Compare minimax and alpha-beta on the same tree, then change the move order.
Back terminal utilities up through alternating MAX and MIN turns. Then switch on alpha-beta pruning to see which subtrees can be skipped without changing the exact root decision.
Model boundary: finite deterministic two-player zero-sum perfect-information trees. Pruned nodes remain visible as part of the problem definition but are labeled not evaluated by the algorithm.
The tree and terminal utilities are visible, but no search event has been revealed.
Core question: When do alpha and beta prove that a sibling cannot matter?
Run and watch: Apply the first-prune scenario, step until α ≥ β, and identify the nodes not evaluated.
Pick a scenario, predict what should happen, then apply it and compare the result with your prediction.
Use the pruning or move-order Guided Challenge. Predict first, reveal the trace, then justify why skipped work cannot change the exact minimax answer.
Use the existing Guided Challenge for the run/reveal step. Responses stay in this browser unless you deliberately copy or print them.
Minimax assumes both players choose optimally: MAX keeps the largest backed-up value and MIN keeps the smallest. Alpha-beta returns the same answer while skipping branches that current bounds prove cannot matter.
A game tree lists legal continuations. Terminal utilities are part of the problem definition, not values invented by minimax.
This lab assumes a finite, deterministic, two-player, zero-sum, perfect-information game and optimal play by both sides.
At a MAX node, keep the largest returned child value. At a MIN node, keep the smallest. Repeating that rule gives the root minimax value and an optimal move.
A high leaf is not enough: the opposing player chooses among the leaves available on their turn.
Alpha is the best value MAX can already guarantee along the current path. Beta is the best value MIN can already guarantee.
Once alpha is at least beta, remaining siblings cannot improve the decision for the player whose ancestor already has the stronger option.
A pruned node still exists in the game tree. The algorithm merely avoids evaluating it because the current bounds prove it cannot affect the root choice.
Move ordering changes when strong bounds appear. It can reduce work dramatically, but it cannot change the exact minimax result on the same fixed tree.
Large games require depth limits, heuristic evaluation, transposition tables, iterative deepening, and other search engineering.
Games with chance, hidden information, simultaneous moves, more than two players, or non-zero-sum payoffs need different models.
Curriculum: Game trees, terminal utility, alternating MAX/MIN backup, optimal play, alpha and beta bounds, safe cutoffs, and move ordering.
Misconceptions to test: MAX always chooses the largest visible leaf; pruning changes the answer; pruned nodes do not exist; alpha-beta always prunes; move ordering changes the game value.
Use Tab and Shift+Tab to move through controls. Use Enter or Space on buttons and arrow keys on sliders or select controls.
Read the current model state in the applet’s text-state panel.
Important results are available as text and do not depend only on color or motion. This does not replace a full human assistive-technology audit.
Predict first, lock the prediction, then reveal the deterministic mechanism.