UKH

Tonight's lottery jackpot had three successive numbers and the whole set of winning digits consisted of one, two, three and four.

Is the probability of this combination still 14000000:1?

In reply to Removed User:

Yes, all draws have equal probability.

In reply to Robert Durran:

I know that's true, but my head can't get round it. 

In reply to Removed User:

Corollary: What is the probability of having 3 successive numbers in the draw and a total of only 4 digits used across all 6 (7) numbers?

It can’t be very high with that set of constraints!

In reply to aln:

Instead of numbers, think of all the numbers as being different coloured pebbles.
The fact that the numbers drawn today are consecutive is totally irrelevant.

edit: just thought that they could use letters, numbers and some other random symbols; then you could have your regular lotto combo(s) as something like 'wanker' or 'anothe'/'rtwoqu'/'idspaf'/'fedupt'/'hefuck'/'ingwal'/'l&*^%£' ...

In reply to wintertree:

It's completely irrelevant what the probability is. It happened. As long as the probability is non-zero it is sure to happen sooner or later. At which point point people will start speculating as to how freak that occurrence must be. 

In reply to Removed User:

The reason I don't play the lottery is when I realised that 1,2, 3, 4, 5 & 6 was a perfectly good choice at winning the jackpot! 

In reply to Heartinthe highlands:

Why?

The only skill in doing the lottery is in avoiding combinations which other people tend to pick for irrational reasons.

In reply to Robert Durran:

Ha! I think most people would just like to win it. If I had to share £10 million with four other people, it wouldn't break my heart. 

I just think I have more chance of most things in life than winning the jackpot, so I very rarely play it. 

In reply to Heartinthe highlands:

Quite.

When I saw the draw I thought no one would win and sure enough, no one did.

In reply to Removed User:

Which is a good reason to pick "improbable" looking combinations of numbers!

In reply to Heartinthe highlands:

If 1,2,3,4,5,6 was picked then you'd be sharing with a few more than 4 people

Can't remember what the number is but your jackpot would (if I remember correctly) probably be below £10k

In reply to Robert Durran:

Quite, pick a combination where you're less likely to have to share (sounds quite greedy when it's put like that).

In reply to Removed User:

There's a lot of different ways a random number can look 'interesting'.   People are good at finding or imagining patterns.   If there's a thousand different potential ways a number could be 'interesting'  and several different lotteries getting drawn one or more times a week the odds of an 'interesting' number coming up in one of those lotteries are a lot lower.

It's the difference between predicting a specific person will get hit by lightning on a specific day and reading in the newspaper that somebody got hit by lightning yesterday.   One is a multi-million to one shot, the other happens all the time.

In reply to Removed User:

Jackpot used to be 14m:1 when numbers were from 1 to 49.

Jackpot now 45m:1 because numbers are now 1 to 59. (59/6 * 58/5 * 57/4 * 56/3 * 55/2 * 55/1)

But the £1m prize for 5+bonus ball has odds of something like 7m:1.

Oh and wasn't one of the balls #18, so that's digits 1,2,3,4 & 8 - oops

In reply to john arran:

Is that actually mathematically provable? Just wondering because although it sounds reasonable, I'm not sure it's necessarily so.

In reply to wintertree:

Not sure about the successive numbers but only using 4 digits across the 6 balls (ignore bonus ball - can always be added later).

59 balls, there are approx. 45m combinations

How many only have 1,2,3,4, in their digits? 11,12,13,14,21,22,23,24,31,32,33,34,41,42,43,44 so that's 16

So chance of one of those as 1st ball is 16/59, 2nd 15/58, etc

Chance of only using digits 1,2,3,4 is 16/59 * 15/58 * 14/57 * 13/56 * 12/55 * 11/54 = 0.0001777

So it'll happen approx. 18 times every 100,000.

In reply to Michael Hood:

Well technically I suppose the long-term probability of it not happening becomes infinitely small.

In reply to john arran:

But with an infinite series of events, which infinity wins, or do they cancel eachother out?

Long time ago, but I vaguely remember that infinity mathematics doesn't necessarily follow the "normal" rules.

In reply to Michael Hood:

I vaguely recall being told that you get different infinities depending upon how you get there and pure mathematicians have arguments about what happens when you divide one by another.

In reply to Michael Hood:

... continuing

4C10 = 210 (number of combinations)

So chance of only using 4 digits (any 4 out of the 10) is approx 4 in 100; i.e. 1 in 25.

