[sourbeaver]

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On point one, value bet the river, in that situation, with AJ, J still high card on board. How big of a bet do you make on the river?

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The generic answer is : you bet as much as you think your opponent will call. Put yourself in his spot, imagine the hand he's holding, and imagine what kind of bet you would call in that spot. If it's obvious he's on a busted draw, let him take a shot at a bluff like fim suggested. If you figure he's on second-pair on TP-weak-kick, make an almost insulting bet, such that he'll be compelled to call, or even raise in some situations.

Let's say the pot is 10, you could bet 1-3.
Pot is 20, bet 2-4.

These are numbers I generally use and get called a nice amount of time with dead hands.