Gambling Trio I

Alice, Bob, and Chad all go to the casino to gamble. They start with $€a, €b,$ and $€c$, respectively, where $a,b,c > 0$ are integers. The dealer selects two of three players at each round to play against each other. Alice, Bob, and Chad are equally skilled at gambling, so all rounds are fair. The loser pays $€1$ to the winner. Find the expected number of rounds played until some person goes bankrupt when $a = 5, b = 10,$ and $c = 15$.