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The phrase the game is not worth the candle (also, and originally, the play is not worth the candle) means: the returns from an activity or undertaking do not warrant the time, money or effort required.

This phrase alludes to gambling by candlelight, a significant expense at the time the phrase was coined. If the winnings were not sufficient, then they did not warrant the cost of supplying the necessary light.

The phrase the play is not worth the candle is a loan translation from French le jeu ne vaut pas la chandelle (later also le jeu n’en vaut pas la chandelle). The English lexicographer Randle Cotgrave recorded and explained this French phrase as follows in A Dictionarie of the French and English Tongues (London: Printed by Adam Islip, 1611):

[s.v. Chandelle]:
Le ieu ne vaut pas la chandelle. It will not quit cost; there will be nothing got by him that toyles, or deales, in it.
[s.v. Ieu]:
Le ieu ne vaut pas la chandelle. The businesse will not quit cost; it is not worth the money thats spent, or paines thats taken about it.

The earliest occurrence that I have found of the phrase le jeu ne vaut pas la chandelle is from Les Adages et Proverbes de Solon de Voge. Seconde Partie. Par L’Hetropolitain (Paris: Nicolas Bonfons, 1576), by Jean Le Bon (c. 1530-c. 1583) [page 15(B)]:

Le ieu ne vaut pas la chandelle.

The first two occurrences that I have found of the play is not worth the candle confirm that this phrase is a loan translation from French le jeu ne vaut pas la chandelle—these occurrences are as follows, in chronological order:

1-: From The Essayes Or, Morall, Politike and Millitarie Discourses of Lord Michaell de Montaigne Knight of the noble Order of S^t. Michaell, and one of the Gentlemen in Ordinary of the French king, Henry the third his Chamber (London: Printed by Val. Sims for Edward Blount, 1603), by John Florio (1553-1625), English lexicographer, teacher of languages, translator and author of Italian descent [The second Booke. The seventeenth Chapter.—page 374]:

I feele my spirit more perplexed to suffer the motions of doubt, and shakings of consultation, then to be settled and resolved about any accident whatsoever, after the chaunce is once cast. Fewe passions have troubled my sleep; but of deliberations the leaste doth trouble it. Even as of high-wayes, I willingly seeke to avoyde the downe-hanging, and slipperie, and take the beaten-path, though myrie, and deepe, so I may goe no lower, and there seek I safety […]. In events, I carry my selfe man-like; in the conduct childishly. The horror of a fall doth more hurt me, than the blow. The play is not worth the candle.

The Essayes is a translation of Les Essais, by the French philosopher Michel Eyquem, Seigneur de Montaigne (1533-1592). The French text is as follows in Les Essais de Michel Seigneur de Montagne, divisez en trois livres (Lyon: François le Febure, 1595) [Livre Second. Chapitre XVI. De la presumption.—page 593]:

[Ie] sens mon esprit plus empesché à souffrir le branle, & les secousses diuerses du doute, & de la consultation, qu’à se rassoir & resoudre à quelque party que ce soit, apres que la chance est liurée. Peu de passions m’ont troublé ce sommeil, mais des deliberations, la moindre me le trouble. Tout ainsi que des chemins, i’en euite volontiers les costez pendants & glissans, & me iette dans le battu, le plus boueux & enfondrant, d’où ie ne puisse aller plus bas, & y chercher seurté […]. Aux euenemens: ie me porte virilement, en la conduite, puerilement. L’horreur de la cheute, me donne plus de fieure que le coup. Le ieu ne vaut pas la chandelle.

2-: From The Holy Court. Or the Christian Institution of Men of Quality. With Examples of those, who in Court haue flourished in Sanctity (Paris: 1626), by the English poet and translator Thomas Hawkins (died c. 1640) [Volume I. The Third Booke. Section XIX. The affection to creatures, and namely the passion of Loue.—page 328]:

Verily, all well considered, the play is not worth the candle. Must you inflict so many paines vpon your bodies, so many torments on your mind, loose so much time, make so many ill tongues talke, to please (I know not what) petty, wicked, & foundred desire which one knoweth not what it is, nor to what it tendeth?

The Holy Court is a translation of La Cour Sainte ou l’institution chrétienne des Grands (Paris: 1624), by the French Jesuit and royal confessor Nicolas Caussin (1583-1651). I have not found the 1624 edition, but the French text is as follows in the eleventh edition of La Cour Sainte (Paris: Chez Sebastien Chappelet, 1633) [Tome premier. Livre III. Section XX. L’amour des creatures.—page 513]:

Certes le tout bien considéré, le jeu n’en vaut pas la chandelle. Faut-il donner tant de peine à son corps, & tant de gênes à son esprit, perdre tant de temps, & faire parler tant de mauuaises langues, pour contenter vn ie ne sçay quel petit méchant, & morfondu desir, qu’on ne sçait ce qu’il est, ny ce qu’il pretend ?