I wouldn't want to go around betting without a pair to test some theory. You are going to be wearing a straw hat to the Christmas tree.

We were talking about how to play A,K and whether to bet it after the flop if you miss the flop.

My ideas are based part on math and part on what I think works. With A,K you pair the flop 1/3 of the time. You can make a profit on that because you have built a pot with a raise. It is best to go for a free card if you miss on the flop. If I was behind one timid man, I might make a small wager if he looked incredibly sad.

Betting A,K is not really in the range of what I call semi bluffs. You only have 6 outs. The hand you are drawing at is only a pair. It is not like you were striking at the nut straight for what will be a monster pot. You really are not in any kind of shape to be building up a large pot when you are drawing at one pair and maybe dead.

In chess, bridge, and poker you plan you future moves, bids, and bets in advance. What happens if you do bet A,K into someone who raises or someone who calls?
Now another trash card comes off, or a dangerous hand making card hops off, or the best card you can hope for hops off. You are not in good shape with any of these.
If you check A,K on the flop, your opponent will often give you one or even two free cards with a wired pair or second button. He could bet you out and some players will bet you out of the pot.

A,K may win showdown if there is no post flop betting. My plan for a sequence of moves with A,K includes raise and check if you do not hit. Surrender to a pot size bet. If I hit it on the flop or fourth, I'll be betting it. However, if fifth street rolls around and I have only one pair, I'm not betting into anyone and probably won't bet after them unless I have a top read going on their hole cards which would have to be A,J or A,Q.

If I am behind one caller and catch certain turns, I''ll bet A,K sometimes on a steal. If I catch a call, I'm quite as a church mouse pissing on cotton the rest of the hand.