Science Forums 2

[CraigD]

Aw, c’mon – after 38 hours, only 1 play?

I was hoping to play the first game until someone won, then try a couple of variation – more difficult pin layouts, and a game where your inputs were subjected to random “inaccuracy” factors – but if nobody plays, none of that’s go’na happen!

Just to assuage any suspicions that the game’s not winnable, here’re the results of a program I ran that played the game for every x value from 1.605 to 5.755 in .01 steps, and every (h,v) from (0,1) to (.86, .510294032886922949) in steps .01 for h (keeping the ball’s speed a constant 1). Excluding plays that removed 0 pins: 7.5% removed 1 pin, 10.7% 2, 8.9% 3, 13.3% 4, 14.9% 5, 14.6% 6, 14.2% 7, 9.7% 8, 5.2% 9, and 0.9% all 10 pins.

If you’d like, you can change the mass of the ball from its given value of 3 times that of each pin. According to the data I gathered via the above program, the way to go with changing the ball mass is not, as you might intuitively expect, increasing it, but decreasing it to about 1.75. For a ball with mass 1.75, the results are: 9.9% removed 1 pin, 7.6% 2, 8.8% 3, 13.0% 4, 13.5% 5, 17.6% 6, 15.0% 7, 9.1% 8, 4.0% 9 and 1.7% all 10 pins.