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I think this it tough multiway. My initial reaction is to take a stab, but then I thought a check might be better, especially since any reasonable bet is a big bet (with four people calling 120). If we bet, and get a call or raise, it makes for a tough decision. I'd like to check, see what people do, and possibly see a turn card. If you are faced with a bet by the button here, you at least get to see what the other two callers do, before deciding. If not, you get to see a turn card and re-evaluate.
However, here are some of my reasons to bet:
(1) Worse pocket pairs (55-TT) are definitely in people's calling ranges, as is A4. If you don't bet, they might, and then it's a tough spot.
(2) You can take down the pot a decent amount of the time.
(3) You have position on two of the players if you get called anywhere.
(4) There's a good chance you are ahead, but if you check you give the pot away to anyone who wants to the bet the turn. Also if you check, you allow a free A or Q to spike the turn. Even a third diamond isn't so great.
Reasons not to bet:
(1) The button has position on you. When he calls, you can't really put him on a hand (he could be floating with a K, with a 4 (or 44), with a flush draw, or even an Ad, or worse pocketpair). What will you do on the turn if he calls, since his range could be wide.
(2) You inflate an already inflated pot by betting and if called will likely face difficult decisions afterwards, or you will have to be be ok with shutting down after taking a stab at the flop. Since the pot is 500, any bet now is a significant amount of your stack.
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