Interesting. If I do the math correctly then there is a ~76 % probability that the conclusion "P(getting a girl) is less than 10 %" is correct. (One sided statistical test with n=74, H0=0.1, c=6)... still 24 % chance that it was an coincidence.

I tried 22 single games and got 0 girls (during an event). That gives already a probability of over 90 % that the chance of getting a girl is indeed smaller than 10 %. (n=22, H0=0.1, c=1)

I guess saving your kobans is the way to go.