[BNM] [OT] Lottery puzzle

[Jason Bailey]

--- On Mon, 22/9/08, Alex Farran <alex at alexfarran.com> wrote:

> From: Alex Farran <alex at alexfarran.com>
> Subject: Re: [BNM] [OT] Lottery puzzle
> To: "Brighton New Media" <bnmlist at brightonnewmedia.org>
> Date: Monday, 22 September, 2008, 7:07 PM
> On Mon, Sep 22, 2008 at 5:46 PM, David Pashley
> <david at davidpashley.com> wrote:
> > On Sep 22, 2008 at 17:36, James Cline praised the
> llamas by saying:
> >> If you bought all for the same draw
> >>
> >> You would have a 52 in 14000000
> >>
> >
> > 52/14,000,000
> >
> >
> >> If you bought each week you would have
> >>
> >> 1 in 1400000 each time.
> >>
> >
> > 52 * 1/14,000,000 or 52/14,000,000
> >
> 
> On the face of it it looks that way, but I don't think
> it's right.
> Imagine that instead of 52 tickets you could buy
> 14,000,000.  Assuming
> they're all different numbers you would be guaranteed
> to win. If
> instead you lived long enough to play the lottery every
> week for 270
> thousand years you'd not have the same guarantee. 
> Though there's a
> tiny chance that you'd win every week.
> 
> If you scale the numbers down so each ticket has a 1 in 100
> chance of

> Therefore the chance of winning is 1 - (99/100)^52
> If you work that out it's a probability of 0.52 for 52
> at once vs
> 0.407 for 1 every week.

If you're talking about the jackpot then the odd are approx 1 /14,000000 (1/49*1/48*1/47*1/46.. number of balls is 6 isn't it?). The 1 /100 you mention is also more likely (obviously) as this is around the level of the lesser ball wins. Can't you still win a tenner for 4 balls?

Also the one in 14 million answer doesn't account for others winning/participating. That just accounts for you getting the six numbers right. Highly unlikely but for say a 20 million pound jackpot someone might go and buy ~13.84 million tickets to ensure that they have a winning ticket, but then so may someone else (or more) and so the jackpot will be shared. What are the chances of 3 people getting the winning ticket if 60 million tickets are bought etc....?

I think you up your chances of increasing your winnings by accounting for the smaller wins (4 balls etc, if they still happen??). i think putting money on the horses/dogs has better odds and it used to be a better night out.

This bloke has written a few books on game theory:
http://www.maths.sussex.ac.uk/Staff/JH/

Jas