Short handed poker, Ed Miller, Bunching Effect, The Price is Right

Ed Miller wrote that the bunching effect is miniscule between acting first in a four- handed game and acting one of the button in a ten-handed game after six folds. (see footnote),

But is there some other effect that comes into play?

The Price is Right puzzle from the Ask Marilyn column:

One prize is behind door A, B or C, you are asked to choose and you guess door A. The host tells you truthfully that the prize is not behind door B and now gives you the option to change your choice. Should you change your choice?

The answer is yes you should. If you change to door C you’ll have a 66% chance of receiving the prize, if you stick with door A you’ll have a 33% chance of receiving the prize.

I hope we don’t discuss this, trust me this is correct. Math professors challenged this answer saying it was wrong. Marilyn then proved the answer to their satisfaction.

Can we apply this same logic to poker?

An extreme example: You’re in the BB with KK. Your opponents only play AA except the SB who’ll steal with every hand if he’s 1st in. It has been folded to the SB who raises. What’s the chance that the SB has AA?

Let’s forget the bunching effect here. My question is: Is there a “Price is Right” effect? I realize it won’t be as dramatic, but does it exist. And if it does, does it follow that the hand qualities, not considering bunching, are better in a ten-handed game after six folds than in a four-handed game?


Footnote: By the way, Ed Miller did explain why there are differences between the four-handed game and the ten-handed after six folds. In this post I’m looking at something different.