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What he studied experimentally with the buttons and threads is know in graph theory as the "Giant component" threshold and is exactly known.

https://en.wikipedia.org/wiki/Erd%C5%91s%E2%80%93R%C3%A9nyi_...

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That's true, but I'm unaware of much work being done on the error bounds for small N (for some concept of small). I started on this during my PhD, but rapidly moved onto other problems that seemed more tractable, and never really returned to it. The results of Bollobás, Erdős, Rényi, and others, are mostly asymptotic. They do, however, seem remarkably good even on graphs of small size (under 10^6 vertices).

Those names make me wonder if mathematicians are arranged in series - Erdos, Erdós, Erdős, ...

That's very interesting adrianN, thanks!

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