The "Pickin' Corn" Logic Puzzle

[pghnative]

While munching on some French toast with my 3-year old at the local chain-restaurant, I noticed one of the games on the back of the kid's menu. There were 10 ears of corn and two players were supposed to take turns coloring in either 1, 2 or 3 ears (the players choice). The winner is whomever colors in the last ear.

This sounded to me like the basis of a good puzzle. First, the rules:

1) 10 ears of corn
2) Each player takes a turn and can color in either 1, 2, or 3 ears
3) The players are smart enough to always color in the number of ears which maximizes their chance of wining

The puzzle:
A) For 10 ears of corn, who will win --- the player who goes first, or the player who goes second.
B) If you played this repeatedly with a random number of ears of corn (for simplicity, let's say between 1 and 100 ears, inclusive), how often would the first player win and how often would the 2nd player win.

[antoniseb]

Just walking backward, and looking at some choices the players would have to make:

-If it is your turn, and there are one two or three left, you have won.
-If it is your turn and there are exactly four left, you have lost.
-If it is your turn and there are five, six, or seven left, you can win, by leaving your opponent with four.
-If it is your turn, and there are exactly eight left, you have lost (against a smart opponent).
-If it is your turn and there are nine, ten, or eleven left, you can win by leaving your opponent with exactly eight.

With a random starting number, the first player wins 75% of the time.

[ToSeek]

What antoniseb said. ;)