Hello,

I know it all depends on the villain, but assuming an "average" villain, what is the best stack-to-pot ratio to play AK?

A high SPR (20 or more) is bad, because you could be outdrawn.
A very low SPR (e.g. 0.3) is bad, because you cannot extract value if you hit flop.

So there must be an optimal SPR between 0 and 20 for playing AK. Anyone has any idea what it is?

I'm not really sure if there is an "optimal" SPR for specific hands because each situation is different. Certain SPRs can make typical hand strengths easier/harder to play in general, but maximising profit will depend on all the usual factors (ranges, board texture, positions, tendencies, stackdepth etc).

Put it it this way, if I have AK on A72 and the SPR is 1, I'm pretty happy. If the SPR is 13, then I might not gain much additional EV, despite having more money available, but I'm not bemoaning my luck. If the flop is AAA, however, then I'd prefer the SPR to be as high as possible. I suppose that the "ideal" flop SPR will depend on how close your hand is to the nuts, and how often it's likely to stay that way as the pot keeps getting bigger.

You could run some sims with a solver if you have the chance, but I have a feeling that the EV for AK on dryish Axx/Kxx flops wouldn't change much with SPRs between 2 and 20.

*Pauses to experiment*

I just had a quick look at what Snowie thinks for AK UTG vs BB on a boring A72r in a 5bb single-raised pot.
At SPR=1, the EV was 5.48bb.
At SPR=13, the EV was higher, at 5.58bb.
At SPR=20 (100bb behind), EV had declined a little to 5.36bb.
At SPR=40 (200bb), EV surprisingly jumped back up to 5.44bb.

All of those EV figures are pretty close.

According to my quick tests with Snowie (which is not perfect) for that particular spot, the EV seems to peak (at 5.86bb) when the SPR is 3.
From personal experience, I think that an SPR of about 3.50 seems just about ideal for AK on a dry Axx, but it's certainly not a disaster if the SPR is 15 or so.

On other board textures (especially wetter boards) the EV probably varies quite a lot more with differing stackdepths, but I don't know to what extent. I might look at this another time.

For me its easier to think of the situation in terms of starting bb size. I think 40bb is probably best against average opponents. The bread and butter of playing AK is just flopping an ace or a king on a dryish board, betting every street for value and getting called every street by a weaker ace or king. Getting raised is not really something you want, so there isn't much point in having a stack deeper than what's needed for just 1 bet each street.

Also at 40bb you're almost always fine with stacking off pre. At 100bb its overrated.