Answer & explanation
The official answer, with Fermi’s reasoning step by step.
Answer & explanation
Official answer
197,281
games
How to estimate it
Fermi’s official “Napkin math”
Chess openings start narrow. White has 20 legal first moves (16 pawn moves, 4 knight moves), and Black answers with 20 of its own, so that is 400 games after just one move each. Assume the second move each keeps about the same branching, another factor of 400.
- First move each (White × Black)
- 20 × 20 = 400
- Second move each, similar branching
- × 400
- 400 × 400
- ≈ 160,000
Rounded assumptions may give a slightly different estimate. The official answer above is the game’s reference value.
Source calculation & reference
- Legal first moves for White
- 20
- Legal games after both play once
- 400
- After White's second move
- 8,902
- After Black's second move
- 197,281
Reference cited by Fermi: Chess Programming Wiki's Perft move-generator validation results (perft(4) = 197,281), also reproduced in Wikipedia's Shannon number article
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