[gaming_mouse]

1) randomizing your bluffing eliminates some, but not all, of the information an opponent could profitably use to determine if you are bluffing.

If you don't look at your the card in question, it eliminates all of it. Aside from that, I agree with everything you say in 1).

2) if you don't look at the last card, then you cannot possibly alter the odds that you are bluffing when you bet by altering the frequency with which you choose to bet

I am pretty sure this is incorrect. Please read over the following and corroborate or refute the reasoning. I think your confusion is coming from looking at it on a case by case basis. Think of how your strategy plays out over many hands. For example:

You are playing holdem and are drawing at a well disguised OESD on the turn (ie, only the river card is yet to come). Your oppo could put you on a whole range of hands, some of which might already have him beat, so bluffing makes sense. Problem is, as in your scenario, this guy can see right through you. No problem. You decide to bet without looking at the river, using randomization.

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. Well, given our strategy -- betting p% of the time no matter what -- in the long run we will have:

P(a bet from us is not a bluff) = p*(8/45)

p*(8/45) = (1/11)

p = .511

So if we bet 50% of the time no matter what, we guarantee a wash -- our oppo cannot use our tells against us.

gm

EDIT: Of course, the downside of this is that sometimes you don't bet when you have filled up. But this is the best strategy against a theoretical oppo who can always read us from physical tells.

Also, it would be more accurate to say that we guarantee collecting our equity in the pot, rather than saying that we guarantee "a wash".