When you see the odds presented as 30:1 or 3:1 that's actually just showing the payout for a winning bet, not the likelihood of that team winning. 30:1 doesn't mean that the team is 30x more likely to win, it means that if you bet on that team and they win you will receive $30 for every dollar you bet.

On a machine that pays 31-for-1, the machine keeps your bet when you make it, but pays 31 units on a win  still a total of 31 on your side after a win. So 31-for-1 is the same as 30-to-1, 16-for-1 is the same as 15-to-1, 10-for-1 is the same as 9-to-1, and so on.