[jason1990]

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1. We could assume that bluff raises are exactly as likely to be called down (and hence shown down) as raises in general (real and bluff combined), and estimate P(showdown | bluff/r) using P(showdown).

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Do you mean you would estimate P(showdown | bluff/r) using P(showdown | raise)? I like this idea, but I think the former might be slightly smaller. For example, if you call my turn bluff raise, then bet into me on the river, I would probably fold more often than if my original raise has been legit. I don't know though. The formula doesn't distinguish between "good" and "bad" bluffs. In principle, some bluffs may be more transparent than others, so that only "good" bluff raises would be as likely to be called down as legit raises.

The second idea seems a little fishy to me. You want to estimate P(bluff/r from opponent), but in the formula you would use P(showdown | bluff/r from gaming_mouse). Maybe it's not that big of a deal, but the mental red flag popped up when I read that.

Also, I think you're multiplying where you should be dividing, so the final formula is the reciprocal of what you wrote.

As a practical matter, do you know how many hands you would need to gather enough data for this?

By the way, are there sites where you can see the folded hands in the hand history? Or is that just a myth I heard.