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Originally Posted by Amanaplan
Aren't these polarized river spots relatively common enough in real poker that a human can reliably use this toy game as a model for 'good play' in such spots? (ignoring villain's option to check-raise).
sure, they do come up, and to the extent they do this toy game can help inform our view of what good play would look like (given the assumptions hold true). i think its very important to note the limitations of the game though (esp wrt villain only holding true bluff catchers), and to be careful not to over-apply the concept. one thing to keep in mind is whether why/how we got to this river spot is consistent with the assumptions of the model or goal of being balanced; if we played prior streets assuming villain was over-folding, he might be left with a strong range otr (ie has some hands that beat our value hands), or there might be an exploitative strategy that is best given our profile of villain. also note that in the toy game villain's option to check-raise is irrelevant since he would rationally never choose to do so.
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I'm likely stepping all over myself with this next part, but I would imagine a hero GTO strategy would have a unique sizing (or check) for every hand in the same spot whereas a human would mostly check (for varying reasons) and that's where we lose sight of things when it comes to emulating such balance??
in the context of this toy game, no. hero will choose a strategy that maximizes his range's ev, which will use a bet size* that allows him as many bluffs as possible while keeping villain indifferent. essentially, the hands in his betting range will (on average) have an ev equal to the entire pot, and thus he wants to maximize the number of hands he can bet with (since all other bluffs will xb and lose). when going all-in, he can bluff with ((spr/(spr+1)) times the number of value hands) (ie hero's % of bluffs equals villains break even equity on a call). i think people check rivers mainly because they don't think the assumptions hold or because they expect villain to play irrationally (betting with pure bluff catchers, etc.).
*hero can also bet a larger size and villain will simply fold 100%, yielding the same result.