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.