Hey guys I just wanted to confirm the optimal play here-

So the set up is each player antes 1, then there are 2 streets of pot limit betting. One guy has a range of 100% K, other guy has a range of 50% A, 50% Q.

So by my calculations AQ guy can bet 100% of his range on 1st street, then bet 75% of his range on 2nd street. On 2nd street, K is indifferent to calling/folding since AQ has 2 parts value to 1 part bluff. In other words, on 2nd street, AQ's range looks like:

2/4 value bet A
1/4 bluff with Q
1/4 check/lose with Q

So to make math simple if we assume the K guy folds 2nd street every time in a GTO scenario, he's only winning the pot 25% of the time if he calls the 1st street bet... which is not enough given that he needs 33% to call the pot-sized bet even if the AQ guy bets 100% of his range.

In conclusion- the best strategy for the guy dealt the K is to fold first street 100% of the time and give up the ante. Is this correct?

yea, seems right. a better way to visualize this is, say, one player gets dealt one of the 4 kings and the other one of the 4 aces or 4 queens. "otr" (2nd street) the polar player will bet pot with all 4 aces and two queens, and the expectation of his entire betting range is the pot. the bluffcatcher will call with two of his kings to make the polar player indifferent.

now, "ott" (1st street) these 6 river betting combos can be viewed as "value" combos, since they (collectively, as a range) win exactly the pot. ev of betting an A is 0.5x6 + 0.5x12=9, ev of betting a Q is 0.5x6 + 0.5x(-6)=0, range ev is 2/3x9 + 1/3x0 = 6. in order to make the bluffcatcher on 1st street indifferent to calling or folding to a pot bet, we need to restore the 2:1 ratio, meaning we should bet those 6 + 3 additional bluffs. but since there are only two queens left (as in your example), the bluffcatcher will always fold.

note that the strategy ev for the polar player is 2. let's say we spot the polar player the Jh in addtion to 4 As and 4 Qs, in order to have a balanced betting range on 1st. the strategy ev of the polar player stays the same (2), but optimal play involves calling 1st 50% and calling 2nd 50% for the bluffcatcher.

edit: regarding my last sentence, i guess optimal play is to call any % from 0 to 50 on 1st street for the bluffcatcher since he doesn't face the thread that the polar play will overbluff him (since they aren't any combos left to bluff with).

OK yea. Due to the setup of the problem- that is, the polar player's range is too strong, the bluffcatcher can't ever bluffcatch vs. a pot sized bet