[btspider]

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I was thinking:
1st play: urs: flop 2BB in, turn 2BB in = 4BB
2nd play: u 3bet, he caps = 4BB

So even when u give him the free card, u still get 4BB in with this play. No difference at first sight.
Now let's say an A or T falls on the turn. With the 2nd play u can now safely bet out and call/reraise when he raises.
So basically, with this play u can get more money in when ur in front. This makes the 2nd play superior IMO.
Correct me if I'm missing things

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(all hypothetically speaking in terms of him making a free card play here)
one thing this doesn't account for is the fact that he will not take a free card when he hits his draw. that's the value in the free card play for him. on the flop, my equity isn't that great if he has a flush or straight draw with an overcard to my weak top pair. so he doesn't mind too much if the flop is capped if that's his holding. on the turn, our equity will be more greatly defined. if he misses, he checks. if he catches, he makes me pay more than in scenario #1 (where i'm bet-folding the turn). unless i'm somehow check-folding a turned deuce of flushes.