Hi, guys!

I'm trying to study game theory atm and am confused in few spots. I know these spots are quite abstract and it's impossible to get an exact answer, but I hope it's possible to find some pretty good approximations.

1. How wide can we defend preflop lets say in BB vs openraise from BTN/CO/MP/UTG, assuming we're offered X:1 (lets say 2<=X<=3), we will be playing HU 100BB Deep and we know exact villain's raising range? I've heard about the R concept, even watched Sean's videos about it, but still struggling with estimating it.

2. Assume we defended a certain range pre. Now we're on the flop and villain bets Z% of the pot. Previously, I thought we had to defend 1/(1+Z) of our range, but I'm not sure about this now, especially when we had very good odds pre: our preflop calling range is a lot weaker than villain's raising range.

My guess is that there could be 3 possible scenarios:

a. The most common one: raiser's range is more polarized and has more equity.

b. Neither range has equity advantage, but raiser's range is more polarized.

c. Caller's range is more polarized and has more equity (probably very rare).

So the question is how to find the worst hand we should defend on the flop in each of these spots.

 
Any input is appreciated!

-- Sergey