In equilibrium, against PioSolver preflop ranges, 77 with diamonds raises 50% of the time and always raise calls. Basically you decide what to do already when you raise, that's why it's important not to raise 100% of these combos not to be exploited. Also in practice 4betting ranges and cbetting strategies might be different, so there's also this to keep in mind.

It's possible to use also a shove raise size on such board texture. Pocket pairs without a diamond which are an underpair to the 9 cannot raise, as they cannot profitably raise/call and the EV of the shove is way worse than ev of the call (and even worse than the ev of the small raise to fold).

AQo is a 50% frequency cold4bet BB vs SB vs CO (monker solver ranges with 5% rake cap 3€), so it's part of the GTO range. It's also a hand that isn't afraid of the shortstacker jamming, as it can comfortably cold4/call against the original raiser and cold4/fold against my shove. It's possible that certain players migh even pure cold4bet AQ here as it's not a standard dynamic, but I didn't make this assumption, I just think BB is going to have a certain frequency of these combos.

Fair enough, I suppose different ranges and sizings will dictacte whats happening. Treshold anyway

Hi, I see different cold4bet strategies being implemented here, as it's a fairly exploitative dynamic (we're 3betting a recreational player with a short stack), some player can adjust, but at 200 NL most people would stick to "default ranges" and I try not to level myself into expecting them to be able to read table dynamics. So readless I tend to assume around 50% AQoff, might be 50%, 100% or even 0% (against total nits).

99 is not a pure bluff when you raise, but becomes a decent semibluff on turns that improve our equity, it folds out some overcards and can x/fold on some runouts. It's a counterintuitive play that solvers love to do time to time.

Consider what would be the major disaster in this dynamic? Calling 100% of medium PPs that you 3betted preflop and finding yourself in tough spots postflop. Solvers randomize every street with marginal hands, not to end up always in uncomfortable scenarios in bloated pots (f.ex bluffcatching against a range full of overpairs). So 99, 88 in particular here will randomize call/folds preflop, call/fold/raises on the flop (we have some traps, so we're not towards the top of our range), and once you raise you face a marginal decision on the turn (although against some players it's a very easy exploitative decision).

It's possible to have 2 sizings, it's not easy to balance the shove here without either being imbalanced towards JJ QQ or overbluffing with overcards. In general with the multiple sizings when you bet big you either want to generate overfolds or overcalls, you don't lose much theoreitcal EV by playing a single size; I recommend to have a checking range though, that's way more relevant than sizing in these scenarios. AT 200 NL it's still common to see range betting strategies on such textures (which I don't recommend), which can struggle against flop raises (therefore this play with medium pairs gains some extra exploitative EV).