Transpositions are particularly common in the opening, where a given position may be reached by different sequences of moves.
Transposition tables are an essential part of a computer chess program.
Transpositions exist in other abstract strategy games such as shogi, Go, tic-tac-toe and Hex.
For instance, the first position can be obtained from the Queen's Gambit: But this position can also be reached from the English Opening: so the English Opening has transposed into the Queen's Gambit.
This position can be reached from the Exchange variation of the Queen's Gambit Declined: The identical position can also be reached from the Classical variation of the Nimzo-Indian Defence: Some openings are noted for their wide range of possible transpositions, for example the Catalan Opening and Sicilian Defence.