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The Ace on the turn makes it more likely villian doesn't have one. Checkraising the turn costs the same as going to showdown. If he doesn't have the Ace it will be very hard for him to call. If he has a lot of outs to beat you on the river this would be a coup. If you are ahead and he calls you down then you win more. If he 3 bets the turn then you can easily fold. By just check-calling it down you're winning less when you're ahead and giving him the opportunity to hit a King or a Queen and draw out on you.