Q2 — Alpha-Beta Mid-Flight: The Cutoff Value of N

Five evals on the current path pin the window at N — the smallest odd value ≥ 11 cuts off, and it's a β-cutoff.

The Question

Alpha-Beta is mid-flight on a MAX-root tree. Evals along the current path (root → N): 5, 17, 7, 11, 9, N — all odd, 0<n<150 < n < 15.

#QuestionOfficial answer
2.1Eval of N that induces a cutoff (pruning N's siblings)11
2.2Type of cutoffB — Beta cutoff

The Topic in 60 Seconds

Levels alternate from the MAX root: MAX(5) → MIN(17) → MAX(7) → MIN(11) → MAX(9) → N.

The window slides down the path:

  • α(MAX1)=5\alpha(\text{MAX}_1) = 5
  • β(MIN2)=17\beta(\text{MIN}_2) = 17
  • α(MAX3)=max⁡(5,7)=7\alpha(\text{MAX}_3) = \max(5, 7) = 7
  • β(MIN4)=min⁡(17,11)=11\beta(\text{MIN}_4) = \min(17, 11) = 11
  • α(MAX5)=max⁡(7,9)=9\alpha(\text{MAX}_5) = \max(7, 9) = 9

N is a child of MAX₅, whose window is (α,β)=(9,11)(\alpha, \beta) = (9, 11).

Deep-dive: Alpha-Beta Pruning.

2.1 — The cutoff value → 11

A cutoff at MAX₅ fires the moment a child's value reaches β=11\beta = 11 (equal counts!). N must satisfy:

N≥β=11,N odd,0<N<15N \ge \beta = 11, \qquad N \text{ odd}, \quad 0 < N < 15

Candidates: 11, 13. The cutoff value is the boundary — the smallest eval that triggers the prune: N = 11 ✓

2.2 — Cutoff type → B (Beta cutoff)

The cutoff happens at MAX₅ — a MAX node hitting β\beta. Per the course convention:

value reachednode typecutoff name
≥β\ge \betaMAXβ-cutoff ✓
≤α\le \alphaMINα-cutoff

→ Beta cutoff ✓

Tricks & Tips

Answers: 2.1 11 · 2.2 B (Beta cutoff)