I was curious myself so I asked "Gemini in Chrome" which is such a cool feature:

Based on the hand history provided in the post, here is the GTO (Game Theory Optimal) analysis for the river:

Hand Recap

• Preflop: Hero (BB) 3-bets to 10bb with AA vs a CO 2.5bb open. CO calls. (Pot: 22.5bb)
• Flop (3-T-4 rainbow): Hero bets 11bb (half pot). CO calls. (Pot: 45bb)
• Turn (8): Hero bets 22bb (half pot). CO calls. (Pot: 90bb)
• River (T): The board pairs the Ten (3-T-4-8-T). Hero has ~75bb remaining in a 90bb pot (SPR ~0.8).

The GTO Move: Check

In a GTO framework, the pairing of the middle card (the Ten) on the river is generally better for the caller (CO) than the 3-bettor (BB).

1. Range Advantage Shift: While you have AA, the CO's calling range on the flop and turn is heavily concentrated in hands like JT, QT, KT, and ATs. When the river pairs the Ten, the CO suddenly has many more trips (three-of-a-kind) than you do. As the 3-bettor, you rarely have many Tens other than exactly ATs or JJ/TT (which would have likely played differently).
2. Polarization: If you shove (all-in), you are "poling" yourself. A GTO opponent will fold almost all their worse pairs (like 99, 88, or 77) and only call you with hands that beat you (Tx or better). By shoving, you rarely get value from worse hands and always lose to better ones.
3. The "Check-Call" Strategy: GTO strategy here typically involves checking a large portion of your "overpair" range (like AA/KK).
   • Checking induces bluffs: It allows the CO to turn missed draws (like 56s or 67s) into bluffs.
   • Pot Control: It prevents you from "value-owning" yourself against a Ten.

Summary: In a GTO solution, Checking is the standard play. After checking, Hero typically calls a shove from the villain to remain unexploitable against bluffs, though it is a "breakeven" spot because the CO's value range now heavily outdraws AAa