im not shitting on your hand wapre, its just an interesting hand to discuss.

I feel that a bet is more +EV than a check (obviously since u have the nuts both plays are +EV) for reasons:

Lets say

he has a huge hand (like he had) 10% of the time, and that he bets/calls when checked to or raises if bet into.

he has a top pair/two pairish type hand 50% of the time and calls up to a 3/4 pot bet but checks if checked to.

the remaining 40% he has nothing or second pair or some crap and knows it can't be good at this point, and will bluff it 100% of the time when checked to (hmm unlikely, but this is hypothetical) with a 13 dollar bet but obviously folds to a raise.

So there are two scenarios, one in which u bet 3/4 of the pot and shove to any raise, and on where u check and shove to any bet.

The ev of a 13 dollar bet is (we'll ignore the current pot since u are always winning that)

(13*.50)+(33.70*.10)= 10.87 dollars

The ev of a check is:

(13*.40)+(33.70*.10)= 8.57 dollars AND THIS IS ASSUMING THAT HE ALWAYS BLUFFS (obv never true).