odds of winning


As a new lottery player, I'd like to calculate the odds of winning.  Each NYLottery 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. 

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, thus you have 2x chances to win.  But, that's the same odds as matching 5 to 10 if key space was 40.

Winning Numbers Matched Per Game: 10
Prize: $500,000
Chances of Winning
on one Game Panel

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%.

Todd's avatar - Cylon 200.jpg

<Moved to Mathematics forum>

Please post in the appropriate forum ... thank you.

Raven62's avatar - binary
In response to Gomar
johnph77's avatar - avatar

The reasoning behind this is, when one picks 5 numbers out of a pool, there are 120 different ways in which those 5 numbers can be picked, ranging from 1-2-3-4-5 to 5-4-3-2-1, hence the game odds are calculated as (39x38x37x36x35)/(1x2x3x4x5). That formula yields 575,757.

Pick 10 is far more complicated, since 10 different games are being played from one draw.

savagegoose's avatar - ProfilePho
In response to Gomar

where you quote 39x38x37


that is correct if you want to get the exact order of drawn numbers, ie 1st ball drawn is a 5, it is indeed 1 in 39, but if the order isnt important then there are 5/39 odds for 1st ball. and then 4/38 for second ball. 3 of 37 balls. etc.

math is something like, 39x38x37x36x35  / 5x4x3x2x1

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