In reply to Removed User:

Something to do with the strength or rank of the infinity.

In reply to Michael Hood:

I think that in this context, "infinite" or "infinity" is just shorthand for saying "given a number p (however small), there exists a number N such that if we have more than N draws, the probability of the event not happening is greater than 1-p. No actual need for any concept of infinity.

I think that is something different, not really applicable here.

In reply to Michael Hood:

Mathematicians understand infinities as a cascading series of different levels. The  set of natural numbers (1, 2, 3 ...) are the first level, the set of irrational numbers are a higher level (not necessarily the next one).

In reply to Michael Hood:

The probability of the numbers ultimately coming up is 0.9999999..., which is mathematically equivalent to 1, i.e. certain.

Worth looking up Zeno's Paradoxes for a simple discussion of how something we accept as mathematically equivalent may still present philosophical difficulties.

In reply to john arran:

Isn't that just a worryingly sloppy way of trying to say what I said in my last post?!

In reply to Robert Durran:

Probably yes, but perhaps easier to take in.

Thank God I just do a Lucky Dip. 

In reply to john arran:

What about looking at it from the perspective of saying that for any number of draws, however large, there is a chance it will not happen.

In reply to Pedro50:

In theory, the odds of a "lucky dip" picking someone 1,2,3,4,5 and 6 are significantly higher than those numbers actually winning (due to the sheer number of people playing on a lucky dip vs the number of draws). I wonder if this has ever actually happened - I would have kind of expected a daily mail clickbait store.

In reply to Heartinthe highlands:

I stopped doing the lottery when I realised I was 13 times more likely to walk down my high street and guess someone’s telephone number!

In reply to Removed User:

If you really want to win the lottery, don’t buy your Saturday  ticket on Monday....you’re much more likely to be dead on the Saturday than be a winner.

Somebody (can’t remember who) once called it “a tax on stupidity” but we keep on doing it....

In reply to colinakmc:

What would be the probability of buying a ticket on Monday, dying sometime before Saturday and then "winning" the jackpot?😊

In reply to Michael Hood:

Don’t all the numbers between 10 and 49 contain a 1,2,3 or 4?

Unless you meant numbers ending in 1-4?

The probability of drawing 1,2,3,4 is the same probability as matching any other 4 numbers. 

The probability of drawing any 4 consecutive numbers would be interesting to work out. But still irrelevant as you’d have to match them, so you’re back to the original probability.

In reply to Removed User:

dunno, but my wife would be ecstatic

In reply to john arran:

No philosophical difficulties at all, just the rather boring insight that 2000 years ago the concept of limits was not well developed yet.

CB

In reply to Removed User:

I’m speechless with admiration for those folk on here who can do calculations like that. I’m sure someone will have an answer, but not me....

In reply to Removed User:

Sunday?

In reply to Removed User:

Death by bus or lightning?

In reply to DancingOnRock:

Numbers ONLY containing the digits 1,2,3,4 - for simplicity I assumed that 1 was really 01, etc - but obviously if you kept 1 as 1 etc. then there would be 20 possible balls with just those 4 digits (rather than 16). Also ignored the bonus ball which would lower the odds if you required it to also have only those digits.

I then in my follow-up e-mail extended it to only 4 (out of the 10) digits, but any 4 (e.g. 3,5,7,9 etc.), in which case it becomes a high enough probability to expect it to happen a few times every year.

Wasn't discussing the probability of matching, just the probability that such a combination would come up with (or should that be in?) the balls.

I remember there was a competition years ago in one of the papers (DM?) where the winner won 25,000 lottery tickets that covered ALL combinations under certain conditions (something like 2 numbers in 1-17, 2 in 18-34, 2 in 35-49, can't remember exactly but that's not important). She won absolutely nowt, zero, nada, £0. I think she was a bit disappointed (maybe I'm understating it ).

In reply to Michael Hood:

I didn't know they had changed it. Means you have nearly twice a good of a chance in a comp where every single address in Britain is put into a hat and they pick one out at random. Would you enter that for £2? Haha. Nope. 

(~25m houses in Britain apparently).

In reply to Robert Durran:

If the number of draws is infinite it MUST happen?

In reply to axor:

... and must happen an infinite number of times?

Chris

In reply to axor:

No. That’s not how it works. Every draw is a separate independent outcome. Past draws do not affect future draws. 

In reply to axor:

But you can't have an infinite number of draws.

Infinity is not a number.