jmc

Let $E_1$ be the expected winnings if a $♡$ or $♢$ is drawn. Since the probability that any particular rank is drawn is the same for any rank, the expected value is simply the average all the winnings for each rank, so $$E_1=\frac{1}{13}(\$1+\$2+\cdots +\$10+(3\times \$20))=\$\frac{115}{13}.$$Let $E_2$ be the expected winnings if a $♣$ is drawn and $E_3$ the expected winnings if a $♠$ is drawn. Since drawing a $♣$ doubles the winnings and drawing a $♠$ triples the winnings, $E_2=2E_1$ and $E_3=3E_1$. Since there is an equal chance drawing each of the suits, we can average their expected winnings to find the overall expected winnings. Therefore the expected winnings are $$E=\frac{1}{4}(E_1+E_1+E_2+E_3)=\frac{1}{4}(7E_1)=\$\frac{805}{52},$$or about \boxed{\15.48}$, which is the fair price to pay to play the game.