Yes. You're almost certainly not understanding it. The "specific case" you present is too specific to be useful in an analytic context; it's got too much information, from too many unfounded assumptions.
Awhaaa?
The case is
too specific, with
too much information?
That's a first, I have to admit that.
They say the glitch may affect the number of people that have to share the price. It doesn't affect the chances of winning.
Quite important, though.
Continuing with my simple example from before. If the RNG selected always the same sequence your chances of winning would be the same, but if you won you would have to share the price with everyone that used it. This RNG would be very bad, because you would never be able to win a big amount of money by using it.
We don't know how bad it was.
It may be "fair" if we look at the single gambler in the
very long run, but it isn't "fair" to the group of people who got "heads" selected for them.
No. You're misinterpreting the numbers.
Out of 1000 trials, the difference between the highest win percentage (always-picks-1) and the lowest win percentage (semi-biased) is 0.034 or 3.4%
Out of 1000000 trials, the difference between the highest win percentage (always-picks-1) and the lowest win percentage (semi-biased) is 0.001 or 0.1%
Out of 100000000 trials, the difference between the highest win percentage (fair picker) and the lowest win percentage (2-6 picker) is 0.000077 or 0.0077%
If ben m had the time/processing power, he could have continued with ever-increasing numbers of trials, and the difference would get closer and closer to zero.
There's a problem with that: In a lottery like this, you don't get to play an infinite amount of times. You can only have so many drawings, realistically. E.g., in this particular Lotto game, we have 52 drawings a year, and it's been going on since 1989, 18 years ago.
The error dates back to December 11, 2002 and was fixed December 21, 2006, which gives approx. 208 drawings. Run that many trials and see that the difference is quite noticeable.
The rules probably already limit damages to the price of the ticket so I did address the issue by saying they should get their money back and void the ticket.
Not to my knowledge. If it did, the organization would be compelled to give the money back. They aren't.
Have you got any links to what the actual problem was? I'm having a hard time conceiving how the Lucky Pick machine could have accidently skewed the probabilities for just 1-9 lower than the other numbers. And how much of difference are we talking about? Are there statistics available for how often each number is picked by Lucky Pick and for regular players?
The links I have seen are all in Danish. We don't know the exact difference, but you can see statistics here:
danskespil.dk
Click on "Spil". Next level, click on "LOTTO". Next level, click on "LOTTO". Sidebar, click "Statistik".
I specifically ran the increasing-numbers simulations to
forstall you from saying that. No, the biased picker does not have a lower chance of winning; all of the "win percentage" quantities are asymptotically approaching 1/6, and scattering around it with a Gaussian error of 1/sqrt
.
Hang on a minute, I'll post a few more decades of the sim when they're finished running.
You don't need to. Just run 208 times, and see what the difference is. That's the real-world number we have to deal with.
Yes yes, I completely concur with the fact that their chances of winning were not affected. The only thing that affects that is the ball picker.
What I am talking about is what people think they are buying. And what they think they are buying (a totally random selection) is not what they bought (a slightly biased selection). Given that lottery marketing sets out to exploit superstition and poor understanding of probability, I think it's perfectly reasonable for people who bought their tickets that way to feel disgruntled.
Lotteries are all about emotions, feelings, irrationality. I would be willing to bet that many lottery players don't understand that sequential numbers have the same chance of winning as any other set, for example. And lotteries pander to and exploit these sorts of irrationalities. For example, the UK lottery slogan 'it could be you' is almost a lie. It almost certainly will not be you. It could be, but I'd be willing to bet £500 it won't be. It will probably be someone. But not you.
It's almost true that lotteries are all about emotions, feelings, irrationality. The one thing that is not, is how the numbers fall. If people expect that their coupon is filled with random numbers, they have a right to complain when it turns out it isn't the case.
And what you are missing is that it does not matter. The only effect is that there might have been more or less people winning particular pots.
I'd say that's pretty darn important.
