Concept

Hotstrat — where it appears

The rule of playing in the component with the highest temperature. It is not optimal and it comes with a guarantee — a player following it ends no more than the largest temperature below the board's mean — which is why every better rule here is measured against it.

Named by 2 essays across one field — each of them below, with the objects they name alongside it.

How far down the stack the guarantee reaches. The temperatures of a sum's components, sorted largest first, with each position asked whether playing in the hottest component can lose more than the temperature sitting there. The first two never fail; the third fails on 681 sums.

A schedule instead of a number

Playing in the hottest component loses at most the largest temperature on the board — the classical guarantee, stated against one number. Sorting the temperatures and reading the guarantee one step further down gives a promise 47 per cent smaller that is never breached over 1,734 sums. Two steps down it fails 120 times, so the schedule has exactly one step of slack in it.

temperature · Strategy

Thirteen cells, thirteen scores. The rule scored in every cell of the unit interval on the designed pool, at three components.

A pool built to have an answer

The coefficient in the rule score a component by t − λa scored identically for every λ in the unit interval, because the rule reads an ordering and that pool's orderings changed at three places. A pool designed to have twelve crossings turns the interval into thirteen different rules, and all three board sizes agree on one cell: between a quarter and a third.

temperature · Coupons

Named alongside it

The objects these essays reach for when they reach for this one.

Approximation Counterexample Disjunctive sum Enumeration Mean value Strategy Temperature Bound Coupon Guarantee Heuristic Sente

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