re: Poker & Harrington's %10 bluffing rule
After reading through this Chuck, it looks like you're taking Harrington's Law out of context (based on OP). The 10% is not about calling when the pot is 9:1 odds, it is part of your hand analysis equation for the overall guesstimate of your chances of winning the hand then compared to the pot odds
to make your decision. The 10% is not used by itself which is why you can apply it to every decision in your analysis.
Take Harrington's example specifically: Hero is UTG with A♦A♣
and raises to 4xBB. Villian (MP, experience and conservative) flat calls and flop comes out 9♥5♣
2♠. Hero bets the pot, villian reraises to put hero all in. Pot odds are 3 to 2 for us to call.
HA time: He could be on a set. If he is, then were about 10% to win. He could be on a big pair and we're 92% to win with 2 cards to come. He could be bluffing with a couple big cards making us 97% to win.
Because he's a conservative player, we give him the minimum 10% chance of a bluff. We also make an educated guess that 50% of the time he has the big pair and 40% of the time he has the set. Now with all that established (guessed), we wind up with:
50% (has high pair) * 92% (we win) + 40% (has set) * 10% (we win) + 10% (bluff) * 97% (we win)
= 50%*92% + 40%*10% + 10%*97%
= 46 + 4 + 10 (all numbers rounded)
= 60% chance that we will win the hand overall based on several factors.
Since pot odds are 3 to 2, we make the call. We don't make it because there's a 10% chance he is bluffing, we make it because we guesstimate that we will by river about 60% of time regardless of what he actually has.
I realize I used the #s right out of the book, but I'm hoping that discussing this whole thing in context using the same numbers might help.
What about the same hand with a super rock villian? Let's say he hypothetically makes this move with either a set or a bluff only (even rocks will bluff - it's one of their perks because they get the credit). Still 10% is the minimum for a bluff, but now 90% is a set.
= 90%*10% + 10*97%
= 9 + 10 (rounded again)
= 19% or about 4 to 1. Since pot odds are still 3 to 2, we now have to fold.
I'm rambling now, but I guess the key is that regardless of where the 10% comes from (I'll take Dan's word on it, tbh), it's only a part of the equation (so to speak).