I'm curretly reading 'Play Optimal Poker' by Andrew Brokos and have a question with regards to the following scenario described on page 93.

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[9-handed game, blinds $2/5$, effective stacks $500]

Hero (BTN) raises preflop to $15 and the BB calls. Hero checks behind on the flop K Q 2 and turn 7 and is faced with a pot-sized bet by the BB on the river 7.

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The author mentiones that "Calling and folding are both reasonable options. You have a medium-strength hand facing a large bet, which means that at equilibrium, you're probably indifferent between calling and folding.".
Can someone tell me why that is? Or to put it differently, is that something I can derive from the calculation for the optimal calling frequency vs. a pot-sized bet (which is 1/2) or is it just additional information that the author provides and you can't derive this through heuristics but rather would have to consult a solver for insights like that?

ur hand?

anyway, if you beat all of villains bluffs, and villains value always beats your hand, you have a bluff catcher. By definition, if villains bet is balanced you're indifferent between calling or folding, blockers aside

EDIT: Hero's hand is J J

But am I only indifferent in a pot-sized bet scenario or in general?

You're only indifferent at equilibrium and more or less to bluntly answer your question it'd be "in-general". As aner0 stated, if your hand only beats bluffs and loses to all value then at equilibrium such a hand with no blocker effects would be indifferent. The author does specify, "at equilbrium you're probably indifferent to calling or folding." If villain bets smaller then presumably he has a wider value range, but in the example you've given even if villain had chosen a smaller size the value region would all still be > JJ.

Whether villain is bluffing enough to make you indifferent, too much and makes you want to always call, or not enough and you should always fold, is a different matter and would fall under exploitative play.

So that is basically the scenario of me holding the Q OOP in the Clairvoyance Game?

If I know what you're referencing, then yes.

Example: 22223 board

villain jams river with 6 combos of AA and 3 combos of 55 and the stack is 100 chips and the pot is 100 chips (so psb) and you have some hand(s) > 55 but < AA, then all those hands are 0ev vs. that spot. Equilibrium would have you call at 50% frequency with those hands

2nd EDIT: should say holding the K and not the Q

Thanks for the answers though!

Of course the smaller he bets the more you have to call. Just think what the threshold is where your hand no longer is a pure bluffcatcher. For example if he bets 10% on the river he could be value betting 88-TT and in that case JJ is no longer a bluffcatcher since it is beating value. Generally if your hand can beat value it becomes a call.

Whenever you have a medium strength hand and you're facing a river bet just think "are there any weaker hands he could be betting for value for this sizing?" if yes, call. If no fold or randomize (depending on how good your blockers are).

Intuitively they're never betting worse than JJ for value, or better than JJ as a bluff, so you can just classify it as a pure bluff-catcher.

Whether or not it's a good bluff-catcher or has the right blockers or needs to be defended vs X size is another question altogether.