Fermi estimate of time it takes to solve chess

Landauer limit 3e-23 J/bit in our current universe background radiation, with
$$kT\log 2, T = 3K, k = 1\times 10^{-23}J/(K\cdot bit)$$

Searching for game nodes has about 2e10 nodes/s on a GPU with 3e12 bits/s, so that gives about 100 bits/node.

The number of chess nodes needed to evaluate is about 1e43.

So we get an upper bound of 1e45 bits needed to solve chess, assuming we can't prune any nodes.

That requires 3e22 J at the Landauer limit.


But if we aren't that optimistic, we use the current 3e-19J/bit rate predicted by ITRS to be achieved by 2050,

That requires 3e26 J.

The world energy production is 5e20 J/yr

So if we are stuck on our current civilization, chess can't be solved, literally not in a million years.

A solar civilization is something humans have no problem achieving in 500 years. It only uses current physics.
The power output of the sun is about 4e26 J/s, so at that time, it takes about 1 second to solve chess.

So my prediction is: conditional on humans progressing at current technology rate and keeping interest in chess, 95% chance within 500 years.

Probability of humans progressing at current technology rate is a whole other problem (ask Future of Humanity Institute for that).

Probability of humans keeping interest in chess for 500 years is that, if humans do keep their humanity (ask FHI again), then it's a 99% chance. There's simply too many artifacts hanging around for chess to be fully forgotten.