Startling bowling result

[BruceZ]

Where I bowl there is a jackpot which you win by making 9 strikes in 9 particular frames. My friend was considering entering the jackpot, so I asked him how many strikes he averages per game. He said 6. This would be out of 11 tries since you average 2 tries in the final frame. So his probability of striking is 6/11, and his chance of winning the jackpot is (6/11)^9 = 235-1. Since it costs $5 to enter the jackpot, it would need to be over $1175 to enter, and it is sometimes over this amount.

Then I calculated how big it needed to be for me to enter. I average 4 strikes per game, so the odds of me winning the jackpot are (4/11)^9 = 8996 to 1! The jackpot would have to be over 45 grand for me to enter as opposed to just $1175 for my friend, and that's just with a difference of 2 strikes per game.