[Nate tha\\\' Great]

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if entity thought this player would fold 45/74, i think check raising has to be the best line. i just don't see most players folding. i'm leaning toward check fold in this hand.

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I'd rather take my 4:1 on a bet than check and hope he checks behind 97 7T or something. I think you show a strong, immediate profit by betting.

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Let's break this down into the three major cases:

Weak made hand (most likely 4x)

Betting costs you 1 BB.

If you check (intending to raise), let's say that there's a 25% chance that he is weak and checks behind. The other 75% of the time, he bets. There is a 10% chance that he folds a better hand to your check raise.

So the EV of this play is

25% ... 0 BB
67% ... -2 BB
8% ... +5 BB

Betting EV: -1.00 BB
C/R EV: -0.94 BB

Missed draw that has > showdown value than yours

I would imagine that a bet folds out his winner at least 85% of the time.

85% ... +4 BB
15% ... -1 BB

I would guess that he bets if you check around 55% of the time, and folds to a raise around 90% of the time.

45% ... 0 BB
6% ... -2 BB
49% ... +5 BB

Betting EV: +3.25 BB
C/R EV: +2.33 BB

Missed draw that has < showdown value than yours

A bet picks up the pot 100% of the time.

A check results in a bet 2/3 of the time; he always folds to your raise, and you pick up an extra bet in the process by inducing a bluff.

Note that I'm ignoring the case of a bluff raise in both cases.

Betting EV: +4.00 BB
C/R EV: +4.67 BB

I would guess that his range of hands is distributed about 45%/20%/35% between these three cases. If that is the case, then a bet shows a 1.60 BB profit, and a check-raise a 1.68 BB profit. That's too close to call, considering how many simplifying assumptions I've made here.