Party game: Even Odd

This party game is suitable for small to medium crowds with audience (e.g. at hosted dinners/gatherings). Invite two teams of two to the front. They will be the players of the game; the rest get to watch until a winner is declared (usually 5 minutes or so).

The game proceeds in rounds. Each round, the team leader will shout either "Even" or "Odd". Immediately, all players must either raise both their hands, raise just one hand, or keep both hands down. Then, count the number of hands in the air. If the number of hands is same as the team leader's call, that team gets to remove one hand from the game. The team that manages to remove all hands first wins the game.

Now, you might be complaining that the game is pure luck and a bit of reflexes, but I must disagree! There is a strategy which significantly increases the odds of winning. Can you figure it out?