[sixhigh]

That's because the approach you use assumes the game (all 10 trials at once) has a normal distribution (with an ev of 6 and an sd of 4.67) of winners where in fact it's a binomial distribution. Now the binomial distribution converges to a normal distribution for a large number of trials, but 10 just isn't large enough.
If this were game normal distributed it would be possible (although unlikely) to get values bigger than 10 or smaller than 0.