Two pair vs a river overbet — call or fold?

The full reasoning

Calling is right, and by a lot. The price: 12bb to call into 32bb once you call, so you need to be good about 38% of the time. The assumed overbetting range is 44, 77, 22, AK, KQ, A9s, 86s, 65s, T8s, J8s and 53s: sets, top pairs and busted straight draws, with A9s as a second pair. Computed against that range, K♣ 9♣ wins ~81% by exact count. That is more than twice the price, so the call is worth about +13.87bb, and folding gives it all away. Why so high? An overbet is polarized: strong hands and bluffs with little in between. The strong hands here are three sets, 44, 77 and 22, and there are few combinations of them. The bluffs are every missed straight draw, and two pair beats all of them. Top pair with a strong kicker, the AK and KQ, bets this way too and loses to you, as does A9s. So only a small slice of the range beats you, and the price is cheap for how often you win. That is the concept: an overbet is polarized, and two pair beats the bluffs and the medium hands.