Bowling a 300 game

What are the odds on bowling a perfect game?

From a casual reading of random articles and posts on the internet, not too difficult.

Most lanes have an oiling pattern (more oil in the middle, less toward the edges) to funnel the ball to the pocket. This leads to more strikes, higher scores and bowlers wanting to return to the alley.

The odds on bowling a 300 game for the average bowler is 11,500 to 1 according to Golf Digest. A PBA  bowlers odds are 460 to 1.

Here is a more interesting stat:


If you have an 80% chance of throwing a strike in any given frame, your odds of a perfect game are (0.8)^12 = 6.8%.

70% strikes: (0.7)^12 = 1%
60% strikes: (0.6)^12 = 0.2%
50% strikes: (0.5)^12 = 0.02%
40% strikes: (0.4)^12 = 0.0016%
30% strikes: (0.3)^12 = 0.000053%
20% strikes: (0.2)^12 = 0.00000004%
10% strikes: (0.1)^12 = 0.000000000001%


So if I can strike on half my frames in a game (that is being generous), my odds of a perfect game are 5000 to 1? Ouch!!!

And that is 5000 to 1 on a “house” lane with oil patterns to make me look good. The oil patterns the professionals play on would make me look even more terrible.