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Re A3o.
In my experience of low stakes SNGs, 3 Bets are relatively rare and usually mean they have the goods. Usually, the smaller the 3Bet the better the hand. You can see the thinking: I have KK, I know I should build the pot but I don't want to scare the raiser off, so I will make my 3Bet small. Please note that I said usually. I have seen small 3 Bets made with AJo and 88, so I know there are exceptions to every rule. There are also a couple of people who obviously read somewhere that 3 Bet bluffing is good and so do this with 86s. But you can usually spot these, because they 3 Bet much more than most.
Having said that, A3o is way behind even a wide 3 Bettor's range. It's crushed versus the AJo and 88, I mentioned. It's even only just the better side of a coin flip against 86s. I don't want to make out that raising A3o in late postion is terrible. It's good, if the blinds are tight and passive. What is terrible is playing A3o and then getting drawn further into the hand by calling a 3bet or playing a big pot when an A hits the flop.
Speaking of getting drawn in, I would not bet out on that flop. I think the villain's most likely holding is QQ+ and if that's right, he's going to be ecstatic if you bet. Even if he has AK or even 88, the pot is big and the flop is pretty dry, so if you bet he might well disbelieve you hit a J and call your bet. After that, you are both committed and so neither of you can really fold and I think the chances are very high that A3o will turn out to be the worst hand.
64s
If you though that you were on the bubble, then calling his shove is a worse play. As I said, calling would be correct in a cash game, but is not here because its a SNG and you need to pay the "ICM tax". ie the closer to the money, the bigger the edge you need in a hand. On the bubble, the ICM tax is going to be bigger, so you would need an even bigger hand/odds to call there. If you think you should have called to eliminate him, then that is wrong. Its not your job to eliminate players, it's to make profitable plays. One thing that tilts me is when a short stacked villain who has played one hand throughout the SNG shoves and gets called by a couple of players obviously calling to eliminate him. His queens crush their hands and he triples up. A couple of hands later I shove, he calls with kings and I'm busto. There's no justice.
I have put this hand into SNG Wiz, which is a program which analyses when it is profitable to shove or call in SNGs. If you are planning to play a lot of SNGs, then you should think about getting it. It has a 45(?) day free trial. Anyway, if the short stack is pushing 50% of his hands, it was actually profitable to call with 64s, but only slightly, so Wiz recommended a fold. If the short stack was pushing any two cards then calling with 64s is profitable.
This is where you need reads to be able to guess at villains ranges. In low stakes, villains tend to shove too tight, so in the absence of any other info, I would guess that the villain is probably pushing any pair, Ace, broadway or decent suited connector in this spot. That's about 30%, so Wiz recommends a folding 64s, though again it is very slightly +EV to call. So as I said originally, its close.
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