The maths is a lot easier around tossing a coin, because there's only two possible events (heads or tails). But you are right - all probability is based upon (effectively) the law of averages. Maybe I'm tossing a coin looking to get a head - I could toss it 10,000 times and get nothing but...
PEDANT ALERT
If you want to add one to the number of consecutive heads then probability suggests that it'll take twice the amount of time. If you want to double the number of heads from 10 to 20 then you'll need to spend 1024 times the initial amount of time (on average).