The odds on that are about 2/7. That gives us a probability of almost 6/7, which is the same as the probability that the first number from the sequence is the correct one. So, all bets are good at the casino, but there’s not much probability you’ll win. For most bets such as these, the bet has a small or negligible chance of losing. For others, you’re at big risk because you can lose the entire bet. For others, you’re even more at risk because you would be losing the whole bet if you were to make a mistake. For some of those bets the odds of a perfect, or nearly perfect, match are quite high. For some bets, you could lose the entire bet if you didn’t make a mistake.
But let’s say you want to make a bet. How likely is it that you can win a big payoff in roulette?
At odds ratio 3-6, you’re unlikely to win a very big payoff (1 million bucks) in a small amount of time. A bet of 50,000 dollars in $100 bills won’t give you a big payoff at odds 3-4. For the exact same 50,000 you’d need just 10-150 to even a slight chance of winning $150,000. If you could only win $25,000, that would be $25,000 more than a little bet at odds of 3/2. And there’s a strong probability of losing that bet. To make a bet of 50,000 dollars in $100 bills would be the same as betting $100, for that same dollar. That would be a bet that’s nearly 10.5 times more likely to win you money than you are to lose. (So if you’re thinking what happens when you bet $100 in $100 bills, think of this example again.)
If you could only win $25,000 you’d need a $50,000 bet to win even that much. Just 10.5 times as likely to win a big payoff would mean that bet would be the same thing as $100,000 in $100. If you bet $50,000 you’d need a $10,000 bet to be even that much, and odds would be about 2/7 for $10,000. Even for $50,000, odds are still 2/7 against making a bet of this size.
But it might be worth making such a bet if you know you’re going to get $100,
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