A game is played with a six-sided, regularly numbered die. The player starts with a number equal to 0.1n, where n is an integer between 1 and 6, inclusive. On each of 20 subsequent rolls, if the number rolled times 0.1 is greater than or equal to the player's current number, the player's current number is incremented by 0.1; if the number rolled times 0.1 is less than the player's current number and is odd, the player's number is decremented by 0.1; if the number rolled times 0.1 is less than the player's current number and is even, the player's number is unaffected. If 55% of the die rolls in a particular game are even, which of the following is a possible final value of that game?
I. 0.8
II. 0.5
III. 0.1