Average number of stones randomly placed on a 19×19 goban so that 2 are adjacent

This time what caught my attention was the average number of stones ramdomly placed on a 19×19 goban required such that 2 stones are adjacent.

So I’ve written a python program (https://github.com/arbolis/pythonstuff/blob/master/goproblem_random/gorandom_1.py) and a R script for the plotting part (https://github.com/arbolis/personalscripts/blob/master/goban_random.R) to solve the problem numerically. It turns out that the number is around 13.1 which, in my opinion, is counter intuitive in the sense that most go players expect that number to be much higher (scarce are the go players who predicted a number below 30).

Anyway here is a summary of the data after 1,000,000 simulations of placing stones on a 19×19 goban until 2 stones are adjacent:

Min. 1st Qu.  Median    Mean 3rd Qu.    Max.
2.00    8.00   12.00   12.97   17.00   49.00

And there comes a bar plot:bar-plot-go-19x19

I find that plot interesting and the summary of the data interesting.

Now I could get similar data for the 8×8 chessboard. Out of my memory the number of pieces randomly placed on a chessboard until 2 are adjacent is around 6.1. I expect a similar histogram than the one for the game of go somehow, except that the width of the distribution should be much smaller.


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