First of all, you aren't controlling a mob of monsters against all the other mobs. You are in the stands, watching the fight, excitedly betting on one monster or another to stay up or go down. There are eight monsters, ranging from the Dragon and Titan down to the Ranger and Troll. Each round of play eliminates one monster, until there are only three monsters left. Whoever winds up betting on the most survivors wins.
Monsters fight each other by means of cards.
If you have no Dragon cards but have a Troll 1, let's say, you can always play that on the Troll to see that he gets killed first. Once every monster has a card on it, and one of the cards is lower than all the others, the lowest-carded monster is eliminated. So a good bit of the strategy of Titan involves finding ways to make sure someone other than your favorite winds up short. One trick when your monster is low man on the totem pole is not to let the round end. Say you're betting on the Dragon, but he's got a Dragon 2 showing and everyone else has 4s and 5s, except the Troll, who has no card on him.