But not for any one 5-digit number. This is simply another way of saying that there are more numbers between 1 and 10000 that have unique digits than the number than have matching digits.
I once got in the biggest, stupidest online argument because I said that I like to play Powerball with the numbers 1-2-3-4-5-6, and that the guy looks at me funny even though that ticket has the same shot of winning as any other (I don’t actually play the lottery, the story was apocryphal, to make a point). One fella said my odds were “slightly less” (he didn’t say what they were), while a few other people said that must be extremely rare because they’d never SEEN a winner with those numbers. Sigh. People don’t understand probability. They think that because something is random it has to look random. As if the balls somehow now their own order and are reluctant to come up in that order. Sigh.
Incidentally, if you buy one Powerball ticket every draw (2 draws per week) for 25 years, the odds of winning the jackpot are one in 50,000 (more like 1 in 53,000, but for simplicity’s sake, I round down). It’s still a long shot (as most players know), but not as impossible as people might think. The chances of winning even in a year are less than one in 1.5 million.
People think that’s way too low, because the odds of winning are so incredibly long for one ticket, one draw (about one in 150 billion) they assume it must not change much over time. It does, dramatically. So the innumeracy cuts both ways, for lottery fans and lottery skeptics. It’s important because most lottery fans DO play week after week and don’t expect to win any one week but hope they will eventually.
I call this the Walt Dropo principle. With time, remote odds become possible, and even likely.
Also, buying two tickets per week for 25 years costs more than buying one ticket. You could buy 500 lottery tickets up front, in one drawing, and increase the odds in the same way if you were so inclined.
It’s about risk and reward. Most people don’t notice a couple of dollars a week, but they do notice $500 gone all at once. Or $2600, which is how much those lottery tickets cost over the years.
wait a tick…
IF all three numbers come up the same, then EVERY time the ball comes up, it has to say “2” or whatever.
If, on the other hand, you go with “456”, then the numbers can come up in any order… 4,5,6 or 5,6,4 or whatever. Thus, in a three-number system, the chances of a number coming up that ISN’T a multiple of 111 are higher, no?
I think in most of these Pick 3 lotteries (I haven’t played one in years) you get to choose straight or box. When choosing straight, the numbers have to come up in order. When picking box, the numbers can come up in any order.
If you choose 2-2-2 and play it straight or boxed (playing it boxed would be a waste of money if they give you that option with three identical numbers) your odds of winning are 999:1 (only one combo would work)
If you play 2-2-1 boxed, your odds of winning are 332.33:1 (three combos would work)
If you play 1-2-3 boxed, your odds of winning are 165.67:1 (six combos would work)
Post number 19.
Yes, but as I described this is how it is done for the biggest lottery (and I think most others).
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I checked the MegaMillions website. Watching one of the drawings videos makes it clear that all of the first 5 number are drawn from a single pot that contains a total of 56 unique numbers. Thus, there is no possibility of a duplicated number in the first five. Presumably, the tickets you buy reflect this by not allowing you to pick duplicates.
If this is correct, it at least ensures there is no selection scheme that will improve the chance of a particular ticket being a winner.