[W. Deranged]

Lil'

I'm no game theory expert either, but I figure I'd give a try at reasoning through one application of this idea.

Let's say an opponent has AJo in middle position. Let's say you raise with some reasonably standard range UTG and UTG+1: AA-88, AK-AJo, ATs, KQ-KJs, KQo or something like that... it's not all that important. Notice that there are certain hands that AJ is well behind, certain that it's racing and/or close to, and certain that its ahead of.

Let's say that your limping range is a little bit broader: You bring in some extra hands that villain is ahead of or racing: 77-55, QJs, J10s or something like that.

Now, it is possible that a smart opponent will overtime deduce that AJ is on average ahead against the range of hands you limp with but behind the range of average hands you'll raise with. It will therefore be correct whenever he is first to act behind you to fold when you raise and to raise when you limp.

Now, obviously poker is a multi-handed game and this is a very specific situation, but you see the idea.

What game theory will tell us is that if you "drop" enough of the big broadway cards down into the limping range from the strict raising range, you can make it such that villain will have a much harder time making such easy decisions. If you structured your ranges correctly, it would be possible to find a frequency with which to raise/limp AK and AQ such that an opponent with AJ would always be dead even to be ahead/behind you. (This is not possible with any range of raising hands; the problem does not always have a solution in the given space defined by the range of hands)

My intuition is that when this is aggregated across all opponents and all hands they may hold, occassionally dropping AK and AQ down into the "limping" range will be a game theoretical improvement over simply always raising them, against intelligent and watchful opponenents.

If you were to take a game theory approach, you are absolutely correct (IMO) that doing it randomly will be the best way. You would need to use some combo of things to get exact frequencies, though. Given the 16 possible combos of AK you could certainly randomize to units of about 6% though.