Game trees step by step: minimax, alpha-beta, three player

▲ MAX node ▼ MIN node ■ terminal (leaf) = v exact value ≥ v lower bound (MAX returned early) ≤ v upper bound (MIN returned early) struck never generated amber changed this step

Step log

What you would write at this node

Deck p.26 pseudocode, live

The highlighted line is the one this step executes.

Trace table: one row per step, the shape of a written answer

The problems, and where each number comes from

Which cut is called "alpha" and which "beta"

The course states the rule twice and the two statements attach the Greek letters to opposite ends of the same cut. Both are internally consistent. This visualiser anchors on the deck p.26 pseudocode and prints the exercise-session naming beside every cut, so a hand answer written from either reading matches.

Source	How the rule is written	Node where the loop stops	Letter naming that cut
Deck pp.25 and 26	min-value: if v ≤ α return v	a MIN node	α (inherited from a MAX ancestor)
Deck pp.25 and 26	max-value: if v ≥ β return v	a MAX node	β (inherited from a MIN ancestor)
Exercise session 5 solutions, slide 26	"Prune: Max node ≥ β"	a MIN node	β (that MIN node's own running bound)
Exercise session 5 solutions, slide 42	"Prune: Min node ≤ α"	a MAX node	α (that MAX node's own running bound)

The safe exam answer marks each cut with the inequality that produced it and defines α and β as the best value MAX or MIN can already secure on the path to the root. Then the drawing is correct under either reading.

Mistake modes: what they are and where they bite

Strict inequality (v < α and v > β instead of the deck's ≤ and ≥). Both versions are correct algorithms, so the root value never changes; only the pruning does, because a tie no longer cuts. Load deck p.27 tie tree and switch the mode on: the correct rule fires 10 ≤ α = 10 and skips the leaf 0 (2 of 3 leaves), the strict rule keeps expanding and evaluates all 3. Use the deck's non-strict version in the exam, because the answers you are compared against were produced with it.
α updated at MIN nodes (min-value writes α = max(α, v) instead of β = min(β, v)). This is the bookkeeping swap the chapter calls the most common error in this archetype, and it is not merely wasteful: on the canonical deck tree it returns root 5 instead of 3, because MIN-3 raises α to 14 off its own first child and then cuts itself at 5 ≤ 14. On quiz 2 and the constructed tree it instead loses the beta cut and evaluates one leaf too many. Each function updates only its own letter: max-value raises α, min-value lowers β, neither ever touches the other.

Game trees, one step at a time: minimax, alpha-beta, three player