White moves first, but then Black gets to move twice. Then White gets to move three times in a row, then Black four times in a row, then White five times in a row, and so on, with continuing escalation as the game proceeds. You cannot move your King through a check or play another move while your King is in check. If, in the middle of your sequence, you give check, you lose any remaining moves in your sequence and your opponent moves and enjoys his full sequence.
Here are a few observations:
1. Games will end rather quickly.
2. 1.d4 appears to be a stronger opening move than 1.e4; can you see why? For one thing, White is threatening to start his next threesome with Bg5, for another his King has some breathing space against some possible checks on f2. (If Black plays d5 and Nf6 in turn, consider the counter of e4, e5, and Bb5+. With the next “fivesome” of White he is threatening to advance pawns to e6 and g6 and take on f7. Qd3 and then Qf5 is another possible threat sequence.)
3. It is often good to give check on the last move of your sequence, if only to tie the hands of your opponent for one move.
4. Sometimes a more exposed King gives you a stronger position, because then the approach toward your King creates a check and ends the sequence of your opponent. This also means that pawn promotion should not always be to a Queen.
“Acceleration chess” is my phrase. And for the dedicated foursome there is “accelerated Bughouse.”
I thank several individuals at Jane St. Capital for relevant observations on this game plus a bit of play.