So what's the big deal about top pair weak kicker (TPWK)? Imagine yourself in the following situation. Your hole cards are an ace and 6 off-suit and the flop comes ace–9–2 (unsuited.) Now you have the strongest possible pair, but your weak kicker makes your hand vulnerable to any other player holding an ace. At the same time, your hand is too valuable to simply fold.
What to do? As with most poker game scenarios, it's all about knowing the advantages and the limitations that any given type of holding can confer. In this case, your weak kicker means that it's seldom wise to play aggressively. Instead, it's usually correct to play defensively and give your opponents the chance to make mistakes.
Top pair weak kicker isn't necessarily a worse hand than top pair top kicker. With a strong kicker, of course, you stand a better chance against an opponent who also has the strongest pair. What a weak kicker gives you is the means and motive to catch bluffs. As a result, the most correct play with TPWK is usually to put it in your checking range. This allows the pot to grow and gives you the opportunity to take advantage of your opponents' air hands, which there will always be a certain percentage of unless you're facing complete nits.
The way to take advantage of opponents when you have TPWK is to induce them to bluff and catch them when they do. Say you're in a six-max cash game and you're dealt king–6 (hearts) in the small blind. Kickers don't come a great deal weaker than that, but you're not going to waste that ace, so you raise to 3BB. The big blind — a player you know to be aggressive — calls and then the flop comes king of spades, 9 of clubs and 4 of clubs.
With your hand, you don't want to bet multiple times and run the risk of getting involved in an insane pot, so it's correct for you to play it slow and check. This helps to control the pot, so it doesn't cost too much to get to showdown, where you'll have a decent chance of having the strongest hand unless the turn and river are disastrous. At showdown, sometimes your opponent will have the strongest hand, but sometimes they'll be holding air, in which case your high pair will take them down.
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