Here's a slightly modified hand I played today (hopefully the code works):
$2/$4 No Limit Holdem
Converted at weaktight.com
Pre-flop: ($6, 3 players) Hero is BB
BTN calls $4, SB calls $2, Hero checks
Flop: ($12, 3 players)
SB checks, Hero bets $12, BTN calls $12, SB folds
Turn: ($36, 2 players)
Hero bets $30, BTN calls $30
River: ($96, 2 players)
Hero bets $40, BTN raises to $80, $40 to Hero ($381.9)?
Now if I say my gut says that if I call I lose most the time... but some of the time I will chop the pot with another Ax hand. That is, I think if I call I will lose 67% of the time, and will chop the pot 33% of the time. And of course then I have 0% of winning the whole pot.
So I have no chance of winning the pot if I call. At best I chop it.
My gut is right, I will mostly lose if I call, and at best some minority of the time I will chop. But I call anyway.