Ok, so my last post about calling with the second nuts created some debate among the readers, so I think I should write a second part – analysing the required probability of our opponent being an overplayer. I wanted to do that on the end of the first part, but it seemed such an obvious call, I let the idea go. It seems it was a mistake on my part.
Ok, so let’s assume 2 scenarios: first is that our opponent is decent, and 3bets only 22 (or TT, but we block that entirely). The second one is that he caps 55. Let’s see the EV difference of capping in both cases.
EV(capping vs decent) = P(win)*V(win) + P(lose)*V(lose) = 0*whatev + 1*(-2 BB) = -2BB
EV(calling vs decent) = P(win)*V(win) + P(lose)*V(lose) = 0*whatev + 1*(-1 BB) = -1BB
EV(capping vs overplayer) = P(win)*V(win) + P(lose)*V(lose) = 0,75*(19 BB) + 0,25*(-2BB) = 13,75BB
EV(calling vs overplayer) = P(win)*V(win) + P(lose)*V(lose) = 0,75*(18 BB) + 0,25*(-1BB) = 13,25BB
So let’s say our opponent is an overplayer x of the times. The EV of capping is:
EV(capping) = P(overplayer)*V(overplayer) + P(decent)*V(decent) = 13,75x + (1-x)(-2) = 15,75x – 2
EV(calling) = P(overplayer)*V(overplayer) + P(decent)*V(decent) = 13,25x – (1-x) = 14,25x – 1
So for the cap to be the best play:
EV(capping) > EV(calling)15,75x – 2 > 14,25x – 1
1,5x > 1
x > 2/3
Meaning that our opponent has to be an overplayer 66% of the times so we could cap here. Given my information on the player (that he is a midstakes regular who I haven’t seen any overplays from thus far), I definitely wouldn’t think he’s an overplayer with a frequency of 66%. Even 50% seemed iffy, but 66? Definitely not. For all the doubters, if you’re sitting in a midstakes game where 2/3 of the “regulars” are bad enough to 3bet 55 here, let me know.;)