Alpha-Beta at the Stalls

Replaying the stall duel with a running best-guarantee shows a provably irrelevant leaf going unread.

Examine Fountain fully: 4, 9, 6 — guarantee 4. Your running assurance is now 4: anything else must beat it. Enter Gate: first report, 8 — no verdict. Second report, 2 — stop. The rival will take that 2 or worse-for-you, so Gate's guarantee is at most 2, and 2 cannot beat 4. Gate's third report — the glittering 11 — is never read: pruned, unexamined, provably irrelevant. Market Hall is examined: 7, 5, 10 — guarantee 5, which beats 4 and wins the choice. Same answer as the full scoring, one leaf cheaper: eight of nine reports read, and on deep trees with good ordering the savings compound from one leaf to most of the tree.