Integer Game Notation is a way to represent the full state of any perfect information game. This method maps all nodes in the game tree to an integer. An example is shown for chess and could be useful in opening book or database applications.

- Set
`IGN`

=0,`PRODUCT`

=1 and the game to its opening position - Let
`MOVES`

equal an ordered list of possible moves from this position `IGN`

+=`PRODUCT`

* the ordinal of the chosen move in`MOVES`

(one-indexed)`PRODUCT`

*= the cardinality of`MOVES`

- If there are more moves, goto 2

- Set game to its opening position,
`IGN`

is given - Let
`MOVES`

equal an ordered list of possible moves from this position - If
`IGN`

= 0 and the cardinality of`MOVES`

is greater than 1, then this algorithm ends `IGN`

% the cardinality of`MOVES`

is the current move (zero wraps around to the last element of`MOVES`

)`IGN`

/= the cardinality of`MOVES`

(round down)- Goto 2

To encode and decode, moves must be ordered. For chess, I have chosen this way to order moves:

- Origin rank
- Origin file
- Destination rank
- Destination file
- Promotion piece: B, N, Q, R

convert PGN to IGN, convert IGN to PGN

[Event "F/S Return Match"] [Site "Belgrade, Serbia JUG"] [Date "1992.11.04"] [Round "29"] [White "Fischer, Robert J."] [Black "Spassky, Boris V."] [Result "1/2-1/2"] 1.e4 e5 2.Nf3 Nc6 3.Bb5 {This opening is called the Ruy Lopez.} 3...a6 4.Ba4 Nf6 5.O-O Be7 6.Re1 b5 7.Bb3 d6 8.c3 O-O 9.h3 Nb8 10.d4 Nbd7 11.c4 c6 12.cxb5 axb5 13.Nc3 Bb7 14.Bg5 b4 15.Nb1 h6 16.Bh4 c5 17.dxe5 Nxe4 18.Bxe7 Qxe7 19.exd6 Qf6 20.Nbd2 Nxd6 21.Nc4 Nxc4 22.Bxc4 Nb6 23.Ne5 Rae8 24.Bxf7+ Rxf7 25.Nxf7 Rxe1+ 26.Qxe1 Kxf7 27.Qe3 Qg5 28.Qxg5 hxg5 29.b3 Ke6 30.a3 Kd6 31.axb4 cxb4 32.Ra5 Nd5 33.f3 Bc8 34.Kf2 Bf5 35.Ra7 g6 36.Ra6+ Kc5 37.Ke1 Nf4 38.g3 Nxh3 39.Kd2 Kb5 40.Rd6 Kc5 41.Ra6 Nf2 42.g4 Bd3 43.Re6 1/2-1/2

Result: 7194381939026059815816432728404500838835011451049668943765896734611284670867176530570061223664286778997380554654077775346194 (412 bits)

1.f3 e5 2.g4 Qh4#

Result: 143395 (18 bits)

- Generic algorithm applies to any perfect information, finite/discrete game
- Easy database search with the mod operator, e.g. find all games that open with 1. f3 e5 by searching for entries with IGN % 400 = 195

- IGN does not distinguish a game that stops before a forced move versus after. If this is important to you, you would add "resign" as a valid move for every step. (Unforced game endings are always distinguishable.)
- This algorithm maintains the entire game path, so two games that reach an identical state, (e.g.
`1. e4 e5 2. d4 d5`

and`1. d4 d5 2. e4 e5`

) are encoded differently.