[Nick C]

[ QUOTE ]
Check/call is only better then bet/fold when your opponent is going to bet more hands when checked to than he will call when bet into.

[/ QUOTE ]

This is probably true for the posted hand. But, to be honest, it's badly phrased and I'm not entirely sure to what extent you didn't say what you meant to say and to what extent what you meant to say is simply incorrect. In any case, the sentence I quoted is oversimplified.

For instance, in some cases (especially if the pot is big), the chance to steal the whole pot (if we have some folding equity) makes a bet-fold the best play, and in some cases (versus a LAG, for instance) the possibility that the entire pot will be stolen from us by a bluff-raise makes a bet-fold far too risky.

But let's say we have no folding equity (and I doubt we have any here except for misclick folding equity). In that case, a bet-fold is better than a check-call only if the amount of worse hands Villain will call with is greater than the number of worse hands Villain will bluff-raise with multiplied by the size of the pot after our bet plus the number of better hands Villain would have checked behind plus the number of worse hands Villain would have bet if checked to.

So, let's say we have a 5 BB pot, and, over the course of 100 hands, Villain will have a worse hand exactly 50 times. Let's say that he'll also call with a worse hand 20 times, but will only bet a worse hand only 5 times. Okay, we're +15 so far on a bet-fold versus a check-call. Now let's say that he'll always call (or raise) with his 50 better hands but will only bet 45 of those. We're down to +10 bets, over 100 hands, on a bet-fold versus a check-call. Now let's say that Villain will bluff-raise with 2 of those 5 worse hands he would have bet. All of a sudden, we're losing money on a bet-fold versus a bet-call -- just barely, but the example is hypothetical anyway. (And note, also, that the river is -EV for us for both options, in this example.)

Er, anyway, in the posted hand, as I've already argued earlier, I think Villain is so likely to have a worse hand he won't call with that bet-folding loses much of its appeal, despite the fact that there isn't much threat of a bluff-raise from this particular Villain. I mean, yeah, we'll get some curiosity calls from worse hands, but we're also going to get some calls from better hands Villain wouldn't have bet himself, and, if my recent NL experiences are any indication, we're going to snap off some bluffs from busted draws (despite Villain's passiveness) that he wouldn't have called with in this pot that no one seems too interested in.

The instinct to bet-fold on the river with a marginal hand rather than check-call versus a loose-passive Villain is a good one, but the action in this hand indicates Villain is going to have diddly-squat a lot. So I don't think he needs to bluff a busted draw with any great frequency to tilt the play to a check-call in this particular instance.