Hi can anyone help, I have put all the birth dates from the last 75 years in draw and twice a day I pick a winner. Assuming I have 22000 members of which 400 visit my establishment every day-you have to be in the building at the time of the draw to win if not it rolls over.
Can anyone tell me what the odds are of someone winning or how many draws will be needed until a winner is produced. I thought that it would have been won at around 150 draws-at the momnet we are on draw 223.:confused: .
Please let me know where I am going wrong.

Do you use a range of birthdays that corresponds to the age of the members (or are you using birthdays up to 2006 when most people are in their 30's or older) ?

If so 30 years worth of birthdays are not going to match anyone

You also have to take into account that even though 400 people visit per day, not all of them are there when you make the drawing. However, knowing when the drawing will be will cause there to be more than average number of people present during that time. This is more of a statistical question than a probability question I would say. At a minimum you'll need to tell us how many people are typically present when you draw the birthday. Total # of members doesn't really matter. Age distribution of members doesn't really matter (unless maybe you want to figure out the probability of more than 1 person with the day you choose).
I think: (assume everyone has a different birthday which is obviously not true)
P(paying out on a given day)=(#people at your store)/(#dates in the drawing)
I guess you have about 27000 dates and maybe you have 30 people in your store at the time of the drawing
P(paying)=30/27000=0.0011 so it should take about 900 days to pay on average. (someone else should really confirm my results and math, my probabilities are rusty)

if you want to speed up the process you could let someone win if they matched the month and year but ignore the actual day. For this you'd have about 900 unique dates so it should take about 30 days to find a winner that way.

Thanks for the reply, we do two draws a day one at 7pm when there are normally 180 customers. We then do the second draw at 11pm with about 300 customers in the building.
I hope this helps.

OK, so add those together, 480 people per day. 480/27000=0.178 and that seems like it should be only 56 days. You may be suffering from bad luck :) or good luck since you haven't actually had to pay out yet

That's ridiculous bad luck though? Assuming gaussian distribution of number of days played to day that something is won, a game not being won until 4 times the mean is very unlikely?

Where's my math wrong? I'm not at all sure that I haven't overlooked something important.

I still say if his club members are mostly in a certain age range (60's and 70's) and he's pulling birthdays in a 75 year range then this would make sense, about 2/3rds of all the birthdays pulled won't match anyone.

I still disagree though :)

so if there's 5 people who are all in their 70s at the store at the time of the drawing there is a different probability of paying out than if there are 70,60,50,40,30 year olds in the store?

Well I mean if everyone (or more realistically most people) in the store are in their 60's, 70's (for example) and he's pulling birthdays from the 1930's to the present day at random then it makes sense.

in 75 years there are 23275 possible birthdays, if the actual people attending are in a 20 year range that's only 7300 birthdays. Therefore 69 % will immediately match no one. If there was a perfect sampling from the last 75 years (if all 180 people there were of ages perfectly spread across this 75 year range) the ods would be 1 in 68 of having your birthday drawn. Taking into account that 69% of birthdays drawn will not match anyone this bring the odds down to 1 in approximately 400 thereby explaining this.

Of course my calculations are based on an assumption that this club (in general) caters to a certain limited age group. The occasional person younger than the "normal" age of members can throw off the calculations a bit.

but the range does not matter, only the actual birthdays matter. 20 people still have 20 birthdays, no matter what the delta between the earliest and latest dates are. (as I said earlier, I'm totally ignoring the possibility that people have duplicate birthdays).

my vote is that some part of the process is being administered incorrectly. The dates are in the wrong range, they're not pulled randomly, no one is paying attention or cares... the list may go on.

I was agreeing, you said the problem is administrational, the dates are in the wrong range, that was my point, if he is using birthdays in the 80's 90's and up to today and no one in this club is in their 20's or younger this will screw up the likelihood of drawing a birthday that will match someone.

I still disagree. Your "69% will immediately match no one" is not accurate. If there's X people (with different bdays each) and Y total dates then Y-X dates will not match anyone, it doesn't matter if all the Xs are next to each other or spread out. When I said "the dates are in the wrong range" I guess I was a bit confusing. I mean that he thinks he did the last 75 years but really missed a chunk or duplicated a chunk or did the 1800s or something crazy like that. If he really has every date from the past 75 years then it doesn't matter the age range of the customers. I guess the only way the customer range would matter is if he's working at a retirement home where a large number of people are over 75 and therefore will never win no matter what number is pulled.

I think his problem is that no one is paying attention to his drawing and so he doesn't have 180+400 people per day but more like 100 people per day. Or... having bad luck. With a sample size of 1 it is really impossible to say. Another problem would be if he is discarding the date each time he removes it from the group. Then each day would make the next day less likely to produce a winner.

as an aside, I wonder how he produced all these dates. Did he print them on paper and cut them out with scissors? Are they in a bucket or box of some type? How big would it be to hold over 27000 dates?

additionally, I ran a simulation with ages from 0 to 75 and 65 to 75 and both give essentially the same results. The average number of days to find a winner is somewhere in the 56 range. There's a pretty big variation and I didn't run it long enough so that it settled down totally. I only ran about 1000 games for each. I've attached my tcl program if anyone cares to look at it. It was quick and dirty so expect the worst :)

Attachment 2869

Of the 400 people who are there, they have a 1 out of 68 chance to win. But that could be

Totally wrong.