MGP's BJCA

[ericfarmer]

Thanks. Understood. Never used that mode, nor was it used in BJA3, as the results are suboptimal.

Don

They aren't suboptimal, they simply make a different assumption about the allowed expressive power in specifying the player's strategy. CDZ- is in fact *more* optimal than the strategy assumed by Cacarulo in BJA3 in that composition-dependence doesn't stop at three cards, so to speak. And CDP1 (roughly what is assumed in BJA3, at least the part relevant to pair splitting) is also less optimal than, say, CDP (also evaluated at least by MGP's and my CAs), where the player can not only consider essentially *whether* he has split a given pair in modifying his strategy, but also *how many times*.

At any rate, for the purpose of this particular issue raised by dogman_1234, the distinction between CDZ- and CDP1 doesn't matter; the same assertion holds, namely, that the expected value of the two halves of the split are identical.

[ericfarmer]

They aren't suboptimal, they simply make a different assumption about the allowed expressive power in specifying the player's strategy. CDZ- is in fact *more* optimal than the strategy assumed by Cacarulo in BJA3 in that composition-dependence doesn't stop at three cards, so to speak. And CDP1 (roughly what is assumed in BJA3, at least the part relevant to pair splitting) is also less optimal than, say, CDP (also evaluated at least by MGP's and my CAs), where the player can not only consider essentially *whether* he has split a given pair in modifying his strategy, but also *how many times*.

At any rate, for the purpose of this particular issue raised by dogman_1234, the distinction between CDZ- and CDP1 doesn't matter; the same assertion holds, namely, that the expected value of the two halves of the split are identical.

I forgot to mention in my most recent longer reply: I was misleading when I stated above that these various other strategies "aren't suboptimal." The intent was to emphasize the difference in allowed information assumed available to the player (composition vs. hand total, whether the hand is the result of a pair split, etc.), but for each of these various choices of allowed information, the numbers that are reported by all of our various CAs are indeed suboptimal... with the arguably lone exception of CDZ-, since that minus sign is essentially an implicit acknowledgment of suboptimality relative to CDZ (without the minus sign).