The climber
Hill climbing is pure exploitation: from wherever you stand, take the step that improves, stop when nothing does. It’s fast, cheap, and honest — and it inherits the landscape’s cruelty. Its success rate is exactly the size of the summit’s basin: drop climbers at random here and only about a quarter of them are born lucky.
Tap to drop climbers; the tally tells the truth.
The jumper
Random search is pure exploration: ignore the terrain, throw darts, keep the best. It can never be trapped — and never learns. Early darts improve fast; then the returns collapse, because blind luck must now beat its own best throw. Watch the best-so-far curve bend flat.
Throw darts and watch the diminishing returns.
Climb from everywhere
Combine them and the arithmetic turns kind. One climb succeeds with probability p; R independent restarts fail only if every one fails — success becomes 1 − (1 − p)R, racing toward certainty. Restart hill climbing is the unglamorous baseline that serious methods must beat.
Raise the restarts; watch predicted and actual agree.
The annealer
Simulated annealing walks the landscape with a temperature: while hot it accepts even downhill moves, wandering across valleys it has no business crossing; as it cools, its standards rise until only improvement will do. Cool slowly and it anneals onto the summit; quench it and it freezes into whatever hill it happened to be on — exactly like the metal the name comes from.
Race a slow cool against a quench.
The tournament
Same landscape, same evaluation budget, three strategies racing live: the restart climber, the blind jumper, the annealer. Then change the terrain and watch the rankings betray them — on one smooth hill the climber is untouchable; on rugged ground it drowns in false peaks while the annealer keeps its head. There is no best strategy, only a best strategy for a landscape — the no-free-lunch truth every optimizer lives with.