Re: 10/20 giving up really easy
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Your hand is still too strong to give up on. Betting is problematic because a king is likely to check raise and price you out of your straight draw. Meanwhile your opponent likely doesn't have many outs. So checking behind the turn seems like a viable option.
However, your hand is too strong to fold on the river (assuming a blank), because you will be getting 6:1 on a call. Your opponent may have a K, an A, or QJ, but he could also have another hand with a T in it, a busted draw like Q9 or J9, or a small-medium pocket pair.
Remember that the key to limit HE is generally not to find laydowns but rather to control the size of the pot with your weakish hands. Here you can use your position to do just this and make a long-term profit by investing one more bet to try to win this 5 BB pot.
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I, too, like the check behind, call the river with this hand. You have something to show down that will be good often enough to justify 1 more bet going in. A turn bet will win some percentage of the time, but in those cases you are likely to snap off a bluff occasionally for more profit on the river. Betting the turn, of course, opens you to a raise that you would have to fold to without a very good read. Show this thing down.
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