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How many cushions will a pool ball rebound off before falling in a pocket on a completely frictionless pool table?

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This is a small experiment that arose from a fairly stupid discussion
I had while playing pool during lunch one day. We were hammering the 
white ball around the table and came to wondering, if the table were 
frictionless such that the ball would keep rebounding elastically off
the cushions forever and you hit the ball in a random direction, how 
many cushions would you rebound off before the ball ended up in a pocket?

The table, ball and pockets are to EPA standards, although the middle
pockets protrude into the table too much because it was easier to
write that way.

The median turns out to be 10 cushions. There you go. 

You'll need pygame to run it:
sudo apt-get install python-pygame

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