A charity is selling $\mathrm{\backslash (}15$ raffle tickets to raise funds. The grand prize is a new laptop valued at $\mathrm{\backslash )}2,200$, the second prize is a bicycle worth $\mathrm{\backslash (}650$, and there are $12$ third prizes of $\mathrm{\backslash )}120$ gift cards. If $2,000$ tickets are sold, what is the expected value for a player who buys $1$ ticket?