I think you could do it this way Assume 14 'games'. Assume you have a 54% chance of winning each game, your opponent 51%. SO
7 have a chance of winning of .54
7 have a chance of winning of .49.
Lets simplify this and just assume 14 'games' and you have an average chance of winning 51.5% of the time on each 'game'.
If there were 1 trial, you would win 51.5%.
With 3 trials you would win .515^3+.515^2x.485x3=52.25% of the time.
Quick guestimation give a 53% to win a 5 game match, and maybe 54% to win a 8 game match. By the time we get to 14 games, you can see we are going to be well above the 55% level.......
A random number generator, 13 trials (to avoid the tie headache)
and every number above .515000000 is a 'win' woudld be a good estimate, and we are going to get a number well above 55%....something close to 56% plus I think.......