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View Full Version : "non-random" raffle on Empire..what are the odds

Uglyowl
09-25-2005, 01:09 PM
web page (http://forumserver.twoplustwo.com/showflat.php?Cat=&amp;Number=3490029&amp;page=0&amp;view=colla psed&amp;sb=5&amp;o=14&amp;fpart=1)

There is an argument about the odds of the 10 winners coming from the same part of the alphabet in this raffle.

09-25-2005, 01:23 PM
Haha I was waiting for this.

10 winners, Aceberber through to CaesarDoggy. Assuming equal distribution of names on the alphabet (A-Z), that's roughly 2.1/26 of the alphabet (all As, all Bs, beginning of Cs). To odds of getting that ten times consecutively should be:

(2.1/26)^10

= (1.18 * 10)^-11

or roughly 1 in 100 billion.

BruceZ probably has some nCr crap though /images/graemlins/grin.gif

edit: I had a look at your analysis and it should be more accurate since you took the sample of actual names on the site. Either way it's a HUGE number. No question their randomization algorithm was [censored] up. I can think of a couple of ways code could be written that would produce a sample like this. One possibility is that the random integer the system returned each time was limited to 32,000 (if it was a code default, or they used the wrong integer type, or some guy missed a 0 in the multiplier /images/graemlins/grin.gif), which would sample about 13% of 250,000 players names stored alphabetically. Seems about right?

jman220
09-25-2005, 01:56 PM
[ QUOTE ]
Haha I was waiting for this.

10 winners, Aceberber through to CaesarDoggy. Assuming equal distribution of names on the alphabet (A-Z), that's roughly 2.1/26 of the alphabet (all As, all Bs, beginning of Cs). To odds of getting that ten times consecutively should be:

(2.1/26)^10

= (1.18 * 10)^-11

or roughly 1 in 100 billion.

BruceZ probably has some nCr crap though /images/graemlins/grin.gif

edit: I had a look at your analysis and it should be more accurate since you took the sample of actual names on the site. Either way it's a HUGE number. No question their randomization algorithm was [censored] up. I can think of a couple of ways code could be written that would produce a sample like this. One possibility is that the random integer the system returned each time was limited to 32,000 (if it was a code default, or they used the wrong integer type, or some guy missed a 0 in the multiplier /images/graemlins/grin.gif), which would sample about 13% of 250,000 players names stored alphabetically. Seems about right?

[/ QUOTE ]

I would think that less names begin with A's B's and C's especially when compared to letters such as RSTLNEP etc. etc. Regardless, this clearly wasn't a random drawing, thats a hell of a stastical outlier.

09-25-2005, 02:30 PM
I would have thought the same, however OP did a sample of a large tournament and came up with 13.8% that fall in the range, which comes out to about 1 in 380 million odd.

If anyone is interested, here are two ways this mistake could have happened.

1. Database query.

It's possible they used a software program to do a query on their player database, but either the function they used or the array they put the data into could only hold 32,000 or 64,000 names. This is common for certain databases and query programs. Given the 13% figure, and the fact that they probably have in the order of several hundred thousand to a million players in their database, you can see how the numbers match up.

2. They selected 10 random numbers using an RNG and matched them with player IDs

An RNG usually returns a number between 0 and 1, which is the mulitiplied by whatever you wish to get a random number range. For example, if you wish to get random numbers from 1-10, you multiply the output of the RNG by 10. It's possible that someone missed a digit in the mulitplier (say 54284 instead of 542874), then you'd only get around the first 10% of names selected.

If there is 10,000 to 1 chance of someone making a mistake like this (and having spoken to customer service, I'd say that's quite conservative), then it's around 38,000 to 1 this is mistake and not a random fluctuation (using Owl's numbers).

Case closed as far as I'm concerned.

PrayingMantis
09-25-2005, 03:36 PM
[ QUOTE ]
No question their randomization algorithm was [censored] up.

[/ QUOTE ]

While your calculation is very clear, I have a very difficult time understanding how exactly you got to the quoted conclusion. In fact I don't see how can any conclusion about the goodness of an RNG be a result of such an "experiment". As I said in the original thread, the probability of getting _any specific group_ of names is equal to the probability of getting _any other specific group_ of names.

It is exactly the same as tossing a dice n times, getting a sequence of n heads in a row and then say: "this dice is clearly biased". Well, it might or might not be biased. The fact that you have a "suspicious" sequence is far from being enough in order to make such a strong assertion about the "randomness" of it.

Here's maybe another perspective to think about it:

Suppose Empire randomly chooses names, with a very good RNG or whatever, and the result is exactly this group of names that goes from A to C. Now they obviously think (like most of the people on 2+2, it seems) that this result won't look random, or in fact isn't random for some reason, so they "delete" it and start again. Won't you agree that there's some problematic aspect in even considering that there's something "wrong" (i.e, non-random) with the first group, if this is the practical result?

To be clear: I'm not trying to defend Empire or anything, as far as I care it could be any other site or company or whatever. I'm only interested in the pure theoretical discussion.

