# Odds of winnnig lottery

1. Jul 21, 2010

### Gomar

I'd like to calculate the odds of winning the lottery. Each game has posted
odds, however, my calculations give different odds. Perhaps I am not doing it right, or
they use a different method, but here are my results compared to theirs:

If we use #'s 0-9, and pick one number, then odds of winning are 1 in 10. Thus, I just have to buy 10 tickets, play all numbers, and will get a winner 100%.
If 3 numbers are picked, then it's 10x10x10, or 000-999, thus 1:1000 correct?

But, in a single Take5 game, numbers cannot repeat. Key space is 39.
thus 39x38x37x36x35 = 69,090,840
To win top prize(all 5 #'s matched), their odds are 1:575,757.

http://www.nylottery.org/ny/nyStore/cgi-bin/ProdSubEV_Cat_405_SubCat_337562_NavRoot_300.htm

How is that calculated?

Pick10 has better odds, eventhough the key space is 80. Since 20 numbers are picked(1/4), and you pick 10(1/8), top prize matches 10, you have 2x chances to win. But, that's the same odds as matching 5 to 10 if key space was 40.

http://www.nylottery.org/ny/nyStore/cgi-bin/ProdSubEV_Cat_406_SubCat_337554_NavRoot_300.htm

Winning Numbers Matched Per Game: 10
Prize: $500,000 Chances of Winning on one Game Panel 1:8,911,711 Isnt it 80^10? In any case, how is that any better than playing slots in Vegas or A.C.? 1c, 5c, 25c, gives more games than$1 on above. I played 1c at a casino in Vegas, and won \$10; that's 1000%.

2. Jul 21, 2010

### CRGreathouse

You're assuming that order matters, that 12-32-11-15-02 is different from 32-12-11-15-02. The lottery commission assumes that order doesn't matter. (Redo your calculations with 5 numbers; you'll get 120 ways of choosing a ticket instead of 1.)

3. Jul 21, 2010

"You're assuming that order matters" - just to support CRGreathouse on this; it's easy to make this error (many of my students do so). A reason, one that they give as justification for their error, is "the winning numbers are always presented on tv/in print in increasing (or decreasing) order". That is true, but irrelevant to the game: it's done simply to make it easier for the audience to read/remember.

4. Jul 21, 2010

### Gomar

Ok, so are you both saying that if the winning numbers are: 34-19-2-8-27 shown on TV as: 2-8-19-27-34, I still win even if my numbers on my ticket are printed as: 19-8-34-2-27?

I saw nowhere it says order matters or not, except for Daily Numbers, so perhaps I was wrong. That explains why several people win prizes instead of just 1.
However, it would seem logical that is 1 person did indeed get the order right, only he/she should get the prize.

5. Jul 21, 2010