Two players, Alice and Bob, will play a game. Alice chooses any integer from 1 thru 9 (inclusive; all intervals are inclusive). Bob then chooses any integer from 1 thru 9, but can’t pick the number Alice just chose. Then Alice chooses any number from 1 thru 9 but can’t pick the number Bob just chose. They go on in this fashion and keep a running tally of all the chosen numbers so far.

The first player to make this running tally reach exactly N (some positive integer) wins the game. A player can never choose a number that would make the tally be greater than N, and if a player cannot validly choose any numbers under the rules, then he/she loses the game.

To clarify, numbers can potentially be repeated during the game, but just not consecutively. There is no guarantee that Bob will get a turn (for small enough N).

If Alice and Bob each play with perfect strategies, what are the 3 smallest values of N such that Bob wins the game?