# The Naked Scientists Forum

### Author Topic: Impossible lottery combinations  (Read 20396 times)

#### Bill S

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##### Re: Impossible lottery combinations
« Reply #50 on: 15/11/2014 21:47:13 »
Quote from: CliffordK
Even if there are a lot of players, it could take a good long time before a payout.

I suspect there would still people who would buy thickets on the principle that the payout could just as well be on the first draw.

#### dlorde

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##### Re: Impossible lottery combinations
« Reply #51 on: 16/11/2014 00:57:59 »
Nothing would happen in an infinite universe.
I don't see the justification for that, but if so, it means your infinite lottery couldn't happen.

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You could not wait an infinitely long time for something to happen, because infinity is not a length of time.
... in an infinite universe in would always be in a state of having been drawn, if the concept of being drawn has any meaning in infinity.
Presumably not, if nothing happens.

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Countable and uncountable infinities are mathematical concepts, but that’s as far as it goes.  A countable infinity is a set with the same cardinality as some subset of the set of natural numbers.  All that means is that whatever the objects in the “infinite” set may be; they can be placed in one-to-one relationship with the set of natural numbers.  Valuable as that concept may be in mathematics, beyond that, it is meaningless.
So your infinite lottery post was proposing meaningless nonsense?

#### Bill S

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##### Re: Impossible lottery combinations
« Reply #52 on: 16/11/2014 17:15:58 »
Quote from: dlorde
So your infinite lottery post was proposing meaningless nonsense?

EUREKA!!!  Dlorde, step forward and take a bow.

The original intention of the infinite lottery scenario was to demonstrate the absurdity of trying to apply the concepts of mathematical infinities to actual infinity, whatever that may be.

#### Bill S

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##### Re: Impossible lottery combinations
« Reply #53 on: 16/11/2014 18:40:54 »
Quote from: Bill S
Quote from: dlorde
Nothing would happen in an infinite universe.
I don't see the justification for that, but if so, it means your infinite lottery couldn't happen.

The justification for saying that nothing would happen in infinity is perhaps a bit lengthy to post in a thread into which infinity was introduced by way of thread drift.  If I can find some time, I might try to put together some sort of justification, and set it up for people to shoot at.

#### dlorde

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##### Re: Impossible lottery combinations
« Reply #54 on: 16/11/2014 21:22:08 »
The original intention of the infinite lottery scenario was to demonstrate the absurdity of trying to apply the concepts of mathematical infinities to actual infinity, whatever that may be.
OK, well I'm sure we can all think up applications of mathematical concepts that would be absurd in the real world, but sometimes mathematical models of the real world lead to apparently absurd conclusions that turn out to be true in the real world, such as the Copernican Revolution, quantum mechanics, or a Mobius strip.

Where possible, these apparent absurdities must be tested against real-world data, or for correspondence with other tested theories.

As I understand it, considering the geometry of the universe, it can have positive, negative, or zero spacetime curvature. Ours has been measured as zero (within experimental error), which gives it a flat local geometry. There are various possible overall 'global' geometries, the simplest and most obvious of which is Euclidean space, which implies infinite extent. There are also finite solutions, with more complex topologies. At present we don't know which might be the case, but we can't rule out a solution just because it is counterintuitive, or seems absurd.

#### Bill S

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##### Re: Impossible lottery combinations
« Reply #55 on: 17/11/2014 00:56:24 »
Quote from: dlorde
Where possible, these apparent absurdities must be tested against real-world data, or for correspondence with other tested theories.

Precisely, which is why it’s worth looking at things like Hilbert’s Hotel, Schrödinger’s Cat and even the “infinite lottery” just to see what emerges.

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As I understand it, considering the geometry of the universe, it can have positive, negative, or zero spacetime curvature.

My understanding is the same. No problem.

One of the reasons I try to maintain a distinction between the Universe and the cosmos is that I have no problem with the use of the term infinite, either in mathematics or with regard to the Universe, provided there is clarity as to how it is being used.  On the other hand, I have difficulty understanding how the cosmos can be anything other than infinite/eternal in the sense that it is timeless and possibly dimensionless in any sense that can be appreciated fully from our 3+1 dimensions.

Please be assured, I am not claiming “this is how the cosmos is”, or ever “I believe this is how the cosmos is”.  I would be poorly qualified to make such a presumptuous statement.  My objective is to gain understanding.  If in so doing I try the patience of others, I apologise, but that doesn’t mean I will stop doing it.

#### evan_au

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##### Re: Impossible lottery combinations
« Reply #56 on: 19/11/2014 11:03:21 »
Quote
the jackpot winners (being a percentage of the infinite number of people taking part) would be infinite

One mathematical trick you can apply when dealing with infinities is to look at the limit as the number approaches infinity. You can then work out what is the probability of a win. And the answer is that "it depends on the rules of the lottery".

For example, if you imagine that the number of balls in the urn is equal to the number of players, and the winner must correctly identify 6 balls drawn from the urn, you find that the probability of someone winning decreases rapidly with the number of players.

So you expect zero winners in a single game following these rules, despite an infinite number of players.

I am sure you could invent other rules that provide no winners despite an infinite number of games. For example: if there are n players and m games, set the number of balls to n, and the winner must correctly identify m balls. A quick trial calculation suggests that this would produce no winners despite an infinite number of players and an infinite number of games (provided the number of players>number of games+2).

By these rules, the only winner would be the person running the lottery (this is not so different from ordinary, finite lotteries!).
« Last Edit: 19/11/2014 11:20:46 by evan_au »

#### syhprum

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##### Re: Impossible lottery combinations
« Reply #57 on: 20/11/2014 21:13:52 »
I think estimate of a 10% payback on average from the cost of a ticket was pessimistic I have always understood  that for every pound you spent on tickets on average you got back 25 pence but you would have to buy tickets for a long time to achieve this.
From a financial point of view the best bet is not to buy tickets !

#### chiralSPO

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##### Re: Impossible lottery combinations
« Reply #58 on: 20/11/2014 22:00:46 »
Here's a fun game (it looks very simple at first, but I promise it's worth a good thought or two):

I will flip a fair coin until it comes up heads (H). However many flips it takes to get that heads will determine your payout:
If the first one is heads (H), you get \$0.50; if I flip tails, then heads (TH), you get \$1.00; TTH gets you \$2; TTTH gets you \$4, and so on. (payout = \$0.05 × 2n, where n = total number of flips)

How much would you pay to play this game? What is the expected payout (for those who know how to calculate such a thing)? What is the probability of winning more than \$50 in a single game?

#### chiralSPO

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##### Re: Impossible lottery combinations
« Reply #59 on: 28/11/2014 00:15:06 »
This is a fun game, I promise!

Here's a fun game (it looks very simple at first, but I promise it's worth a good thought or two):

I will flip a fair coin until it comes up heads (H). However many flips it takes to get that heads will determine your payout:
If the first one is heads (H), you get \$0.50; if I flip tails, then heads (TH), you get \$1.00; TTH gets you \$2; TTTH gets you \$4, and so on. (payout = \$0.05 × 2n, where n = total number of flips)

How much would you pay to play this game? What is the expected payout (for those who know how to calculate such a thing)? What is the probability of winning more than \$50 in a single game?

#### The Naked Scientists Forum

##### Re: Impossible lottery combinations
« Reply #59 on: 28/11/2014 00:15:06 »