Allan, Brian, and Charlie had a chess set and an afternoon with nothing to do. A chess tournament was suggested but to three towering intellects such as these, regular chess is a frivolous, juvenile pursuit. Accordingly, they set themselves to play some high-stakes horsie-push.
For those unfamiliar with the sport, the rules are as follows. The squares on a chessboard are numbered in sequence from one to sixty-four. The players each place a potato chip in a dish beside the board. These are the stakes: winner takes all. The first player (Allan, because it is his board) takes a knight and places it on any one of the first five squares. The next player, Brian, then must advance the knight at least one but no more than five squares in a straight line. If Allan's first move was to place the knight on square three, then Brian must move it to one of 4, 5, 6, 7, or 8. Charlie, who has funny looking ears and a yellow tooth, goes last following the same one-to-five squares rule as Brian. Play proceeds until a player is able to move the knight to the final square where he wins the game and three disks of salty deep fried starch.
But on this day Charlie had an objection. "It's not fair. You guys are just going to gang up on me. "
"Don't be a wimp," countered Allan.
"If you don't play fair, I'm going to take my bag of chips and go home."
This was a forceful argument. The source from which all the wagers were drawn was Charlie's bag of chips. Compromise became the rule of the day and it was agreed that Charlie could move the knight from one up to nine squares when it was his turn.
Assuming perfect co-operation between Allan and Brian and the unlikely event of best play on both sides, who will win the game?