Verify random battle and capture routines against the original engine

docs/PLAN.md

@@ -235,14 +235,15 @@ their scripts and story progression are supported.
 - [x] Player switching and every non-ball battle item, with the stats screen
 - [x] The PC and boxes (catching with a full party)
 - [x] The introduction's naming and clock screens
-- [ ] Controlled-seed comparisons with the original for random-driven routines (accuracy, criticals, damage variation, capture). Damage, types, stats and experience curves are compared.
+- [x] Controlled-seed comparisons with the original for accuracy, criticals and damage variation, including random-stream consumption. Damage, types, stats and experience curves are also compared.
+- [x] Controlled-input comparisons of capture odds, success and ball shakes with the original, including random-draw counts. Hardware RNG timing and the full capture sequence remain outside this comparison.
 - [x] Acceptance: one continuous playthrough of the opening quest with save/reload (`tests/playthrough.test.ts`, driven through the world's inputs rather than the browser UI)
 
 Introduce native player, party, Pokémon, inventory, money and quest models. Read species, moves, growth curves, evolutions, encounters, trainers and items through typed ROM decoders. Define serialization/migrations before persisting new systems.
 
 Expand script calls, choices, scene state, inventory commands and native special handlers. Translate routines reached through assembly calls into explicit native services; never fall back to emulator execution in the shipping game.
 
-Meeting Mom, Elm's introduction, the starter, the aide's Potion, Route 29, Cherrygrove, Route 30's trainers, Mr. Pokémon's house, the Cherrygrove rival battle, the return to Elm, capture, the catching tutorial, the PC, the introduction's naming and clock screens, and switching and healing items in battle run now. Next: controlled-seed comparisons of the random-driven battle routines.
+Meeting Mom, Elm's introduction, the starter, the aide's Potion, Route 29, Cherrygrove, Route 30's trainers, Mr. Pokémon's house, the Cherrygrove rival battle, the return to Elm, capture, the catching tutorial, the PC, the introduction's naming and clock screens, and switching and healing items in battle run now. The opening milestone is complete within the recorded acceptance boundaries. Next: party and bag menus outside battle, MOVE PKMN W/O MAIL and evolution.
 
 Complete and validate the native battle engine: deterministic randomness, stats, move selection, accuracy/critical checks, damage, status, turn order, switching, fainting, experience, capture and rewards. Compare controlled seeds and states with the original, including integer rounding and overflow behavior.