I've found that Dota2 has a very good implementation for multi-monitor behavior. When you're in a menu or waiting to find a game in queue, you can move your mou

I've found that Dota2 has a very good implementation for multi-monitor behavior. When you're in a menu or waiting to find a game in queue, you can move your mouse off to the second monitor, and click on something and the game will minimize. When you're in game, the game captures the cursor, and doesn't let it move to the second screen unless you alt-tab out of the game window.