[milesdyson]

i check. his relevant hand range is Ax, Kx, 4x. ignore QT/QJ for simplicity because they aren't many hand combos and they likely fold anyway.

if you don't discount the hands (like AQs or 42o) at all then the breakdown is 43%:28.5%:28.5% Ax:Kx:4x because two Ks and two 4s are visible. i've never looked at it this way but i think it's right.

so undiscounted he can only have a worse K ~29% of the time. so in order to get to about 55% for his Kx hands, you have to discount Ax and 4x quite a bit. you should discount Ax a little because of the flop and river action (not a ton though because this board is bad for action w/ A5), and you should discount 4x a bit more because of preflop and turn action. so let's make some assumptions.

discount Ax by 30% and 4x by 60%, Kx becomes 41%.

discount Ax by 50% and 4x by 80%, Kx becomes 51%.

Kx is not becoming enough of his range even when we very significantly discount his better hands, so i think it's safe to say it's a check.