Lotteries & Rationality...

If I bought a million different tickets for each lottery, then I would be certain to lose £500,000 in the first lottery and win £1,000,000 in the second lottery.

If, on the other hand, I just bought the million tickets for the second lottery, I would double my money every time.

I know which lottery I prefer.

Regards,

No

Probably not because one-in-a-million is so close to zero that it may as well be zero. If you buy one ticket every week the average time before you win would be about 10,000 years so not worth playing.

If such a lottery existed, perhaps it would be worth organising a syndicate to purchase all (or nearly all) the tickets so you could (have a reasonable chance of) double your money. However even if you had 1 million quid to spare actually buying 1 million tickets would be difficult - at 1 per minute, 8 hours a day, five days a week it would take about 8 years.

Even with 100 tickets the chance of wining is still incredibly small so I still wouldn't bother playing.

Averaged over a very long time, if you played every week, you would expect to double your money on your 2nd lottery whereas on the 1st one you would expect to half your money. Obviously doubling your money is good, halving is bad. However, you don't get the average; you either win or loose.

What exactly does "a one-in-a-million chance of winning" mean in this context? Is it just the probability (i.e. could it mean

Clearly if there were only a million tickets, you could buy them all, using borrowed money if needed, and in lottery 1 you would be guaranteed to lose half your stake, while in lottery 2 you would be guaranteed to double your money.

If you had to choose whether to play in lottery 1 or in lottery 2, would you not rather go for the one with the bigger prize, given the chances of winning it are the same?

Well, you shouldn't, because it's a lottery that other people enter too. You may be able to cover every possible combination with your million tickets and guarantee a win, but if others luckily choose the winning combination as well, the prize will be shared between all the winners. It won't all be given to you.

No lottery organiser can possibly say in advance what the chances are of your winning a certain amount. All they can do is state your chances of selecting a winning combination of numbers. They do not know and cannot tell how many will select the winning combination.

"David Uri" wrote

Do you have a million pounds to spend? ;-)

If you hadn't noticed already, the question is aimed towards someone buying a small number of tickets in relation to the number required to guarantee a win.

"Ronald Raygun" wrote

OK, for the sake of the discussion, let's say it's something like a thousand-in-a-billion(!) -- sufficiently large numbers that no-one is going to cover *all* possibilities.

It's only meant to be a thought experiment from the position of the punter, so don't worry about what happens if the organisers have to pay out several thousand lots of a million!!

"Ronald Raygun" wrote

Who could you find that'd lend you a million quid?! ;-) [If you tell them why it is secure, then they'd buy the tickets themselves instead, wouldn't they? If you don't tell them why it's so secure, then why would they lend it to you? :-( ]

"Ronald Raygun" wrote

It's not a choice between the two. It's a matter of looking at the two questions "would you play lottery1?" and "would you play lottery2?" and considering your two answers in isolation. Would the answers be the same, or different? If different, then why?

"Gareth" wrote

"Gareth" wrote

If it helps you, instead consider two lotteries where there's a one-in-a-thousand chance of winning 500 (lottery1) or 2,000 (lottery2), and suppose that each player is limited to a maximum of 10 of tickets in each draw.

What are your answers now?

"Norman Wells" wrote

Oh, no it won't!

"Norman Wells" wrote

Oh, yes it will ! - when I said "a ... chance of winning X", I meant just that. You get X.

"Norman Wells" wrote

Yes they can - look at the Lotto and consider getting 10 for three matching numbers.

The organiser of my lottery just needs bigger pockets to be able to guarantee the payouts, that's all.

"Norman Wells" wrote

That doesn't matter in my proposed thought experiment - everyone with the winning combination will get the million (except Gareth, who wants to play for a better chance, but of winning only 500 / 2,000).

Its been done before, consortia have covered literally all the numbers.

"Tumbleweed" wrote

As a matter of interest, do they buy all the tickets "centrally", or get each member to buy a few?

If a central "committee" buys all the tickets, how do they manage to buy them all within the week?

If the tickets are instead bought evenly by all the members, then how do they stop the one member with the ticket for the "big prize" from running off with all the lovely loot, and not sharing it out?

In that case I may well play lottery2 every week. On average I should win £2000 every ~two years at a cost of ~£1000, so a net profit of ~£500 a year.

Then it's a raffle, not a lottery.

"Norman Wells" wrote

Surely in a raffle, there would be only *one* person getting a particular "combination" (the number on their ticket), and hence winning a specific prize (there is usually only a fixed number of prizes in a raffle, no?).

In the proposed lottery, you could get any number of people with the same combination, each winning a million.

"Gareth" wrote

Oooops - when I said "maximum of 10 of tickets in each draw", pretend I said "maximum of 10 of tickets in each lottery" (over all time).

And who would run a competition, whatever you call it, with rules like that? Can you point to any that do?

It was a few people who did it as a 'company' from what I remember. How they did it was to actually print the tickets with numbers filled in, and then pay people to go into shops and feed those packs of many many tickets into the readers in shops. Pay people to spend most of the day feeding the tickets in.

How it worked was by (probably now not doable) targetting smaller countries lotteries who had fewer numbers than we have (IIRC around 45-48), where after a few rollovers, the payout exceeded the amount needing to be spent to buy every single number. And they had to take the chance that they would share with someone else. The one I recall hearing about they had to spend about USD equiv $5-10M for a roughly guaranteed $30M payout so I guess as long as they didnt have to share with more than two people they were guaranteed break even at worst and they were taking the chance it could all go pear shaped if more than 2 won. I also recall reading about a similar group getting into trouble as although they won, the rules stated you had to fill the cards in with pen or pencil and theirs were (1) printed and (2) not the actual cards but their printouts of them- I dunno what the outcome of that was , I suppose the lottery organisation would have no proof of that as its the receipt that counts not your entry slip (otherwise I suspect there would be quite a few winners every week :-)

"Norman Wells" wrote

I doubt if many people (unless very generous!) would run a 'Lottery2' -- but who cares, anyway? This is a *thought* experiment, not meant to be real-life...

"Tumbleweed" wrote

Are companies allowed to buy tickets?

"Tumbleweed" wrote

What's to stop those people keeping the tickets and legging it on their own if they get the "biggy"?

Or just legging it with the stake money and not bothering putting any tickets on!

Well, why not have a thought experiment in which someone will give you a twenty pound note for every tenner you give him? Why complicate it with terms like 'lottery'?