Mixing up your play

[togilvie]

Assume that you are able to accurately estimate the EV of your actions, giving you an EV Triple for any situation:
(EV[Fold], EV[Call], EV[Raise]).

How should you play this "optimally"? That is, given the following EV Triples for a 3-6 game, how often would you Fold, Call or Raise? Any theoretical basis for this? (I'll post my answer in a separate thread, though it's just a guess.

(0, 4, 4)
(0, -1, 5)
(0, 1, 1)
(0, 2, -3)
(0, 3, 7)

[togilvie]

I was thinking through this problem over the weekend, and decided that I thought the best technique was a two-step process:

1) Determine P[Fold] by looking at the maximum EV(i.e. ignore negative values if they occur, as well as big differences between EV[Call] and EV[Raise]. I use a subjective scale to figure out how frequently I'll play.

2) Determine how often to take each action by distributing the hands I call with ratably:

P[Call] = (1-P[Fold]) * EV[Call] / (EV[Call] + EV[Raise])

This led me to the following answers:
(0, 4, 4) 0%, 50%, 50%
(0, -1, 5) 0%, 0%, 100%
(0, 1, 1) 40%, 30%, 30%
(0, 2, -3) 25%, 75%, 0%
(0, 3, 7) 0%, 30%, 70%