Purple Lottery 1

[pcad]

Exactly, just like the flip of a coin, or the roll of a die.

The only differance is what the probability is for each round. In one case it's 0.94 and the other is 0.5 .

All I report is the probability of surviving X number of rounds in a row. I've never said the probability for a single round is anything other than 0.94 .

If we wipe the slate clean each round and allow people to pick new numbers each round without any knowlage of previous rounds fine, then the past does not matter. But this isn't the case here. To get to the current round you absolutely must survive all the previous rounds and we can't change our numbers midstream. To get there you need to have picked good numbers. Currently the fewest numbers needed to survive is 8. That has been rising steadily during the lottery. It isn't going to decrease either, only increase. What happens when that number reaches 10, 12, 14, 15 ? It's going to become less likely that you've picked just the right 15 numbers to survive that many rounds.

The history is important since you must survive every round to win. Despite this, the probability of surviving each round is the same.

I think we'll have to agree to disagree. We both agree that the odds of a single event is constant and we agree on how to calculate the odds of surviving a number of rounds in a row. We disagree on whether the past rounds have anything to do with who eventually wins. I say the winner is whoever wins the most consecutive rounds. You say it's whoever survives the current round. Of course the number of people in the current round keeps on getting smaller.

If you're correct we may have another 30 rounds to go or more. I don't think we'll get to round 40 in this first lottery. Let's see what happens.

[pcad]

Let's try a different scenario. Let's say a person gets to pick 10 numbers. Now the odds of a single round is about 0.80. The odds of surviving 10 rounds in a row is less than 0.10 . For those with 15 numbers it will take about 30 rounds to get those same odds. Of course the odds of matching in each round is still 0.80 . So there could very well be some people with 10 numbers still in the running. I can guarantee you that people with 7 or fewer numbers have been eliminated. Probably some with 15 numbers have gotten the boot too.

[maztec]

Stop looking at it as the odds of a single person staying in, and instead look at it as the odds of one person in the group being eliminated each week.

[Naz737]

In!

[pcad]

How can we figure those odds if we don't know how many are playing and how many numbers they have ?

[maztec]

How can we figure those odds if we don't know how many are playing and how many numbers they have ?

Odds of the pool versus odds in general. How large of a pool do you need to have to guarantee someone should be eliminated in a specific drawing versus given a smaller pool what do those odds become. And you only reasonably need to run the odds for people with 15 numbers.

Each individual has a 6% to 7% chance of losing each week. How many people do you need in the pool to make it 99% likely someone will lose in any given week. Then calculate the odds of one person in a small group - say 5 people with 15 numbers each - of losing in a given week.

[pcad]

You could have just pointed me to the gamblers fallacy. At least that I can understand. None the less I still like the way the probability decreases as the number of trials increases. As for the lottery, it could be over with the next draw .....or not.

[maztec]

Maybe, but I also wanted you to run the statistics and share them because I am curious what the numbers come out to.

Also, you keep assuming a random distribution of number choices among the entrants. Reweight your odds if you get rid of the random distribution.

As it is, if someone picked the numbers from 1 to 15, then their winning streak is from December 8, 2012 to now. It is amazing how good that set works.

[pcad]

Other than calculating the probability of matching at least one number for a single trial and prob ^ # of trial I haven't done any other calculating.

I'm not imposing any sort of distribution for the numbers each person has picked. I've understood from the beginning that all sets of 15 numbers are equally good. We only find out what the best numbers are after each lotto drawing.

I noticed that the 1 - 15 selection has been surprisingly effective a while ago. You'll notice that there aren't many sets of 15 consecutive numbers that allow one to survive 28 rounds.

Considering that a minimum of 8 numbers are needed to get to round 28, a person with 15 numbers has as many as 7 numbers that could be anything. That's a whole lot of combinations that would get you to round 28. Who knows or cares what the distribution of these non critical numbers are.

Seeing as there's only one number that hasn't come up, it's safe to say everyone has matched 14 or 15 of their numbers at one time or another. But what are the fewest needed ?

I look for numbers which cover as many rounds as possible with the least duplication. I start with the ones with the most occurrences and look for numbers to fill in the gaps. Somewhat trial and error but still doable. Most people will need more than the minimum to survive and that's fine. It does place a lower limit on how many numbers are needed to survive. When that number is 11, everyone with 10 numbers have been eliminated.

Looking at 1 - 15, you don't need all 15 to get to round 28 . You need at least 8 numbers which must include 7, 2, 11 and 12. Adding 3, 8, 1 and 6 fill in the gaps but there are other numbers that could work too. It should come as no surprise that this includes the highest frequency numbers 11, 12 and 3.

[pcad]

Saturday May 25th, 2013
Lotto numbers for the
29th round of the Purple Lottery

5 - 6 - 26 - 30 - 33 - 40 - 43

Still out.

While updating my tables I found a 7 number combo that allows at least one match for all 29 rounds.

The frequency range for today's numbers is 3x for 26 - 6x for 6 .

While an individuals chances for matching at least one number remains the same for each round, the probability for someone with 15 numbers to match 30x in a row is 0.13 .

Personally, I think there'll be a 30th round for this first lottery. Good luck on Wednesday.