[Dogpile]

mathematically;

Ace-Seven is about a 2.9-1 underdog vs Ace-King

Ace-Seven is about a 2.5-1 underdog vs King-King

those are the odds you would need given each hand. so long as your opponent doesn't hold AA, which would be rare since you hold 1 ace -- then you should ALWAYS call so long as you are getting 2.9-1. this is because when your oppenent has KK QQ JJ TT 99 etc..., the odds are in your FAVOR and you would be a noob for not calling if you KNEW he could have one of these hands at least some of the time. when he does have an ace with a bigger kicker, you will be 2.9-1 but you are getting 2.9-1 so this has breakeven expectation.

you could do all the math and come up with a precise number based on all the hands he COULD have but this is not really all that important. in general, so long as you hold an Ace, you are never more than a 3-1 underdog -- except against AA. but the times he actually has AA is offset at least somewhat by the times your opponent is bluffing or by the times he has a pair that is under 77 -- in which case you are not much of an underdog and again would be a noob for not calling.

you can see that math is based on what your opponent could be holding rather than what he is holding -- since you will never know what he actually is holding. you can take these concepts and come up with a number. you have to make estimates on what % of the time he is bluffing in that particular situation. I have made some calls where I felt very strongly that I was beat but the odds were close based on the size of the opt --- and magically some of the time -- your opponent is bluffing and you win that 1 big extra pot -- which can be the difference between winning and losing overall.

but in my opinion, the real crucial factor in poker is, how do you handle a bunch of bad beats that happen in a series. waiting for KK for an hour or two and then getting nailed with it by a noob is tough mentally. now what if you are dealt QQ the next hand and lose again to the same noob. now you make a straight and lose to a full house on the river. these things happen and the question is do you tilt off another stack holding AQ, a good hand on its own but a bad hand in most all-in situations.