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I have heard of Shannon's number (10^120) which is the supposed number of possible chess games computed in the 1950s. But Shannon's estimate is criticised for including illegal moves. What is a truer estimate under the given parameter

  1. no illegal positions
  2. FIDE rules of 3 fold rep and 50 moves are in force
  3. we start from the regular starting position
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Peruse this link. Also see link for possible duplicate.

Sum-up of first link:

  • Longest game under FIDE rules: 8848.5 (Fabel)
  • Maximum mobility number: 218 moves
  • Shannon's number, assuming 40 (full) moves, 30 moves per ply, ignoring FIDE rules and duplicates: 10^120
  • Upper bound: 10^34082
  • Realistic lower bound (Monte Carlo): 10^29241
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  • Noted, with thanks. Your attached link is very helpful.
    – anti - Marshall
    Commented Feb 29 at 8:04
  • Also Shannon's number is an estimate of the number of positions possible after 40 ply or 40 moves?
    – anti - Marshall
    Commented Feb 29 at 8:21
  • I doubt that there are that many positions taking longer than either (although the retro genre knows many exceptions - but I bet they are rare).
    – Hauke Reddmann
    Commented Feb 29 at 19:27
  • The answer might be better if it at least summarized the link's estimate on the answer to the question. Links can disappear.
    – D M
    Commented Mar 1 at 5:20
  • The gap between the upper bound and lower bound is HUGE.
    – Zuriel
    Commented Mar 2 at 3:25

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