I'll be very interested to read your reply and more opinions.

Uglyowl
09-25-2005, 06:59 PM
The odds of winning powerball are 1 in 146,107,962. Compare this to the odds of the alphabet abnormality and I think it is clear that something is amiss here.

Jimbo
09-25-2005, 09:33 PM
[ QUOTE ]
The odds of winning powerball are 1 in 146,107,962.

[/ QUOTE ]

And yet someone still wins.

09-25-2005, 11:38 PM
[ QUOTE ]
No question their randomization algorithm was [censored] up/

[/ QUOTE ]
This was a poor choice of words on my part. Did you read my second post?

Firstly let me say that this case doesn't involve their RNG or software used in gameplay. I'm 99.99% certain that's random or close enough to random that it doesn't matter.

Drawing the winner would have consisted of an employee sampling a database or writing a piece of code to pick random numbers between 1 and N(the number of players who took the survey). There are many ways this can go wrong, some of which are listed above in my second post. It's not a long shot to see how this could happen.

[ QUOTE ]
It is exactly the same as tossing a dice n times, getting a sequence of n heads in a row and then say: "this dice is clearly biased"....

[/ QUOTE ]
Not really. The difference in this case is that the results generated are exactly what's you'd expect if someone screwed up in picking the numbers. If the names went JJKKKKLLLL I'd be less inclined to believe there was a mistake, even though it's also a long shot. The result that happened in this case is very explicable in terms of another hypothesis, and even given 10,000 to one against them making such a mistake, that leaves 38,000 to 1 in favor of the mistake hypothesis. We're talking huge numbers here. Additionally, there aren't that many ways in which randomly selected names can look incredibly suspect.

[ QUOTE ]
this result won't look random, or in fact isn't random for some reason, so they "delete" it and start again. Won't you agree that there's some problematic aspect in even considering that there's something "wrong" (i.e, non-random) with the first group, if this is the practical result?

[/ QUOTE ]
I agree. However, if they can prove that the draw was flawed in some way, then they should redo it IMO. Just being a long shot with no further evidence is not enough though.

Finally, if there are an infinite number of multiverses, then in every 380 millionth one this is going to happen and someone will cry bullshit! Maybe Empire customer service just happened to be in the wrong multiverse that day. /images/graemlins/grin.gif

09-26-2005, 12:45 AM
[ QUOTE ]
[ QUOTE ]
The odds of winning powerball are 1 in 146,107,962.

[/ QUOTE ]

And yet someone still wins.

[/ QUOTE ]

Someone wins powerball because there are millions of entrants playing several games each. Each powerball draw is equivalent to Empire holding a raffle hundreds of millions of times.

Have you ever seen the powerball numbers come 1,2,3,4,5,6? How about 2,4,6,8,10,12? These are the kind of odds we're talking about. However in this case we can see the draw happening (the balls getting tumbled around), so this would most likely be random and just a freak occurrence. In the Empire case, a software program or some employee written code is picking the numbers.

09-26-2005, 07:30 AM
[ QUOTE ]
[ QUOTE ]
The odds of winning powerball are 1 in 146,107,962.

[/ QUOTE ]

And yet someone still wins.

[/ QUOTE ]

LOL but the odds of "someone winning it" are not that remarkable if enough are trying

AaronBrown
09-26-2005, 09:51 PM
It's not quite as bad as some people suggested.

The 90 runners-up seem to be a reasonably random selection of names. If we assume these are in fact random, then the 10 winners are all in the top 22 of the names by alphabetical order (AceBarber not only won, he was a runner-up as well). However, the 12 other names in the first 22 by alphabetical order averaged 54th place, what you would expect since they had to be between 11 and 100. The 78 names not in the top 22 seem to be randomly placed as well.

That suggests Empire drew 10 names at random out of the first 22% of the names in alphabetical order, then selected the runners-up at random. It's easy to see a programming mistake that could let that happen.

I'm ignoring the fact that the 9 winners second-place winners are in alphabetical order, they might have been listed that way after selection. The first-place winner is the first among the 10 in alphabetical order (although only second among the whole group).

If you put weight on that fact, an obvious hypothesis is the programmer considered the names in alphabetical order, then flipped a coin to decide whether or not they got a prize. He may not have used a computer at all. When he was up to 10, he could have tossed all the remaining names in a pile (plus AceBarber's) and picked 90 at random.

If you are picking names at random, the chance of picking 10 among the first 22 in alphabetical order is 1 in 26 million.

09-27-2005, 03:29 AM
The flaw in your analysis is that you assume the 100 people were the only entrants. The 22% figure is not representative of the proportion of the sample (Aceberber - Caeser) in the entire population of names. According to research done by OP 13% is closer.

Even so, it's still a HUGE number.

AaronBrown
09-27-2005, 06:56 PM
I didn't see OP's analysis but I wouldn't call my assumption a "flaw." I stated the assumption. It's one way of guessing the answer. It's true that the larger the number of people in the sample, the lower the percentage fraction, but also the less that fraction declines as you pick people. It doesn't make that much difference to the conclusion.