[syhprum (OP)]

For theatrical effect the winning number is produced by a crude mechanical machine blowing out marked balls.
There are of course more subtle ways of producing near random numbers how does the method used compare with the best of them.

[alancalverd]

The frequency tables are published. Currently 40 has appeared most often (331 times) and 20, 21 only 261 times.

Worryingly, if you consistently picked the 6 "best" numbers you would be 1.9 times more likely to win than if you  consistently chose the 6 "worst".

[Bored chemist]

The frequency tables are published. Currently 40 has appeared most often (331 times) and 20, 21 only 261 times.

Worryingly, if you consistently picked the 6 "best" numbers you would be 1.9 times more likely to win than if you  consistently chose the 6 "worst".

If the machine was truly random, how "unlikely" would that outcome (That the "lucky"  numbers are roughly twice as good as the worst) be?

[evan_au]

Worryingly, if you consistently picked the 6 "best" numbers you would be 1.9 times more likely to win than if you  consistently chose the 6 "worst".

I would change the tense on that statement: "Worryingly, if you had consistently picked the 6 "best" numbers you would have been 1.9 times more likely to win than if you  had consistently chosen the 6 "worst"."

Because this mechanical generator is sufficiently random that the results of the past X draws is useless as a predictor of the next X draws.

how does the method used compare with the best of them.

This method wins on transparency (both literal and figurative).

The best random number generators include: Quantum effects, noise from Zener diodes, banks of free-running silicon oscillators, and timing keyboard clicks or disk seeks on a computer.
- All of these are almost totally opaque - even someone familiar with the technology would have trouble certifying that it is working truly randomly (let alone a panel of witnesses drawn from the general public)
- Among the worst methods must be complex pseudorandom algorithms, which could (in theory) be simulated or modified by someone who had access to the code.
See: https://en.wikipedia.org/wiki/Random_number_generation#%22True%22_vs._pseudo-random_numbers

[alancalverd]

I would change the tense on that statement: "Worryingly, if you had consistently picked the 6 "best" numbers you would have been 1.9 times more likely to win than if you  had consistently chosen the 6 "worst"."Because this mechanical generator is sufficiently random that the results of the past X draws is useless as a predictor of the next X draws.

It's an interesting question for a statistician (I'll confess to having slept through most of the course!). X is actually very large (>2500) and although there are several machines and ball sets, one machine and ball set stands out as being used significantly more than any other combination.  Compared with the statistical bias in, say, the orientation of proton spins in an MRI field, this does seem to indicate a physical phenomenon buried in noise.

So the test is simple. Invest £1 each draw in both sets of numbers. After the next 2500  draws you should have won 1.9 times as much on the "good" set, at a cost of £5000, if there is something odd about the balls.

The individual number frequency chart looks remarkably un-smooth, with "33" standing out as clearly the least favoured number. A politician or climate scaremonger could make a living from that.   

If you tossed a coin and found, say, 300 heads to 200 tails, wouldn't you be just a tiny bit suspicious?

[Bored chemist]

The individual number frequency chart looks remarkably un-smooth, with "33" standing out as clearly the least favoured number. A politician or climate scaremonger could make a living from that.   

Not sure how a climate scaremonger could make anything of that lot of balls.

However, as scientists, we  really ought to be pointing out that the effect is almost certainly a cognitive bias rather than a mathematical or mechanical one.

[alancalverd]

I would like to think so, but I'd need some statistical formalism to support that assertion. My limited appreciation of stats is sufficient to convince me not to waste money on an experimental investigation, but I'd really like to know the probability of the "best six"/ "worst six" ratio being as high as 1.9:1 by chance. Could be an interesting exam question.

[evan_au]

My limited understanding of statistics is sufficient to tell me not to invest in something which, by legislation, must return less than you put in (on average).

[alancalverd]

Absolutely so. At least with football pools and horse racing, there is an element of skill and knowledge involved in making your bet, but truly random lotteries are just a tax on ignorance and poverty. At least they were until an infamous rollover in the Irish Hospitals Lottery (which does at least fund hospitals) made the prize worth more than the total number of tickets, all of which were bought by a syndicate of Legitimate Businessmen.

[nudephil]

Some insight from yesterday's show - we put the question to Tim Revell from New Scientist:

https://www.thenakedscientists.com/articles/questions/are-lottery-numbers-really-random

He points out the discrepancy but seems to think the gap falls within acceptable randomness, and should close as time goes on.