One way to look at this story of a $1 million (yes, $1,000,000) win on a $5 bet is that that’s a great game to be playing! How cool is that? The correct way to be looking at it is that it’s a terrible bet, a right stinker.
What matters is not the amount that can be won on a single bet. It’s the combination of how likely is it that the bet is won alongside how much you win if it does. It’s payout times odds that is, not just payout multiples. Once we grasp this rather important point about all games of chance – and of skill in fact – then we can evaluate the story:
A man playing poker at an Atlantic City casino won $1 million on a $5 bet. The man, identified only as Harold M. from Lakewood, made the three-card poker “6 Card Bonus” bet Saturday afternoon at the Borgata Hotel Casino. He then hit a royal straight flush of diamonds, a hand that overcame 20-million-to-1 odds.
I’ve no idea of the rules of that particular game but then we don’t need to know them in order to be able to evaluate the bet.
He got a 200,000 times his stake payout. Is that great or what? Nope, it’s not great, it’s terrible. For the odds against there being a payout at all were 20,000,000 to one. The winnings were two orders of magnitude out. In a fair game the payout would have been $100,000,000.
Note what is meant by fair here. The casino didn’t fiddle anything, their odds are known in advance, there’s nothing unfair about what they’re offering. But there’s another meaning of fair here, which is “according to the odds”. A fair bet, by this definition, is one where the payout is equal to the odds times the stake. A 20 million to one shot with a $5 stake is thus a fair bet at a $100 million payout.
A sensible bet is one where the payout is higher than that odds times stake. These are rare in casino games and about the only time you’ll manage it is card counting at blackjack. You’ll also be politely asked to leave the casino if you do it. They’re there to make a profit after all. It does happen with lotteries sometimes. The UK lottery odds are about 14 million to one, so a payout of more than £14 million is a sensible bet to take. This does happen occasionally.
All of which rather explains why casinos are a nicely profitable little business really, doesn’t it?