Let $ E_1 $ be the expected winnings if a $ \heartsuit $ or $ \diamondsuit $ 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 $\clubsuit$ is drawn and $E_3$ the expected winnings if a $\spadesuit$ is drawn. Since drawing a $\clubsuit$ doubles the winnings and drawing a $\spadesuit$ 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.