Let's assume there is a set out there. Let's also assume that we will get stacks in on the turn against whoever has the set, but no other money is going in. Let's also forget about backdoor flush outs for a second.
We will miss on the turn and fold, let's say 41/45 times. We will hit and dodge a board pair, let's say with probability (4/45)(34/44) = 34/495. We will hit and see the board pair, let's say with probability (4/45)(10/44) = 2/99.
So we lose $20 41/45 of the time: -$18.22
We lose $218 2/99 of the time: -$4.40
We win $318 34/495 of the time: +$21.84
So given all of these assumptions, our EV is -$0.78.
This is an extremely pessimistic estimate and it has us almost breaking even.
Here's why this is pessimistic:
1) We ignored the backdoor outs. If we hit a diamond or an 8 and are allowed to see a cheap river, we could win stacks with a backdoor flush or straight.
2) We have position, both absolute and relative. There are two other people who could put money in the pot here. If the preflop raiser bet/folds the turn and we stack off against the other guy, that increases the positive term while not changing the negative terms. (Even better if they both stack off!)
3) We don't lose to a boat as often as 10/44 of the times we hit. First of all, since this pot is multiway, it's likely that there are blockers to a board pair, which is good for us (the large negative term drops and the positive term increases at the same time). Second, if we hit the 4
, then the 6
is not one of villain's redraw outs. (Granted, this is an extreme fringe case.)
It's hard to take all of this into account in precise calculations, but given how close it is without considering these factors, all of which only help us, I think it's fair to say this is a +EV call, though it does appear to be close because of how shallow the effective stacks are.