Lottery syndicate - is this guy breaking any laws?

Isn't there something called a "lucky dip", which looks a bit like a random ticket?

When you play this week, you have a 63% chance of winning. When you play next week, you have a 63% chance of winning that game. The following week you still have a 63% chance of winning. Eventually, you might be lucky, but you might not. It never approaches certainty.

This is a common mistake made by gamblers who believe that because they have lost on a number of previous occasions, they are guaranteed a win this time.

But that's the same thing.

How should I know? Do you think I'm daft enough actually to play the lottery? :-)

"Ronald Raygun" wrote

You really shouldn't state something as categoric as "you can't buy random tickets", when you actually have no idea. Shame on you!

"johannes" wrote

Exactly! Previously, you said: "The probability of something, which is not imaginable, must be zero by definition, yet not impossible." Which is rubbish.

Imagination creates information (even if only on fantasy). Anything that can be "known", *can* be "imagined"

- before it has ever been known to have happened. See?

Well I don't play it either, but I do see the ads around the place.

How do we know the lucky dip is actually random? It might all just be a big con!

Erm, wait a minute, ...

No it's not rubbish. You have a false vision of probability as absolute and universal, this is not the case. As I explained at length, probability is tied to a vantage point. If something is not imagined or anticipated at a given point in time, then the probability is zero by definition. (hindsight not allowed).

That is totally different from our discussion.

You can't improve your chances of winning but you can influence the amount you'll win. If, for example, it's true that people pick birthdays then you'll expect numbers between 1 and 31 to be picked more often, and so, if you always picked numbers above 32 then if you win you'd expect to share your win with fewer people, on average.

You could also win more, at the expense of winning as often, if you always bought 10 tickets with the same numbers. If 1 other person chose the same numbers as you, you'd with 9/10ths of the prize.

I think there's also a system, which is what I initially thought the OP was talking about, where you pick, say, 10 sets of numbers, but you recycle the numbers used, such that if you win once, you'll probably win with all your numbers, but again, you're restricting the range of your numbers and therefore reducing your chance of winning.

What actually happens (in Italy, for instance) is that the mafia pays good money (over the odds) for winning tickets, for exactly that reason. I don't think the mafia are stupid enough to just randomly buy them in advance, though.

It's never described as random. Perhaps there's a reason for this.

Perhaps, but in the light of this...

| No, I'm just being realistic - there's no point | in considering "scenarios" that don't exist!

...you're not talking like one :-)

Where you say you can't play games of chance with (even countably) infinite possible outcomes in the real world. I dare say that's true enough, but the real world is such a limiting place!

Peter

This has happened once (by accident) when two people in the same syndicate bought the weeks tickets. They only realized this had happened when two different people arrived at work waving the winning ticket. IIRC there was one other winner - would have been a bit of a shame for them if they had been the only winner.

Tim.

Further proof using Bayes's Theorem:

P(A|B) = P(B|A)*P(A)/P(B)

Hence you can have P(A) = 0 while P(B) > 0 QED.

"johannes" wrote

You still haven't given even a single example, of anything which satisfies your comment (ie that is both "not imaginable" and "not impossible").

I still contend that anything that is "not impossible" (ie, it is possible), is also imaginable - even before it has first happened (ie without hindsight).

I'll even give an example : flying machines were imagined well before any had been built (Leonarda Da Vinci).

Which amounts to virtually the same thing when the number of tries gets very big. My use of "on average" was meant to indicate that I was taking into account all sets of coin tosses that have happened, thus x is a very large number. Sort of similar to saying, "The average person in the UK uses 10 gallons of water per day." The words "on average" obviously refer to the whole population of the UK.

I am probably not explaining what I mean well enough rather than misunderstanding probability.

And what I have stated in no way implies that past results influence future results - I am perfectly aware of that particular fallacy!

What I *am* saying is that if you were to play a hundred games each with 14 M random tickets, you would have approximently 100 wins. If you played 1000 games you would have approximately 1000 wins ... etc. The more draws entered the closer the number of wins equals the number of draws

What you neglected to take into account with your figure of 63% chance of a win was the balancing probability of having more than one win in a single game. This means that the number of wins can equal the number of draws over a large number of draws despite the probability of winning in any one game being 63% - without involving the gambler's fallacy at all.

Even if you have 14 million tickets all with the same numbers (which is a tiny possibility if all tickes are random), you would *on average* win the same number of times that you play, though you would have to play a heck of a lot of games before getting close to that position. In that case you would lose almost all the time, but when the numbers did come up you would clock up 14 million wins in a single game.

which is a probability of 0.63. Two different arguments, one is what is the probability of winning, and the other is, what does a probability of '1' mean.