Challanging Ed Miller's Criticism of Lee Jones

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For instance, say you think your opponent either has an ace or a lesser hand, and the chance of each is 50%. Also, suppose that he would check EVERY time, no matter what he has. But after you bet, he would check-raise with his good aces (say 50% with a strong kicker), and just call with is bad aces (the other 50%). He check-calls 100% of the time if he has less than an ace.

Thus, 25% of the time, he has a good ace and check-raises. The other 75% of the time, he check-calls, and you don't know what he has. But he has less than an ace 2/3 of the time (50% of the total divided by the 75% that he check-calls).

So his prior probability of having an ace was 50%, but after he checks and calls, he has an ace only 33% of the time!

You DO gain information when bad players check and call... you gain information that they didn't have a hand strong enough to raise

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Not strong enough to raise another paired ace.

But Leavenfish is talking about holding a pair of kings.

So he isn't getting quite as much nformation about the strength of a non-raising opponent's hand compared to his own as you suggest.