I used to think the 'Stop and Go' was laughably bad. I was wrong. Strong tourney players have BB flatting ranges 10bb deep. (And there's the usual array of mixed strategies).
Optimal short-stack play is - in it own way - just as confusing and counter-intuitive as deep-stack play. You can't "solve" pre-flop just by thinking about it.

This. This right here.

I don't know what's with this obsession with going balls deep pre-flop. You have a deep stack, play multiple streets.

Who cares wtf the EV of your 5/6/7-bet ship vs villain's range is. There's five more cards to the hand. ****ing play poker.

It's not arbitrary. The possible number of hands is finite. At some point, a raising range will represent exactly AA and only AA and a competent player will only have AA in that spot. Since poker is a game of partial information where deception has value, you don't necessarily want to play your hand in a way that it is face up.

Why would a competent player have no bluffs remaining at that point?

Let's say that optimal strategy requires having a certain ratio of value hands and bluffs, with the number of value hands decreasing with each raise. Since we have a finite number of possible hands (unlike the [0,1] game in The Mathematics of Poker), that breaks down when we whittle our value hands down to AA. You could only decrease you value range by flatting with some aces and you might be down to only raising with one combination of aces with a fraction of a hand as a bluffing range, if you want to hold to the ratio. So, it doesn't quite work under extreme conditions. You are left with the choices of being willing to raise an infinite number of times with AA plus some bluffs, never raising at some point, or letting your bluffs approach zero so you only raise with AA.

I am no game theory expert, but that is my guess as to how the game theory approach would look at this. (Well, actually, I think the game theory expert would look at this as a multi-street game and work on the river range, which dictates turn range, which dictates flop range, which dictates preflop range....) In practice, most players will 4bet and 5bet bluff less than game theory optimal strategy would suggest (sometimes because exploitative strategy is more profitable than optimal strategy), so it will take fewer raises to reach the point where they have only aces in their range.

Each time there is a re-raise, you fold some of the bluffs that didn't work... until your range is nuts and nuts only. (To use a ludicrous post-flop example, imagine there is a 7-bet on the river, 300bb deep. Do you ever 8-bet bluff, when it's basically impossible for villain to 7-bet/fold anything?)

FWIW, when I was subscribed to Snowie, it rarely 5-bet or 6-bet with anything outside of of KK+/AK (and pretty much had no 5-bet/folding range). In many spots, kings are a flat of the 3-bet 100bb deep, so 5-bet/6-bet ranges at 150bb+ are extremely small, and often it's just AA for pure value, and AKs because of the blockers and equity against a similar stack-off range. HU 200bb bots also seem to 4b/call kings in my (limited) experience.
Mixing is also appropriate, so in some cases the 5-bet is KK+/AK, but none of those hands 5-bet at 100% frequency, and are in fact flatted occasionally to strengthen the 3b/call or 4b/call ranges.

Because he has run out of hands to use to balance against his AA.

That is the reason I was thinking deeper stack sizes would mean we would want to open wider and 3 bet wider, etc, in the first place; so we would not run out of hands to use to balance our AA jams.

If we played a toy game where we raise or fold only (and so does villain) at each decision point we would need more hands in our starting range to get to a point where we could jam AA for value and have something left over to balance against the AA.
I still think that's the case but I'm starting to wonder if that wouldn't hold in a real game situation????

If this is true, then for sufficiently deep stacks, would this mean you have to open for a raise with 100% of starting hands?

Actually, it's not your raising range it that limits you, it's your opponents calling range.

If you are deep enough that after a number of reraises your opponents raising range would be only AA and a few bluffs, then you wouldn't want to reraise them because they would call profitable with AA and fold their bluffs if they maintain a balanced ratio of bluffs to value hands.

Nice post. I really like this way of looking at it. It's not about playing a certain percentage of hands at certain stack depths. Instead, we get dealt two cards and we play em one hand at a time. When it's my turn preflop in an unopened pot, the effective stack does have an influence on which hands I play as I noted earlier. However, the percentage of hands that I'm playing isn't a goal to aspire to play up to. Instead the percentage of hands I'm playing is a result of opening with profitable hands preflop. Make profitable decisions and let the frequencies fall where they may.

OK, that actually makes some sense.
Suprised (well, more like embarrassed) that I missed this..
well said. Yup. Ok, so this at a minimum would mean that the following actually could be true without necessarily meaning we should have more hands for deeper stacks in-game.
1) We would open wider for deeper stacks in a raise/fold only toy game
2) having hands in our ranges that want to call at each decision point could not require us to open LESS hands or even get to each decision points with less hands.

Both of those facts can actually be true without it being = we should open more hands the deeper we are, if only because our opponent having flat calls in his range could change the game dramatically in ways that are not immediately obvious (at least to me).

Thank you.