Let x be the %-age you are looking for. Then (100-x) will be your losing percentage, and...
the money you win in the long run minus the money you lose in the long run equals zero, ie.
110x - 100(100-x) = 0
Solving for x gives:
110x - 10000 +100x = 0
210x = 10000
x = 10000/210 = 47.62