If you are in a situation where you have been dealt an unsuited King/7, and the flop delivers a K/4/2, under most circumstances you would be sitting pretty, and you can internally give yourself a little high five. Of course if one of your opponents has a cat that ate the canary smile on their face, and begins acting like a bully during the next betting round, this means one of two things. They are either trying to use the King on the board to facilitate a bluff or they are holding one of the three remaining Kings.
You can never rule out the bluff, but let's assume for the moment that your opponent is on the up and up. It is unlikely that they have a pair of Kings in their hand, but you can probably assume by their body language and aggression that they have a single King sitting in their hand. This means that your hopes are all pinned on that seven in your hand - that your kicker beats their kicker.
If your kicker was a 2 or an Ace, the decision would be simple. A seven is a little trickier because it sits somewhere in the middle of the deck with five cards of less value than it and seven cards of greater value than it. Statistically speaking, chances are that your opponent has your 7 beat with whatever their second card is, but you're not beat by much.
So you have two hopes here. You can hang in there and take your chances with the next two cards. There is always the opportunity that the turn and river can deliver you a tie or a victory. There is also the chance that your kicker has them beat. Your chances of this are a little less than 50/50, but if you are a risk taker, you might like those odds.
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