Johny's a one trick ponny, but it's a good trick: all-in!
-Dan Harrington, "Harrington on Online Cash Games"
The short version is : I don't like posting microstakes hands as there is nothing to gain for me and analysis was done long time (few days) ago, but homework requires it so here we go.
The longer story: the definitions of player types in pokerstrategy.com lack a one well established archetype : All-in Johnny (at least Harrington gave him that name) : a player who raises preflop only to all-in (and sometimes, like in this case also limps from time to time preflop). A simple strategy to counter it was suggested to call with ATs+, AJo+, 66+, if his range is A8o+, Axs, 22+ (or ~15%), when his raise is ~50BB and there is 4.5BB in pot (he recommeds raising 3BB, but that's another story, and I'm still thinking whether it would be better for SH).
The hero's story on hand however is:
NL Holdem $0.02(BB)
Hero ($2.30)
BB ($1.26)
UTG ($2.15)
UTG+1 ($2.87)
CO ($1.79)
BTN ($5.73)
Dealt to Hero Q♣ K♠
fold, fold, fold, BTN raises to $0.06, Hero raises to $0.18, BB raises to $1.26 (AI), fold, Hero ???
To explain more on the situation : BTN usually raises 4bb from other positions and this was obvious resteal situation for me. BB's stats were ~30/10 through 30 hands and all 3 times he shoved. This isn't big enough sample to put him on exact range, but:
My pot equity calling is 41.86%
Against 10% range (77+,A9s+,KTs+,QTs+,AJo+,KQo) my equity is 39.4%
Against 15% balanced range (77+,A7s+,K9s+,QTs+,JTs,ATo+,KTo+,QJo) my equity is 46.21%
Against 15% ace/pp based range (22+, A2s+, A8o+) my equity is 38.78%
How exactly should I put enemies like him on a range and calculate my equity, when it's impossible to get more extensive sample size, due to the nature most of these players play. (well obviously KQo was a mistake, but only analysing it, I realised how close that spot was)
Spoiler
If anyone cares, he had AA and floped full house, but the decision, in my opinion, should be based against their range and not specific hands when playing with this type of players.