btn v. bb: 3b/4b/shove

here are some sims that are similar to the 5/6-bet stuff below, but where players have smaller stacks:

• btn opens to 3bb w/ top 50% 
• bb 3bets to 11bb w/ top x%
• btn 4bets to 26bb w/ [JJ+, AK, var1% of others] 
• bb shoves 100bb w/ [TT+, AK, var2% of others]
• btn calls [TT+, AQ+]

if we vary the 3bet range of bb, btn 4-bet air range, and bb shove air range, we get the following (notice scale changes):

notice that there is not equilibrium point for btn 4-bet range. that is, v. a 3b range this tight, 4-betting w/ any air is exploitable, ldo.

pretty light post, but i havent been able to play all week and dont want to spend too much time on this stuff right now...

[i also wanted to clarify something i wrote earlier - relevant to this and previous posts - about the GTO strategy being independent of the opponent (by definition, a GTO strategy occurs when a player cannot increase his expectation by acting unilaterally). i went on to say that strategies are dependent on stack sizes and the hands in hero's range. for example, i stated that the optimal frequency to 5-bet bluff, was dependent on hero's 3-bet range. that statement isn't strictly true, the optimal bluffing frequency is actually dependent on the number of combinations of value/nut hands, but since i had defined the bluff frequency as a % of non-value hands, it sort of looks like it's dependent on the range of hands going into the decision point.]