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The basic idea behind a larger 3b size is to set a higher price for villain to make you play postflop OOP. When you raise to $1.1 here, you make it only 0.8x pot. If you want to make it 1x pot from the BB, you raise to $1.25 and for 1.2x pot, you raise to $1.4.
Your profits are less OOP than IP, so you somewhat compensate for that by building a bigger pot from the get go. Note that obviously this is assuming that you are profitable when you play 3b pots OOP. If you loose on average when you play 3b pots OOP, then you are only loosing more when you make the pot bigger.
You can't really say that this is only for fold equity, because your sizing should be the same whether you are bluffing or value betting otherwise what you are doing becomes transparent pretty quickly. However assuming villains are more likely to call 3-bets when they are IP, then yes, when you 3b-bluff you should bet more to improve your fold equity.
So in short:
- when you value-3b, you bet more OOP to boost your profits which are diminished by the lack of position
- when you 3b-bluff, you bet more OOP to boost your fold equity which is diminished by the fact that villain is more likely to call IP.
Also, just like postflop, when you value 3b, you have to bet enough to deny your opponents odds of drawing out on you. For example, if you 3b a PP, you want to deny two higher cards the odds of flopping a pair or better. For example, AK will beat QQ OTF about 28% of the time, so when you 3b QQ, assuming villain has lots of AK's in his calling range, you should offer him odds significantly worse than 28%.
You could say "but if I am more profitable IP, do I not want to build an even bigger pot IP?". Well yeah, it would be nice and you can probably do that against fish, but reasonably good players do not like to flat 3-bets OOP, so you should give them a better price to entice them to do so, and when you bluff there is a better chance that they fold OOP so you can get away with betting less for an equivalent fold equity.
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