How do they calculate the odds of winning lotteries, say 6/49? The odds of being dealt a royal straight flush?

Answer 1

It's pretty much just straightforward statistics. But even straightforward statistics can get pretty complicated.

For your typical lottery with a bunch of numbered balls, the machines are designed to make each ball equally likely of coming up. So we only need to worry about the numbers.

So if you have 49 numbers, and you want to know the chances of the six you've picked coming up, you just figure the odds for each ball and multiply them out.

Since you've picked six numbers, the chance that the first ball is one of them is 6 in 49 (there are 6 right numbers out of 49 possibilities). After that ball, you've got five numbers left and 48 balls, so the chance the second ball is one of your five is 5 in 48. And so on down to 1 in 44 for your last ball. Multiply those all together and the chances of them all coming up is 720 in 10,068,347,520... which works out to 1 in 13,986,816. Which is what is says on the back of the tickets.

It gets more complicated for the lesser prizes because there is more than one way to win them statistically. In other words, it doesn't matter whether you guess the fourth number wrong or the fifth number wrong, as long as the rest are right. To see a long explanation of all these various odds, see link 1 below.

The same kind of thing applies to cards, but again there are lots of ways to get certain kinds of hands at cards (there are four royal flushes, for example). So again this involves a pretty protracted explanation, which is linked for you in link 2.

If you really want to know all the ins and outs, I recommends studying statistics as a whole. It will give you a lot better understanding of all these things. Watch out, though, because the math requirements can be kind of rough!

Answer 2

If you must pick 6 out of 49 numbers, they do this: (49x48x47x46x45x44) / (6x5x4x3x2x1) is how many ways you can pick 6 different numbers; one over this is the probability of winning. The odds of winning are 1 to (that answer minus 1)

For a royal flush, (52x51x50x49x48)/(5x4x3x2x1) is the number of possible 5 card poker hands, and there are only 4 royal flushes, so 4 over this is the probability of a royal flush. The odds of getting it are 4 to (that number minus 4)

Answer 3

Doctor Why is right.

Here is a simple way to do the math.

The number of possible combinations of 49 things taken 6 at a time is 13983816. Any decent calculator can find 49C6. Now one ticket has a 1 in 13983816 chance of being the winning number. So, basically we are talking about a snowball's chance in hell.

He He! Don't be fooled by the notion that "you cannot win if you don't play." It's more like, "You will not win even if you do play!"

Answer 4

The secret to winning the lottery is don't pick obvious numbers the human brain always does this for some strange reason so you have to defeat your mind. Play the irish lottery like me and win more often £501 for a pound last wed i won with 5 7 25 thats the 56th time i have won on the irish since it started back in sep 1994...

Answer 5

i guess for the powerball it would be 50x49x48x47x46x50(I'm guessing that the numbers go up to 50 and that there are 6 #s drawn including power ball).
Royal flush is much harder to calculate, b/c you get 7 cards to make 5 in most forms of poker.

Answer 6

6/49
Multiply 49x48x47x46x45x44
Because numbers can't be repeated, you subtract one from each successive multiplyer

Royal straight flush
52x51x50x49x48
Same principal