Learn German: Kalkulieren müsste man den Stoß, um das Spiel zu gewinnen. - One would have to calculate the stroke in order to win the game.

In German, you can move an infinitive or past participle to Position 1 to strongly emphasize it or create a contrast. Here, it stresses the action itself: Calculating is what you would have to do to the stroke, rather than just guessing. The conjugated modal verb müsste stays in Position 2.

Normally, infinitives go at the end of a main clause. Does anything replace Kalkulieren there?

No, the final position of the main clause just remains empty. The standard word order would be Man müsste den Stoß kalkulieren, but fronting the verb simply extracts it and moves it to Position 1, leaving the rest of the sentence intact.

Why use müsste instead of muss?

müsste is the Konjunktiv II (Subjunctive II) form of müssen. It softens the statement from a hard fact ('one has to') to a hypothetical or conditional necessity ('one would have to').

Why do we use an um ... zu clause here instead of damit?

You use an infinitive clause with um ... zu when the subject of the main clause and the subordinate clause are the same. Here, the indefinite man (one) is both the person who must calculate the stroke and the person who wins the game. If the subjects were different, you would have to use a fully conjugated damit clause.