I keep seeing players write how overbetting allows them to bluff more in a theoretical sense. If I know you're bluffing 50%, I'm calling a 1/3 or a 3x pot. I know my odds are worse facing an overbet and I DON'T HAVE TO call as frequently but why wouldn't I if you're bluffing more than with a smaller sizing?

If you know Villain is bluffing 50% or more, you should never fold, because you never get worse than 1 : 1 pot odds. But a good player will adjust his bluffing frequency according to pot odds, and you can't assume it's fixed.

If he's balanced (having a 2 : 1 value/bluff ratio when he bets pot, 3 : 2 with twice the pot, etc), he's making you indifferent towards calling or folding with your bluffcatchers. Since you're indifferent, whatever you do, the result will be the same as if you fold. So a balanced Villain who knows you have a bluffcatcher, effectively wins the pot every time he bets. By betting bigger, he gets to bluff more (while keeping you indifferent), which means he gets to bet more often, and therefore he wins more pots.

Understanding the concept "indifference" is key here. When you get that, the paragraph above will make total sense.

true on the river since calling gets you immediately to showdown

Wait a sec, didn't you just say he'd need a 3:2 value:bluff ratio for 2x pot? if you need more value, how are you bluffing more?

Yes, I was thinking about river play only and should have written that explicitly.

For pot: 2 : 1 value/bluff ratio means 1/2 = 0.50 bluffs per value hand.
For 2 x pot: 3 : 2 value/bluff ratio means 2/3 = 0.67 bluffs per value hand.

So the bluff ratio increases. The pot-odds notation isn't about the absolute number of value/bluff hands, but the relative portions. 3 : 2 means 2 bluffs for every 3 value hands, not 2 bluffs and 3 value hands.

When the pot-odds goes towards infinity, you'll approach 1 bluff per value hand. This makes total sense, since you should never be bluffing more than 50% on the river, because your opponent is never getting worse than 1 : 1 on the call, regardless of how much you bet.

Ok that all makes sense now. I was thrown off at first when you wrote that pot meant .5 bluffs per value hand and 2x pot .67 bluffs per value hand. I thought you were saying that pot allows you to bluff 50% and 2x pot 67% but it's really more like .67bluff/1.0value+.67bluff.

And the whole reason this Q was confusing to me at first was that I hadn't realized that every bet must always have MORE VALUE than bluff. At least in my game and the game of many people, there are often cases where I know neither of us has as much value as we do bluffs. It's alien to think that I must always have more value.

It makes me wonder about a lot of things if this is really supposed to be balanced. Consider cbetting! 1/2 is common from a lot of HU players and this SHOULD mean that they are ONLY BLUFFING 25%! I think a lot of guys are bluffing closer to 50% and yet it's a standard strategy. Why would you need to balance this if the other guy is also playing a lot of random hands and JUST WON'T HIT enough? When you cbet 72o on A46r, they're still not going to call Jx even if your range is literally 100% on that flop and I doubt the mystical GTO would say to call so wide too. If they're only supposed to bluff 25% you'd probably have to be cbetting even good Q highs and checking back many gutshots etc. It suggests that so many of our betting ranges are wrong but the conclusion seems even more ridiculous.

BTW: It's not just that our opponent is never getting worse than 1:1, it's that it can never actually be 1:1 right?

The strategy discussed is valid on the river. You are generally allowed to bluff more on the flop and turn. It's a bit complicated, but it has to do with the strength of your range vs his range, and how likely it is that you will have a strong hand on the river.

I think it's worth mentioning that you at least have to also consider that a good 5-10% of the time, the villain THINKS he is bluffing, even though he has the best hand.

So for our calculation purposes, are we considering that a bluff, or a true bet?