[Man of Means]

If you're bringing in game theory that implies you have an opponent who recognizes that you're using mixed and not pure strategies.
Many opponents will, when you check, quickly narrow your range to something like 90%air / 10%monster and play accordingly, so your job is more to exploit them, rather than preventing them from exploiting you. i.e. check to extract bets from bluffers; bet to extract bets from chasers.

OK suppose it takes them a while, but in a game of smart players, they eventually adjust and learn that a check or bet could mean anything, but the probability of each possible event is able to be estimated. Now we bring the game theory. Recognize there are some situations where an optimal strategy will be 100% bet and 0% check.

I am intrigued by this stuff; maybe make the board bone-dry J72 rainbow or something so it's easier to quantify things.