Re: Flush Draw Check, Bet, or Check/ Raise
With a flush-draw, you need two callers for a bet to be +EV. Even then, it's only very slightly +EV (1.9:1 to hit the flush by the river) so any play where there's a good chance someone will fold is -EV.
If you check-raise, there's a good chance that MP1 will fold, leaving you with one-caller. That's definitely -EV since you'd be paying 2 bets at 1:1 and you need to be getting 2:1.
If you bet out, there's some chance MP1 will call and then MP3 raises. That's your best case, and it's only slightly +EV. There's also a chance MP1 will fold and MP3 will call, which is -EV, and there's a chance MP1 will fold and MP3 will raise, which is very -EV.
I'd check-call. This also makes it easier for you to check-raise later if you do hit your hand.
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