Mark,

If the probability of something hapening once is 1/9 then you are right that the prob of three times in a row is 1/(9*9*9).

If the fair odds are 6/1 (failures/successes) , then the event would have a probabilty of 1/7 . The probabilty of the event happening three times in a row is 1/(7*7*7).

I hope that helps.

Ray Stefani