Even the king can be beaten.
All the models you had rely on having a single betting round. But in poker, you often play multiple rounds. What would happen if we had 6 betting rounds instead of a single ?
Considering big enough stack sizes, the challenger can apply the following pot-sized bets strategy:
1 3 9 27 81 243
Ax B B B B B B |
4% B B B B B B | -- Core 1/8 range that will bet to the end
6% B B B B B - <- Extra range that will bet on the 5th street, but not on 6th
9% B B B B - - |
14% B B B - - - |
20% B B - - - - |-- And so on, growing the range by 50% each street
30% B - - - - - |
10% - - - - - - |
On the 6th street, calling and folding to a bet is EV equivalent (33% chance to win a 2:1 pot odds), so King effectively looses the pot when he faces a bet.
Since he will face 66% of the time a bet he will looses pot to, it is equivalent for him to call or fold on the 5th street, because calling a pot size bet with 33% equity is equivalent to folding to it.
Recursively, when facing a bet on a Nth street, since on N+1th street King will face 66% of the time a bet he will "fold" to, it is equivalent for him to fold in the Nth one. Even on first street, where Challenger bets 90% of his hands.
So at each street, there is no point calling or folding, it's all the same, all of this because of the possibility he might as well be building an enormous pot for aces.
This is an unexploitable strategy for Challenger. And we proved that it unexploitably pockets 90% of pot equity, beating the King.
The more betting rounds, the more uncomfortable it is to be face up
The important difference between a single betting round and a multiple one is that information of how much will be bet is partially removed from the caller.
This is what makes it possible to dynamically adjust the range, and be on the 1st street way above the bluffing frequency of a single street example.
Real life poker lessons
This is part of the explanation why things like continuation betting are so popular, and why stack depth matters : on a hand where the aggressor could hold the nuts, calling down on several streets is hardly profitable. Aggressive poker player always threaten to bet on several streets, yet not doing it all the time, in order to obtain the exact same effect than with this theoretical example.
Another lesson is to avoid face-up situations altogether by playing strong hands in different ways. Being able to have a nuts hand even only 1/100th of the time as the King player would be enough for him to call down all bets and actually come out ahead of the game. Protecting a weak range with nuts is the reason why Cepheus never 4-bets even if this might look profitable.