exchanging with one tile in the bag

[andy-k]

Summary

when only one tile is left in the bag, some configs (Spanish among them) allow that tile to be exchanged, and the previous PEG-1 solver declined every such config because its enumeration modeled only plays and passes. this teaches the one-in-bag solver to handle the exchange. with one tile in the bag an exchange is a one-for-one swap: return a rack tile, draw the lone bag tile, and the returned tile becomes the new fully-known one-tile bag with the opponent to move -- so the bag stays size one, the position stays fully known, and the game is still finite and exactly solvable. one_in_bag_minimax_ex now enumerates each distinct rack tile as the returned tile alongside the plays and the pass, and the decline is narrowed to only the configs that genuinely cannot be solved this way. the second commit documents all of this in lab/endgame.txt.

Changes

• solve the one-in-bag exchange as a one-for-one swap (return a rack tile, draw the lone bag tile, returned tile becomes the new one-tile bag), keeping the bag at size one and the position fully known.
• because a pass leaves both racks untouched, a run of passes resolves to the same leftover point margin (the plain solver's two-pass shortcut); an exchange changes a rack, so that shortcut no longer holds and the search tracks consecutive-pass and consecutive-zero counts, ending the game by the config's num_passes_to_end / num_zeros_to_end rule (a pass advances both counts; an exchange counts as a zero, resetting the pass count and advancing the zero count).
• memoize on (mover, both racks, bag tile, pass count, zero count); the board never changes in the bag phase so it stays out of the key.
• narrow the decline to configs where an exchange is legal but scoreless turns can never force an end, so an exchange chain need not terminate -- an honest "not solvable" instead of a wrong number.
• document the swap, the pass-collapse-but-not-exchange reasoning, the memo key, the clairvoyance assumption, and the remaining declined case in lab/endgame.txt.

Correctness

the empty-bag solver and the no-exchange path are untouched, so every English and empty-bag value is byte-identical. the result is exact given the same per-hypothesis clairvoyance the PEG enumeration already assumes (within each guessed bag tile the mover is treated as knowing it), an upper bound on what a real player can guarantee and the same assumption every pre-endgame solver makes. tests add a Spanish-style config (English tiles, one-tile exchange, short scoreless end) and check the fast search against an independent un-memoized reference for both movers and several bag tiles; a hand-checkable position where swapping a lone Q for a bag A beats passing; and that a solvable config is answered while an unsolvable one is declined.