Glad you liked it

Sorry I missed this the first time through. If we make 3bet 3bb -> 9bb and a 4bet is to 20bb then UTG will be risking 17 to win 13.5 so we can't fold more than 56% of the time. I think a reasonable approximation then is to have roughly a 1.25:1 bluff:value ratio. Generally I think the best hands to add are suited aces or possibly some 98s type hands which can be nice for a bit of board coverage.

With more and more people opening closer to 20% UTG and calling a decent amount vs a 3bet I think a more linear, wider range can make a lot of sense too.

So there are two things that happen when you bet bigger.
1. You can bluff more. This is the commonly cited reason for bigger being better. But your opponent calls such that these bluffs are breakeven, so even though you bluff more you don't make any additional EV from bluffing. You bluff more so that he can't exploit you by folding to much, which brings us to part 2.
2. Your opponent has to put in more money on average the larger you bet to keep your bluffs breakeven. Vs a 1/2 pot bet, he has to call 66% of the time, 1/2 * .66 = 0.33. Vs a pot size bet he has to call 50% of the time, 1 * 0.5 = 0.5.

Since he's putting in more money on average, your value hands make more money and your bluffs breakeven still, so your EV increases.

Thanks for your quick reply Steve. I already knew your two bullets, but I don't see how that relate to a very polarized range? I can only see it apply if the polarized range has a larger EV than a more "merged" range - is this the case? I should probably have modelled that before I asked the question, actually, but it sounds like you know the answer.

Edit: So, I just read your last paragraph again. I think I see the connection now.

Well those points are really only true of a polarized range. If some/all of your value bets are not the nuts (ie if your opponent has some chunk of stronger hands) then bigger is not necessarily better because the hands that beat you become a larger and larger part of his calling range as you bet bigger and bigger.

Polarized ranges perform better than merged ranges (eg 20 combos of half nuts/half air is waaay better than 20 combos of hands each with 50% equity) but unfortunately in holdem situations where your range is truly polarized to nuts/air just don't happen all that often. However, when your range is very polarized, you bet big because that maximizes your EV (because of the points in my last post)

Yeah I just confused myself about some preflop scenaries I was thinking about where I've seen Ben bet polarized. I was thinking about the EV of our whole range, but it's obviously the value part we're looking at because of the neutral EV while bluffing-"assumption".

Thanks Steve.