It's 15 to call 47.50. 3.18 -1 or so.

Indeed, from a theory of poker standpoint where your opponent knows he has the worst hand. In that case, he needs to have enough outs to improve to best 24% of the time.

However, if you're him, and he has a solid hand, there is a good chance he is allready ahead. If you assume that the rest of the money goes into the pot,
he has to call 28.75 to win 61.25. He needs to win this 32% of the time.

Say he has AK... here he has 6 partial outs to improve to TPTK and some percent chance it's best allready. So he has to fold this with only a 7% chance of improving... unless the chance his opponent is bluffing (with a worse hand) is greater then 25%. (we know he's drawing dead here, of course)

If he has something like AA he probably has to call here. We know he will only very rarely win here... but the range of hands his opponent could have compares very favorably to his needed 32% win rate. KK it goes down (since AA beats him now and KK only ties), and QQ it gets worse. Any big pair though is tough to fold when you're getting better then 2-1 to win and you know the board is all undercards! It all depends on the range of hands you put your opponent on.

In the hand in question... if your opponent thinks (wrongly) that his pair might be good if he DOES improve, then even a min raise (10 to call, 42.50 in the pot) doesn't improve his odds enough even if he counts all 6 as full outs. So decreasing the size of your raise shouldn't have your opponent calling if he doesn't have a pair... and pushing him in should still have him calling with a lot of overpairs, so you definantly didn't play too fast. He just didn't have a good enough hand to call down with.

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-You may not know this, but poker is a game of incomplete information.