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Can my hand win?
It's that simple :P
No - the question is whether to bluff or not, which is just math:
If the pot it 50, and a bet of 10 will win it once in 4 times, it's a good play. Reads are clearly important here.
Yes, I have the uber hand and I want to go broke with it:
This is easy, bet. The exception is if you think your opponent has nothing (maybe he has played like he is on a draw, and they all missed). Often it is better to check (OOP) and give them a chance to bluff.
Yes, I have a hand that might win, but it's not great:
Now we must decide whether to bet or check. The weaker your hand is, the more you should check. Not just because your hand is weak, but because if you bet, you will often not be called unless beat, where as if you check, your opponent may bet hands YOU beat (see my hand has no chance to win, above) and you can make a little more.
This is where we are here. We have position, and a marginal hand. It's important to note opp called the turn with A555 board. Yes, there is a flush draw out, but even fish can typically fold a flush draw with 555 on the board. So we assume opp either has a PP, or the A, or the 5. Or he may be making a weird call with nothing hoping to bluff you out on the end. But on the river, we can throw out nothing, since he checked. Also, if he has nothing, you can now check and win the pot. If he has nothing, he will not call your bet. If he has 22-44, he MAY call. As the PPs go up, he is more likely to call. If he has the A or the 5, he will call all day. There is only one range, 22-44, where the river push is a good result. And I think you'll agree 22-44 are the least likely holdings.
The other option to consider is whether opp will fold a better hand. At first glance, it seems like opp might fold 77-KK here to the river push. However, the fact that this is a blind war and (again) the fact that he called on the A555 board make that very unlikely.
The irony of this hand is that the reason Hop's opponent played this hand so 'well' is that Hop repped the A nicely. Opp assumes (correctly) that if someone has an A on that board, they are never going to stop betting, and is able to check quads on the river, knowing the A will lead.
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