Dear Sirs/Madams,

in a hypothetical hand, villain limps and get four callers, including hero with AKo. After some betting, calling, and folding, villain and hero (equal stacks) are left looking at a board of K4242r. Villain shoves. Hero has half his stack left to call with.

Hero's hand blocks three combos of AA, three combos of KK, seven combos of AK, some combos of K4 and K2. The board itself blocks several combos of 22, 44, 42, 4x, and 2x. Thus hero should call because it is very unlikely that villain has anything of value here.

At the same time, hero and villain remain in this hand exactly because they both happen to connect with this board in some way. The board has 'selected' these players. Hero should fold, fearing that trips, quads, or boats has beat his two pair KK44.

Which is it?

A question as hypothetical as this belongs in the theory section where the theory monsters can get into all sorts of bambozzling hypotheses.

There is no practical answer to the question, because the hand is patently unrealistic (in real terms), and there are gazillion unknowns.

Personally, I don't know what the theoretical answer is but if it were cash, I'd call against many villains and if it were a tourney I'd consider ICM factors & villain tendencies.

It may be your underlying question is simply "how important are blockers"; my own view on that is relative to other factors, they are not the most important thing, but always some sort of consideration.

This decision is just a hand-reading calculation.

But because it's been framed as a weird hypothetical question which doesn't provide enough information to do any hand reading, it's not really answerable. I will say we should probably discount AA here a lot for example and I also don't know WTF hero is doing overlimping AKo.

Blockers aren't some kind of weird magical concept. They reduce combos that's all. So put your opponent on a range, reduce that range based on action, repeat. Now you are facing a shove, it's a mathematical question. How much equity do you need? How much equity do you have?

On this board I would be more scared by a loose player than a tight player.

In limped pots, blocking effects are of minimal importance, because the ranges start off so much wider. In multiway pots that get to the river, the winning hand will typically be much stronger than top pair. Villain can have a lot of 4x and 2x hands, even though there are two of each on the board.
I'm guessing that hero limped AK and wonders how someone made a full house when hero blocks top pair. If he'd raised pre, villain folds random stuff like A4, K4s, Q4s, J4s, 64s, 54s etc etc.

Thanks for trying to answer. I totally get that multiple factors affect the read of any hand. It was a stupid example, my bad. Let me re-phrase: on average, should we put less weight to blockers from the board than to blockers in our hole cards?

The idea being that the board has a tendency to select those who play it.

I don't think it makes much sense to even ask the question. There's no "average", as such. It's simply the case that if a particular card rank is on the board, then it removes some combos from a person's range (the 'card removal effect' is just a fact), but if they are betting and raising on that board, they are representing that they did indeed connect with it.

e.g. On a K72 rainbow board, not many hands connect, because there are no flush or straight draws, and only 9 combos of sets, often no two pairs combos (unless you're playing the 72 game, or villains limp in with K2o), and people don't play many hands with a 7 or a 2 in them, but if two players are building a big pot, then it's likely that they have at least a decent king.

Card removal simply exists. Blockers tend to be used strategically when considering make bluffs or for bluff-catching, especially on the river, when ranges have condensed more.
You can say for sure that "there aren't many playable combos containing a 4" if the board is K444, but it doesn't mean it's impossible for villain to have quads. You have to take the action sequence into consideration too.