How much should a gambler stake if he receives $\$30$ if there are four or more spades among the six cards drawn? Being new to this chapter I chanced upon the following question which left me scratching my head as I do not know how to approach this question.

A game is played such that a gambler pays a stake to draw six cards
  from one pack, without replacement, and receives $30 if there are four
  or more spades among the six drawn. Otherwise, he receives nothing.
  What is a fair stake price for him to pay ?

The ans is $0.86$
I have tried ways to reach this ans however to no avail, help me please?
I have a feeling that this $E(X) = \int_{- \infty}^{\infty} x P(X= x)$ formula is used to solve this question.

Fair stake price = $n\cdot p=30\cdot\frac{\binom{13}{4}\cdot\binom{39}{2}+\binom{13}{5}\cdot\binom{39}{1}+\binom{13}{6}\cdot\binom{39}{0}}{\binom{52}{6}}\approx 0.86$, where $p$ - probability to draw at least 4 spades.
