(a) Analyze Giveaway Chess, played as follows:

(1) Captures must be made, although a player may choose which capture to make, if more than one is available.

(2) Pawns must be promoted to queens if they reach the eighth row.

(3) The kings obey the same rules of moving and capturing as in ordinary chess, but there is no such thing as "mate," and neither player loses if his king is captured.

(4) The first player to lose all of his pieces wins.

(b) Analyze Escalation Chess, where white gets 1 move, black 2, white 3, etc. If a player is in check, he must get out of check on his first move. A player may not move into check or take his opponent's king, but he can place his opponent in a "multiple check," etc. A player is checkmated if he can't get his king out of check on his first move.