Fri 24 Jan, 2014 12:15 pm
I look after a lottery at a large company. The lottery itself has 2866 members. We hire a guy who has his system online. The lottery is a simple numbers game. Most people pay for 10 numbers. I.e. Joe Bloggs has the numbers 1,2,3,4,5,6,7,8,9,10. There are some people that pay for more, i.e. another guy could have 50 numbers. i.e. 11,12,13,14, and so on to 60.
We sell numbers in multiples of 5 from 10 up to 50. So, some people will have say 25. So someone with 50 shares is 5x more likely to win than someone with 10 shares.
It's pretty simple: If one of your numbers is chosen by the system the guy we hire has, you win.
Each week 7 winners are chosen, with addtion of an extra winner (for a car) every 3 months and 20 extra winners at xmas, so in total 387 winning numbers to be had per year.
There is a lottery member who makes note of people who have won more than once in, say a year, or even a few weeks. He is concerned that there maybe a problem with the system. So he has asked me to look for the advice from a third party, hence why I'm trying this forum.
Below is a list of list of winners that have one more than once in a period of time. It would be great to get some feedback from guys in the know, like I'm sure you guys here are.
Sorry about the format here.
1st column is their shares, 2nd name, 3rd how many times they'v won, and then the period between wins.
25 shares, Mr Miller, Won X 2, in a period of 2 weeks – 14 winning numbers possible
10 shares, Mr Cooling, Won X2, in a period of 1 week – 7 winning numbers possible
20 shares, Mr Smith , Won X2, in a period of 3 weeks - 21 winning numbers possible
10 shares, Murray, Won X2, in a period of 2 months – 56 winning numbers possible
25 shares, Mr Tipping, Won X2, in a period of 11 months – too many numbers to count!
30 shares, Mr Cook, Won X3, Same week and then 10 months apart then (too many numbers to both to count!)
There are about 10 more with the same trend
I would greatly appreciate your feedback here, so I can forward what you come up with to our concerned member!
Thanks a lot in advance!
How about some more details on the selection of numbers. Are you sampling with replacement? In other words, does each number have the same probability of being chosen each time a number is selected? Or, since you mentioned 7 numbers per week, are these sampled without replacement? In other words, does the hired guy select 7 different numbers at once, and does he do that each week (repetitions allowed in the following weeks)?
Are the extras every 3 months done separately, or does the hired guy select 8 different numbers at once? How are the 20 extras handled at xmas?
Are you charging the same amount per number? Does a block of 50 cost 10 times as much as a block of 5?
How many numbers does the hired guy have to choose from?
<edit> After giving this more thought, I'm not sure that any of this matters.
Ignore my previous post. Instead of looking for closely grouped wins by a person, plot each person's wins vs. owned numbers over the life of the lottery. Someone who owns 30 numbers should be winning three times as often as someone who owns 10 numbers.
Thanks very much for your help! You're thinking what I am too: those with 30 shares will be 3x more likely to win. Each winning numbe within the 7 in the week can win more than once that week, so once it's drawn it goes back in 'the hat' to have another chance of winning. So would you say it was strange if say a guy who had 30 shares won twice in a week, then one year later?
Thanks for your help- appreciate it!
I wouldn't necessarily think that's strange. In addition to focusing on long-term win rates for individuals, I'd also look at the long term distribution of the selected numbers to determine if there is a bias built into the selection scheme.