For example if the chance of a collision (transaction) 9.7x10-29 how would that compare to say winning the lottery (US powerball)
Winning it 2 days in a row? Everyday for a week? Month? 700 years?
According to Wikipedia, probability of hitting the Jackpot in US powerball is 1 in 131,278,024. So the probability of you winning each and every day for more than 20 quintillion years (or 20 million trillion years) is roughly the same as finding a collision. That's about 1.5 billion times the age of our universe. If you win every second, you'll still have to win for 234 trillion years.
Dear god, no, that's completely wrong. You did (1/131M)/(9.7E-29), when it should be log(9.7E-29)/log(1/131M) = 3.45. So it's like winning the lottery 3-4 times in a row.
Flipping a coin and getting heads 1000 times in a row? or 100000 or flipping it every 10 seconds and getting heads for 6 months?
Getting heads constantly every second for a time interval that is about a trillion times the age of the universe.
Again, no. It's like getting 93 heads in a row: log(9.7E-29)/log(0.5).
The point remains, though. That's an extremely small probability. Collisions aren't going to happen and there's no need to be concerned about it (assuming the PRNGs used are half-decent. They don't need to be good).
That's a hell of difference in math.
Not that I don't have faith in either of your calculations but can someone else help settle this?