Be7hug

have some serious conflicts in my thoughts, so my question probly wont be that clear, but pls help me out here,.

1. OTR, we want to have a perfect betting range and frequency to make our opponent indifferent from calling or folding with his bluff catchers.

2. will we @NE when we have a perfect polorized range OTR, since our opponent is indifferent with all his bluff catchers, so the EV both calling and folding on his end is zero. therefor, his EV is always zero no matter what he does, if the statement above is true, can i say " once we have a perfect polarized range otr, our opponet can call with all his bluff catchers or fold all of them. if this statement is true, whats the pros of our perfect river betting strategy. is it only to make us not being exploited?

3. can i assume , once we have a perfect polorized range otr to make our opponet indifferent, we will reach a NE, since neither player can unilaterally increase their EV by changing their strategies.

suppose hero is facing a preflop ALL-in with AQcc, and somehow he knows his opponet plays this way if and only if he holds 67ss, or AA. each player started the hand with 100bb stacks, there is 40bb in the pot , and it would cost hero 80bb to call. what is his play?

solution 1- first the EV of folding is 80bb, (in this case, we r doing the EV caculation by the expected stack by the end of the decision node). Villain holds 76CC, 76HH, 76SS, 76DD, and 3 combos of AA since we blocking one A, if hero calls, he will run into AA 3times and 67s 4times, he is equity against that range is 40.49%. there will be 200bb in the pot if we call, so 200x40.49% = 80.97bb 80.97>80, so its call.

solution 2- we r risking 80 to win 120, so 80/120=2/3 how do i caculate how often do i have to be right or how much equity do we need to make the call. i did it two ways. 2/3=66% and 3/2+3=60%, and i think they r both wrong, if we need more than 60% of equity to call, then clearly this is a fold but i know for a fact that solution 1 is correct, (from a book) pretty dumb question but im really confused here.. thanks guys!!

game just started, i think if not all then majority of the guys knows each other on the table. 10 handed.

I dislike the word "hero" alot so im gonna use "boss" to represent "hero" here. not even jking.

 BOSS opens UTG with AhAd to 75,  good reg flats the CO, loose aggro fish who like to spazz once in a while flats the BTN,  another fishy guy calls from BB, 5k effective each piece.

my opening range UTG in these games are like 17%-19%,  22+, A2s+, ATo+, 67s-9Ts, JTs, J9s, 97s, QJs, KTs+,

FLOP: QdTd7s  pot($235)

BB leads $200,  BOSS??   I thought flatting was good, given we hold the Ad, although i dont know how much that matters, and i could be wrong. do i have a flop raising range here in this spot?? So i decided to call, and good reg calls, fish OTB calls.

TURN: Ac pot ($1035)

BB checks, BOSS???? i decided to bet $550, i thought it was gonna get checked around alot on this card unless someone had KJ, good reg calls and the rest all folded.

RIVER: 5h. pot($2135)

BOSS?????   i decided to check just because i thought the value of him bluffing is greater.  i dont think there is any strong in his range that could call a river bet given we block alot Ax,  after i check he bets 2k fairly quick. BOss?????

any thoughts on any streets would be appreciated. thanks guys:-)