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Isn't this a standard spot for a free showdown raise on the turn? We're committed to showing down, we may be ahead, and we've got lots of outs if behind. Yeah it sucks getting 3-bet, but he's in the BB, so he could easily have a crappy spade and go passive if raised.

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Please explain why raising has a better expectation than calling.

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Because we're already planning on calling down the river. At least, I am. Raising for a free showdown has us putting in the same amount of bets if he does or doesn't have the flush. In the unlikely event we get 3-bet, we lose one bet but get back a portion of it for those times we fill up on the river. If we're 3-bet on the turn or donked on the river we can fold our set, and occasionally, raising the turn here might induce villain to fold out a superweak flush.