Quote Originally Posted by aceside View Post
Can you just specify a little more on this example? Greater understanding comes with greater responsibilities. I have received several dislikes and try to learn a little more into this.
There are several interesting wrinkles here, I'll just mention a few. First, the phrase "maximizes expected value" almost always requires clarification. There are two senses in which we can rarely actually claim to *maximize* achievable expected return. One is when restricting attention to total-dependent (vs. composition-dependent) strategy. That is, although composition-dependent strategy is more complex to *specify*, it's generally easier to actually *optimize*, i.e. to compute a strategy that actually maximizes the expected value of some appropriately-defined random variable. That's because composition-dependent expected value can be defined and computed recursively, while total-dependent strategy can have circular dependencies that require a "global" optimization approach that no CA I know of actually implements. For example, should I stand or hit with 10,3 vs. 10? That's a total of hard 13 vs. 10; resolving to hit requires ensuring that the EV of hitting is greater than that of standing... but the EV of hitting depends on making EV-maximizing decisions after the hit as well, e.g. 10,3,3 vs. 10, and the *probability* of even encountering that hand depends on having already resolved all decisions that *could* lead to that hand.

(Granted, I'm willing to let Nairn pass on this here, since he sort of sidesteps the issue by explicitly specifying a fixed playing strategy in his Appendix A. It simply would have been clearer/more correct to remove the claim of EV maximality altogether.)

Computing truly EV-maximizing total-dependent strategy is technically hard even if pair splitting were not a thing. But here we're focusing on pair splits, where things get even more complicated. This second problem is that any explicit strategy, whether total- or composition-dependent, computed by almost any CA (including mine), does not actually maximize the expected value of any easy-to-describe random variable, because of the complexity of accounting for pair splitting. For example, what should you do with 2,6 vs. dealer 5? If we temporarily ignore that pair splitting is a thing, we might resolve that the best strategy is to hit... but what if we encounter this hand as the result of splitting 2s against the dealer 5? Knowing that we're in half of the split might suggest that doubling down is optimal... but worse, if we now "retroactively" change our "zero memory" strategy to *always* double down 2,6 vs. 5, whether we are splitting or not, can *raise* the overall EV for the round.

(Various CAs expose various options for configuring how sophisticated our splitting strategy can be to deal with this sort of thing. For example, my CA's "default" strategy option, referred to elsewhere in this forum as CDZ-, is to stick with the "split-agnostic" strategy of hitting, applied after pair splits as well. There are other options like CDP1 or CDP, that allow us to "know" if we are in a split hand to modify strategy... but the holy grail referred to as CDZ (without the minus) that computes the "overall" EV-maximizing strategy that depends only on the dealer's up card and the composition of the player's *current* (possibly-split) hand, is beyond our current ability to compute AFAIK.)

There is more, but that's hopefully a conversation starter.