Legal chess positions versus IPv6 addresses

Based on recent minimal research, it seems like there are probably more legal chess positions than there are addresses in Internet Protocol version 6 (IPv6). Wikipedia explains that there are 3.4 x 10^38 IPv6 addresses, and explains that Claude Shannon estimated the chess figure at 10^120, though other estimates exist.

If there are more chess positions than IPv6 addresses, it means you could devise an algorithm to represent the address of an internet-connected machine using IPv6 as a legal chess position, and that there would be enough chess positions to represent every possible IPv6 address. For instance, you could devise a set of rules that would produce an exhaustive set of chess positions, then generate the whole set and start numbering them using IPv6 addresses. You would start with a legally set up board, then assign IPv6 addresses to the positions that can be achieved through every possible move. Then, keep going until your rules have produced the gigantic complete set of possible legal chess positions. It would be like a rainbow table.

That would be a neat way to express the addresses in a human-readable form. It also means that you could translate the address of any device into a playable chess game, though a lot of them would be very lopsided, in terms of which colour has the advantage.

Author: Milan

In the spring of 2005, I graduated from the University of British Columbia with a degree in International Relations and a general focus in the area of environmental politics. Between 2005 and 2007 I completed an M.Phil in IR at Wadham College, Oxford. I worked for five years for the Canadian federal government, including completing the Accelerated Economist Training Program, and then completed a PhD in Political Science at the University of Toronto in 2023. View all posts by Milan