So a comment on other thread I started (http://www.runitonce.com/nlhe/how-do-minimum-fold-equity-to-bluff-an/) by Prangman 2

"[...] your river bluffs should be the same % as the pot odds you offer (assuming no villain bluff-catchers beat any of your value combos [and your bluffs don't beat their bluff-catchers]) if you want to make them indifferent to folding. So for the pot sized bet villain should have 33% equity to call - that 33% being the % that these bluff hands are in your river betting range"

kept me thinking...

What when our value bets are not 100% winners?

Let's suppose we arrive at the river with 30 absolute nutella combos. The pot is 1 and we bet 1, so we add 15 bluff combos. We get called and win 66% (30 out of 45 times) and lose 33%, so villain equity when calls is 33%.

Now we are in the same spot and we have 30 value combos, but they're far from being nuts. So a reasonable assumption would be we win 20 out of 30 times for a PSB, now if we add 15 bluff combos, villain would win 25 out of 45 times! He would have an equity of 44%! And would have an incentive to call with all of his bluffcatchers. So if we would want to keep the same ratio of 33% equity for villain, we should bluff.... 0 combos!? Is that correct?

(In fact I have seen Snowie in spots where he has some ratio of 97% value/3% bluffs.)

How can we calculate the value/bluff ratio when we don't win 100% of our value hands?

Thank you very much :)