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The difference is that at any step point, his algorithm can only chose from a maximum (less when near edges) of 84 squares -- a 13 x 13 diamond pattern -- surrounding his current position.
Your code, by virtue of not tracing a path, but simply picking any random square from the full set, has the full 10,000 choices each time.
To correctly calculate his odds, you would need to factor in the odds of one or more of those 84 possibilities being contaminated, and then 1:84 chance that he will pick one of them.
Ie. His odds of contamination are less, because he has less chance of reaching all of the cells. Or rather, any given contaminated cell.
With the rise and rise of 'Social' network sites: 'Computers are making people easier to use everyday'
Examine what is said, not who speaks -- Silence betokens consent -- Love the truth but pardon error.
"Science is about questioning the status quo. Questioning authority".
In the absence of evidence, opinion is indistinguishable from prejudice.