70's wiring in new sockets

"South Africa's lottery probed as 5, 6, 7, 8, 9 and 10 drawn"

 

Indeed - and my point, of course, would that (as the 'probing' might end up concluding) that is actually no less probable a set of numbers than any other set.

That is precisely the method I use to help people understand how very unlikely it is that they will win the UK lottery. Most people seem to understand, in principle, the concept that any set of six numbers is equally likely to be drawn. Having got them to acknowledge that, I therefore then ask them how likely they think it is that this weeks' drawn numbers will be 1, 2, 3, 4, 5 and 6. The great majority of people then say something along the lines of "that would be virtually impossible", often adding something like "..certainly not worth betting on". If I then point out that they have agreed that no other set of numbers would be any more likely to win than that set, at least some people then grasp the fact that winning with any set of numbers is also "virtually impossible"

However, a good few still can't get away from the 'intuitive' idea that a 'special' set of numbers (such as 1,2,3,4,5,6) is far less likely to win than is a set of random (or 'carefully selected' ) numbers!

Kind Regards, John

 

If one used the same method to choose one's ticket numbers, as the lottery uses to pick the winning numbers, i.e. to select six balls from the same machine, what are the odds of the lottery selecting the same six balls twice in the same week?

 

Yes the Copper Belt, used to advertise for tradesmen in the UK papers in the 70s, I knew a couple of sparks who went, had a great time by all accounts, during UDI sanction busting became a national obsession & forced the growth of lots of home grown industries

 

I don't really understand the first part of the question but, as far as the bit I've highlighted in concerned, once the first draw of the week has selected a certain set of six numbers, the probability of the second draw of the week also producing the same set of numbers is the same as was the probability of the first set of numbers being what it was - i.e. around 1 in 45 million for a "6 out of 59" lottery.

More generally, the probability of that particular set of numbers coming up in any draw is the same.

However, if you picked a set of six numbers, then the chances of 'the machine' picking that number in two particular draws (whether in the same week or not) would be "(around 1 in 45 million) squared" which is such a ridiculously small probability as to not really be worth calculating (around "1 in 10^15", I think).

Kind Regards, John

 

What I meant was, if they let you use the machine to pick your numbers and then for those numbers to be chosen in the next draw.

However, you have confused me with this:

What is the difference between this and above?

 

That doesn't alter my answer. No matter how you chose the numbers (and that includes using the numbers last chosen by the machine), the probability of the next draw (or any other draw) producing that same particular set of numbers is around 1 in 45 million.

In the first case, you have chosen a set of numbers (which happens to be the set most recently chosen by the machine) and are asking about the probability of the next draw producing that same set of numbers - hence 1 in ~45m.

In the second case, I was talking about the situation in which you have chosen a set of numbers (by any method) and then want to know the probability of the next two sets produced by the machine ('both sets this week') both being the same as the number you had (independently) chosen. However, as I said, I did not understand the question you were trying to ask, so that question I was answering was probably not to the one you were trying to ask!

If I now understand correctly, you were effectively simply asking about the probability of the second lottery of a week producing the same set of numbers as the set previously produced in the first lottery of that week (i.e. per my first case/answer above) - and, as I said, the answer is simply 1 in ~45m (i.e. the probability of any particular set of numbers, no matter how chosen, coming up in that second draw of the week).

Is that clearer?

Kind Regards, John

 

I should perhaps have added that what you were talking about was exactly the same as my "1,2,3,4,5,6" method of trying to get people to 'understand' - i.e. if you chose the numbers the machine had picked for the Wednesday draw to use for the Saturday draw that week, you would be no less (or no more!!) likely to win than if you had chosen the numbers in any other way.

Kind Regards, John

 

It's simple enough of an equation John! (yes, I am just killing time!!!)

(59!/53!/6!)^2 = 2030175963260676
≈ 2 quadrillion!

 

Yep, but I don't think I did too badly to only be out by a factor of about 2 with my very hasty mental arithmetic which resulted in my "around 1 in 10^15"

However, as I'm sure you will understand, my "not really worth calculating" comment was nothing to do with my (or my calculator's!) inability to calculate the actual answer but was really just a way of saying that it was an incredibly small probability!

Lets, face it, if one did the lottery twice a week, with the same set of numbers for both lotteries in any week (but not necessarily the same numbers every week), then one would, on average, win both lotteries in a week around once every 39,041,845,447,320 years (assuming 52 weeks per year) (which counts as an 'incredibly small probability' in my book )

Kind Regards, John

 

People sometimes find it very hard to understand the difference between (assuming its not a dodgy dice) "if I roll a dice 6 times what are the odds of 6 sixes?" and "Ive rolled a dice 5 times and got 5 sixes, what are the odds of getting a six next time?".

Be interesting to do a survey of reactions to:

"I buy a random lucky dip lottery ticket each week"
and
"Every week I pick the numbers that came up the week before".

Guarantee there would be far more "thats barking mad" reactions to strategy 2.

 

The human brain is not very good at understanding random numbers. Like pigeons*, we search for patterns and explanations even when there is none. Hence religion.

You can hear the same pundit say "36 has come up twelve times this year, it's on a run" and "20 hasn't come up for six months, so it's due to come up soon."






*B.F.Skinner
https://www.psychologistworld.com/superstition

 

speaking of luck,

"Zimbabwean President Robert Mugabe won the top prize in a lottery organised by a partly state-owned bank.

The president, who... awarded himself and his cabinet salary hikes of up to 200%, hit the 100,000 Zimbabwe dollars (about $2,600) jackpot in a promotional draw organised by the Zimbabwe Banking Corporation (Zimbank).

"Master of Ceremonies Fallot Chawawa could hardly believe his eyes when the ticket drawn for the Z$100,000 prize was handed to him and he saw His Excellency RG Mugabe written on it," the bank said in a statement.

BBC 28 January, 2000"

What were the chances, eh?

 

Indeed so.

I'm sure you're right - they would be the same people who tell me that to choose (1,2,3,4,5,6) would also be "barking mad"!

Mind you, at some level I can't blame them. Even though I have far better reason than most to understand "the truth", there is still a part of my mind that 'can't help feeling' that (1,2,3,4,5,6) 'has simply got to be less likely' than some random set of six numbers.

Also, one has to be careful about issues of probability which appear (incorrectly!) to be 'intuitively obvious', even to most mathematicians and statisticians. A real classic is the "Monty Hall problem", about which I have seen eminent academic statisticians almost 'come to blows' over 'the answer'! Another which is extremely non-intuitive, at least to non-statisticians, is the "Birthday Paradox"!

Kind Regards, John

 

True, but we are obviously talking about the opposite here, since it's when they see 'patterns' in lottery numbers, like (1,2,3,4,5,6) or (2,4,6,8,10,12) etc., that they think they are looking at sets of numbers which "couldn't possibly win" - whereas, in most situations, they are (as you imply) 'attracted to/by' structured patterns..

Kind Regards, John