A Math Problem

The house deals from a huge, essentially infinite, deck of cards composed of spades, hearts, diamonds, and clubs in equal proportions. Each person plays separately against the house. On each round, cards are dealt until a heart appears. The cards are counted. If there are an odd number, the house wins, and the player pays one dollar to the house for each card. If there are an even number, the player wins, and the house pays him $1.04 for each card. Is this a fair game?

Explain.

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