When Al suggests "double or nothing" to Judge Smails the judge accepts. That means that the Judge and Doctor didn't owe anything and shouldn't have had to pay up. That's what Double or nothing means. We can assume that Al simply meant to say "let's double the bet" but he didn't word it incorrectly.
Um, double or nothing means "we are playing for double the money, or nothing at all". I'm not sure what it means where you are from, but EVERYWHERE i have been to, it means just that.
"Double or nothing" is actually what you say after you've lost a bet. Basically, you're asking for one shot to break even; if you pull it off you owe them nothing, but if you fail you owe them double the original wager.
Smails was a moron for taking that bet anyways. They were in position where the worst that could happen was a push if he makes the putt. It was a somewhat long putt, but it wasn't so crazy that a good golfer doesn't stand a decent chance of making it. I always chalked it up to the pressure getting to Smails too much, forcing him to stupidly accept the amended bet.
That's what they were going for, but it doesn't make any sense either. Maybe if it was a double or nothing bet on Smails making the putt himself, his ego would have forced him to take the bet, but there was no reason to take that bet. The whole ending ruined the movie for me. I get that Smails is supposed to be the villain, but the Dangerfield character wasn't any better and was worse in many ways, but the movie expects us to be on his side for some reason.