first know how we would play out the rest of the hand. In other words, we have to know the parts of basic strategy "above" the total of 9. This is presumably why most strategy generators begin with player totals of Hard 17, then proceed "downwards" through all hard hands, then soft hands, then splits: One follows the other.

What is less obvious is that in order to determine the correct way to play out the rest of the hand, we must first know how we will play 9 v 2!!! Total-dependent basic strategy requires us to construct a probability distribution indicating the frequency of each possible composition for a given hand total. But the contents of that probability distribution depend on how one plays the hands "below" it (ie, on typical strategy charts).

This suggests the need for an iterative function in order to determine proper BS. Has anyone calculated BS that way? Perhaps there are no real examples in which the effect would result in changes to basic strategy. But it would theoretically be the right way to compute optimal strategy, I think.

The reason I started looking at this is because I want to build a strat generator, the right way. So ultimately, my question is: If not through such an iterative function, how else would one determine an accurate probability distribution for a given total?