(a) Find the optimal strategy for the game of Poker Coins, the rules of which are:

(1) A player throws N coins; he then puts one or more aside and rethrows the rest.

(2) This throwing is repeated until he no longer has any coins to throw (i.e., all the coins have been put aside).

(3) Each of the other players takes a turn at throwing N coins, according to rules 1 and 2; the winners are those players with the maximum number of heads

(b) Analyze Poker Dice, which is played according to the same rules except that N dice are thrown and those players with the highest score are the winners.