Ahh, now it makes sense. So one confirm on deposit should always be there. Wouldn't the site somehow realize it's a double spend before the first transaction of a withdraw? Wouldn't they realize that the previous deposit he made and lost with, was a double-spend hence freezing his account from withdraws until it has been checked? Or does that just bring too much hassle when people could just wait for their one deposit confirmation.

Then again some people would say it would be in the dice site's self interest to allow instant deposits (so players don't have too much time to think if they should or should not continue playing) but that's a different discussion.