p.boxed
  | White plays one move, then black play twice,
  | then white plays three moves...

p.
  At the very first move of the game, white make only one move - as usual.
  However, after that and for all the game, each side must play as many moves
  as the opponent just played plus one.

p.
  If a move gives check, then the sequence stops here, but the opponent can
  still play as many moves as would be theoretically possible.
  Also, if a checkmate or stalemate situation occurs before the maximal number
  of moves are played, the game ends.
  There are no en-passant captures.

figure.diagram-container
  .diagram
    | fen:rnbqk2r/pppp2pp/4p3/8/1b1P4/4pN2/PPP1PPPP/RN1QKB1R:
  figcaption "Mate in 1"

p.
  On the diagram white mates with the sequence of 5 moves c3 Ne5 Qd3 Qf5 Qf7.
  Moves' notation is replaced by ∞ (infinity) when there are four moves
  or more to print.

h3 More information

p
  | You can start from the 
  a(href="https://en.wikipedia.org/wiki/Progressive_chess")
    | Wikipedia page
  | , which points to 
  a(href="http://users.ics.aalto.fi/tho/chess.html") this page
  |  with several commented games.