Probability question

clint_silver

Lotto based.

100 people write out 6 numbers from a pool of 1 too 45

Each draw you cross off a number from your 6.

Is there a way to work out wow many draws would it take for someone to cross off their 6 numbers accepting noone is going to get the 6 numbers on the first night?

And then of the 100 people, how many people could theoretically cross off 6 numbers on the same date.

Trying to run a draw based on the lotto numbers, I dont mind if noone wins for a few weeks but what I dont want to happen is for 10 people to win on the same night.

Yakuza

What do you mean by "Each draw you cross off a number from your 6"? What are the criteria for crossing off a number?

clint_silver

Yakuza wrote: »

What do you mean by "Each draw you cross off a number from your 6"? What are the criteria for crossing off a number?

If your number comes up in 6 numbers in a lotto draw, you cross it off your selected numbers, sort of like bingo.

I cant see how it could be worked out as theres a probability that someone could win it the first night if all 6 numbers came up. the side benefit being which case theyed have the winning lotto numbers but thats an aside.

Was trying to see if theres a mathematical way to say from 100 people, someone should win it every 3 or 4 weeks theoretically x amount of people could win it that night.

Yakuza

This would be very hard to derive mathematically, you might be better off doing it with some form of simulation.

Michael Collins

As suggested by Yakuza I think this is a tricky one to solve, since it combines both replacement and nonreplacement type problems.

So, inspired by Yakuza's post, I've tried to simulate this, and it's coming out with an expected number of draws to uncover all 6 numbers of 17.7 i.e. you would have to play it, on average, roughly 18 times before you'd have a set including all your 6 numbers.

From reading your post, however, it seems you're more interested in how many people win on a given day - this is a different question.

The standard deviation of the number of draws before a win might be more useful in this respect, and it comes out to be about +/-8.5 - a decent spread, so it seems unlikely too many would win on the same day.

The above calculations are based on a simulation of 1 million draws, more draws would help the accuracy, but I think the above is fairly close to the analytical expected value/standard deviation - the values seem to have converged to within a significant digit at least.

Incidently, in those 1 million draws, the minimum number of draws required to win was 2, the maximum was 98. So no-one won the lotto in a million tries!*

(Not really surprising since the expected number of plays to win the lotto is about 8 million.)

clint_silver

thank you for the work michael.

Im involved in a sports club that wants to fund raise by playing this sort of game where the idea is that x amount of people (say 100) do 6 numbers. after each lotto draw both wednesday saturday they tick off their 6 numbers if one of the numbers came up in the actual draw.

I hadnt heard of this type of draw before and was wondering realistically how long a draw could go unwon.

I would guess the quicker it is won, the fewer people who will be joint winners.

I was told another club ran it and there was a winner roughly every 4 weeks (unsure whether that's 8 draws) but I think the club would lose out if it started to run longer than that as it's expected to start a new game after each win @ once a month and annual revenues would be calculated on that time frame.