Lifetime odds of winning?

[Icewynd]

A question came up as part of another discussion that I thought was worth discussing on its own:

If you buy 100 tickets for a lotto draw, you are reducing your odds of winning the jackpot for that draw from 1:13,983,816 to 100:13,983,816. If you then buy 100 tickets for the next draw have you reduced your 'lifetime' odds to 200:13,983,816? Or do the odds reset with every new draw?

Hopefully, someone out there has the math/statistical background to answer this

 

[time*treat]

The odds "reset" every time. Look at it this way, if the drawing results for week #2 match 6-for-6 one of the 100 tickets you bought for the drawing on week #1 -- you still don't win anything.

You must have the correct numbers ... for the correct drawing. You'd probably be immediately non-plussed buying a quick pick (lucky dip) and seeing that you were given the number set that matched the previous drawing.

 

[Icewynd]

Good point, time*treat!

That matches up with what I thought the answer was.

 

[rigged2lose]

I have to disagree. The odds "reset" only if you are calculating each draw as its own separate event. If that is the case, the term "overall lifetime odds" cannot be applied.

Suppose I buy an 'advance buy' ticket with the numbers 1,2,3,4,5,6 for the next 10 draws. What are my overall all odds for the lifetime of this ticket?

 

[garyo1954]

I have to disagree. The odds "reset" only if you are calculating each draw as its own separate event. If that is the case, the term "overall lifetime odds" cannot be applied.

Suppose I buy an 'advance buy' ticket with the numbers 1,2,3,4,5,6 for the next 10 draws. What are my overall all odds for the lifetime of this ticket?

1:13,983,816 per draw one would say.


However, (insert logical reasoning here specifying the odds of the lowest 6 consecutive numbers to turn out during the same draw).

 

[Frank]

If your ticket remains constant throughout your lifetime then it is straightforward. You divide 13,983,816 by the number of tickets you bought (with those same numbers) in your lifetime. If that was say 5000 draws then your lifetime odds are 13,983,816/5000 or 2797 : 1.

If at any time you change the numbers on the ticket, the problem resets to a different one since you now have two lifetime tickets, one of which you can win with (its live), the other you can no longer win with (you're no longer betting on it).
Your (new) lifetime begins at the date you purchased the new set of numbers.

 

[CMF]

Lifetime chances of winning first prize in 6/49 Lotto

Odds are a ratio based on random selections and remain the same for each draw. As the number of plays you make increases by playing an undistorted or random set of 100 numbers then so do your chances of winning the respective prizes. The important point is that for any prize an adequate sample is used to make the calculation relevant.

For your first draw with 100 plays a Three win is very likely as is two by Three wins for the odds of 1 in 57. However, all the other prizes are possible with a varying degree of likelihood. After about 10 draws with 100 plays per draw you can expect a Four prize as the odds are 1 in 1,032.

For the Five prize the odds become much higher at 1 in 54,201. If you define a lifetime of regularly playing Lotto once per week as 60 years then the chances are you will get a Five with just 1 play per draw. With 100 plays per draw you have 60 x 52 x 100 = 312,000 chances of getting a Five so you could have about 6 Fives in your lifetime.

For the first prize your 312,000 chances doesn't figure very highly (312,000/13,983,816) with only a bit over 2% probability. For a reasonable chance of success with an adequate sample size some would say 25 lifetimes others maybe 10.

In other words even if you play consistently weekly over 60 years spending what I consider a high amount for 100 plays you are still reasonably certain of not winning first prize so I would suggest playing only about 22 plays per draw. (Apart from my birthday multiples of 11 figure prominently in Lotto number set analysis.) This is still much better than not playing where your chances of success are zilch.

Colin Fairbrother