This is only loosely related, but I thought it was interesting.
On the topic of sensible moves, let's say there are, on average, 5 reasonable options per move. So now:
About 10^1.4 for a pair of moves ->
28 pairs of moves per game ->
10^39 reasonable games.
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28 because I discovered about 30% of moves per game involve little to no consideration e.g. an obvious recapture, or moving out of check, and 70% of 40 is 28 (ok this is also an estimate, but anyway, just going with it)
... now I spent some time trying to relate number of games to number of unique positions. Some of my attempts at estimating resulted in nonsense numbers, so I obviously don't have good intuition for this step, but after a few initial stabs at it, my guess is you can knock off about 9-10 zeros, so maybe 10^30 sensible positions.
#1919
The proof game I gave is the shortest. Your trolling 'proof game' is not the shortest.
Well, see if you can come up with shortest proof games for any of the final positions in the ICCF tournament you mentioned earlier in the thread, then if they contains any blunders we can get rid of some more legal positions - yippee!
Btw., hate to mention it, but, if you're considering solving the competition rules game, your shortest proof game doesn't reach the correct position. Check the FENs.