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What if he's got a hand like AK? If you only bet $3 then he's getting the correct price to call. You need to at least bet enough to make it incorrect for him to draw out on you if you're ahead.
Edit: Too timid, yeah.

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You typically call getting 3:1 with nothing but overcards? Good luck with that.

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http://twodimes.net/h/?z=1353460
pokenum -h js jd - ah kc -- 8c 8h 4s
Holdem Hi: 990 enumerated boards containing 4s 8c 8h
cards win %win lose %lose tie %tie EV
Js Jd 752 75.96 238 24.04 0 0.00 0.760
Kc Ah 238 24.04 752 75.96 0 0.00 0.240

Typically I don't, but if he knew what you had, it would be a correct call.

I just prefer to make a little larger bet in this spot, typically about $5, which is also what I'd bet if I had an 8.

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You realize you can't count on him giving you the turn AND river for $3 right?