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it all adds up to checking and then calling the river being the smartest play. the weird spot is when he checks the river to you again. would he ever c/r there?

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Losing 1/2 the pot 20% of the time is a pretty big deal here and requires an opponent who would bluff with a pretty high frequency / checkraise a high number of diamonds that he wouldn't 3bet on the flop. The preflop+flop doesn't lead me to believe that he'll have Ad too often here so I think a bet is better. When checkraised, given the fact that you have 4 outs and your opponent will be pure bluffing and may give up sometimes, I'd call and fold to a river bet UI.

The fact that Alex never believes Schneids has anything probably compounds this since I'd guess he's somewhat more likely to check-call with hands that Q9 crushes here, but I'm not sure how it effects his likelihood to checkraise bluff/checkraise a more liberal range of flushes.

Anyway, I'd betcall and fold the river, like I said, mostly because of how much that chopdraw is worth (~.55BB or so) and the combo of implied odds+stopping bluffs. If forced to chose between bet/fold (getting 8.5:1, I think) and check-behind and call, I suppose I'd tend to check behind and call though. I just wouldn't opt to make that play in this spot without knowing a lot more about how Alexsem tends to play the flop with a big diamond+overs or how he plays the turn with hands like 8x8d.

Rob