In a new paper published in Psychological Science, psychologists show that the odds of getting a winning combination—especially the last one—can never be less than 1 in 100.
This means that the odds of winning this particular round are roughly the same as if you were betting 100 cents on a coin flip. That doesn’t sound so bad until you take into account that the odds of winning a hand of 10 roulette spins, as I did, is 1 in 3.2 million.
Why is that? The math doesn’t add up.
To understand, imagine that we pick the random numbers and spin them until we get a combination of numbers and outcomes that meet the odds of winning at least once in every 100 tries—roughly 1 in 1,000. (The odds of a winning hand of 10 flips is 1 in 8.5 million.) The probability that these odds will all meet in the first 100 spins is also 1 in 500.
On average, the 1 in 100 odds of winning the lottery are about 100 times greater than the 1 in 500 odds of winning a lottery hand of 10 spins. But if you’re really lucky, you might get a lucky combination of numbers. In some cases, you will be lucky enough to get a combination that meets the odds of winning this specific game. But that’s a lot more rare than rolling the dice and then flipping a coin.
We can use the previous example to show the absurdity of the odds. If 1 in 100 odds equals 1 in 3.2 million, that means that you should be more likely to have a chance to win the lottery lottery than to win the coin toss. How is that possible? Because all the coin flips have equal chances of matching each other’s odds, and then the 1 in the 100 odds of winning is multiplied by 3.2 million to get the chance of seeing either 3 or 1 of those outcomes.
The exact process is the same for roulette: Each roll gives an expected output, with the outcomes ranging from 1 through 9 for any given combination of numbers.
So if I win the game, I’ll be about as consistent as a coin flipping, except that, theoretically, I’ll always be twice as likely to get three outcomes—four if I have a combination of numbers that meets the odds of winning at least once—instead of only twice as likely to get one.
“We should always be twice as likely to see at least a 3 if a roll has an expected value greater than
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