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It has been discussed before that sometimes raising PF can buy you a "free" turn card when everyone checks to you on the flop allowing you to check behind. It's also been discussed that this "free" turn card really isn't free because you've put 2SBs in PF which would've been the equivilant of calling 1SB PF and then 1SB on the flop - in effect seeing the turn card for the same price. I've recently had some thoughts on this and am curious what the board thinks...

(1) Is equity related to the size on the bet we're currently faced with or about to make? An example would be a small pocket pair (say 33) in late position (similiar to jason_t's "Post in the CO" thread). We're quite likely to have the best hand PF. So does a PF raise with an equity advantage have more value than putting in 1SB PF with an equity advantage and 1SB on the flop with a smaller equity advantage (or possible equity disadvantage) or does it not matter.

(2) If #1 is true then wouldn't it ring true that in effect our check behind on the flop actually is seeing the turn for "cheap"? It's obviously not "free" but given that 1SB PF + 1SB on the flop is less valuable than raising PF wouldn't this be the case?

Maybe this is lame semantics, hogwash or possibly has some value. I'm curious what you guys think.

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I understand what you're saying, but I think the problem here is that many times in a large field (and this is where people are talking about raising a small pp), the flop will not be checked to you anyway. Now you just threw a way a sb.