[jason1990]

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Say the pot is offering him 10:1 on his final call. Well, you have 8 outs, and there are 45 cards left. We need to determine the percent p such that if you bet out p% of the time on the river -- without looking at the river card -- the odds against your bluffing will be 10:1.

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My understanding of the game theory argument suggests that we want

P(a bet from us is not a bluff) = 10*P(a bet from us is a bluff)

which, if we play as you suggest, yields the equation

p*(8/45) = 10*p*(37/45).

The only solution to this equation is p = 0.

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EDIT: Of course, the downside of this is that sometimes you don't bet when you have filled up.

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Apparently, from the above, the only way to implement the "optimal" strategy without looking at the river card is to *never* bet, which means that this downside doesn't happen sometimes, but in fact it happens always.