Powerball Odds and Statistics

[umber]

You seriously insulted me and people I'm close to.

To recap: you didn't know who Arcana was, as a self-confessed numbers hobbyist, in a CoH-related forum, in a thread were darn near every other post is a numbers post by Arcana.  There's nothing wrong with that at all but as I said I was a "little surprised" of that being the case and asked "If you don't mind my asking, do you have any experience with CoH?" 

And *that* makes you angry and is considered an insult?  As you admitted in the next post there actually are a couple of CoT developers who never played CoH.  You honestly do not see how that could have possibly have been a valid question?  And I'm at a complete loss of how a question specifically for you somehow become an insult to "people [you're] close to"? 

I'll offer this, no insult was intended.  But I won't offer up an apology for imagined slights.

[Arcana]

I sure hope those who never played CoH pre-shutdown will be behind the content/powers. Sorry, no offense, but you will not capture what makes CoH, CoH. IP sell and all, with someone behind the wheel who has never touched the game before :/

Technically, Geko had no experience playing CoH before designing the powers system.  I'm not sure he had any experience with long division before designing the powers system.  Decimal points and percentages also seemed to be not in his wheelhouse.  Come to think of it, I'm not convinced his calculator had a number four on it.  Not sure what happened to Champions Online during development, except to say you shouldn't get your copy of Excel off the back of a truck in Hong Kong.

I'm not exactly sure why someone who had never played City of Heroes before would volunteer to try to make a replica of that game for little money or recognition, but we should probably cut them some slack until they release actual content to judge.  If I was hired by NCSoft to conduct an audit of the development of City of Heroes back in 2003, I would have recommended they set fire to it for the insurance money.  City of Heroes at launch was a dumpster fire of an MMO, but it was a warm and soothing flame.  It is hard to tell what people will like until they see it.  Fairness dictates that we judge product, and not resumes.

[Arcana]

To recap: you didn't know who Arcana was, as a self-confessed numbers hobbyist, in a CoH-related forum, in a thread were darn near every other post is a numbers post by Arcana.  There's nothing wrong with that at all but as I said I was a "little surprised" of that being the case and asked "If you don't mind my asking, do you have any experience with CoH?" 

And *that* makes you angry and is considered an insult?  As you admitted in the next post there actually are a couple of CoT developers who never played CoH.  You honestly do not see how that could have possibly have been a valid question?  And I'm at a complete loss of how a question specifically for you somehow become an insult to "people [you're] close to"? 

I'll offer this, no insult was intended.  But I won't offer up an apology for imagined slights.

They haven't even released a beta of the game yet, and already they are replicating the experience of communicating with the devs.  That's a good sign?

[umber]

They haven't even released a beta of the game yet, and already they are replicating the experience of communicating with the devs.  That's a good sign?

Back in the CoH forum days there were a coupla incidents where devs said stuff that they probably should not have said.  One in particular comes to mind, an incident where a dev spoke about the PvP player base that was not what one could call an tactful statement (I bet MM3 remembers this one, along with several others here).  Now I didn't care for CoH PvP at all, to me it was a waste of resources to pour into a bottomless pit, the game wasn't built with PvP in mind and would have taken a foundational overhaul to make it PvP competent, but even this non-PvPer saw that posting and went "whoa, there is a person who lacks the customer service oriented skills to be making public statements about his product". 

I suspect avelworldcreator is this sort of developer.  Probably a great guy if you knew him in real life, probably has the best of intentions at heart.  But the impression this reader gets reading his posts is that of someone who is perhaps a little too thin-skinned to be posting in a forum with somewhat limited people skills.  I'm just not sure of what to make of someone who feels the need to brag of their math skills.  Not everyone is cut out for customer-facing duties, nor should everyone be held to that standard.  But these people probably need to be kept out of the public eye as much as possible to prevent missteps.

But looking back I can see avelworldcreator might have had a valid point in one area, in my trying to be a little less laser-focus damning in my critique I ended up painting with way too broad of a brush.  I should not have said that the CoT team could use some PR work when precisely what I meant to say was that avelworldcreator, a CoT team member, could use some PR work.  To all members of the CoT team I will indeed apologize for my careless statement, keep up the good work!  As for avelworldcreator specifically, just from your postings in the past couple of days I do not believe you are serving as a good public face for the CoT team.  If you want to be angry and insulted over *that*, now that I understand.  My impression stands.  But hey, I never cared for Posi's forum postings either so you're in good company.  If you're ever in the Virginia area (after the SNOWPOCALYPSE passes) drop me a message and I'll buy you a beer, see if we don't grind each other's gears as much in person.

[Teikiatsu]

Is it wrong that my inner baby statistician has had to squee a little during these last few pages?

EDIT: I too did not know of Arcana before I came to this forum, though I think my wife did mention 'Arcanaville' when we were working on her guide to the Master of Statesman Task Force.  I wasn't much of a forums guy.

[avelworldcreator]

Nope.  You are multiplying two statistical factors that are not independent factors.  Consider this: suppose the lottery asks the entrant to pick a number from 1 to 1000.  Suppose exactly one person enters, and guesses 12 as his entry.  What are the odds of someone winning this lottery?  One in a thousand.  What are the odds of you being that winner?  The same: one in a thousand.  It is not P/N.

If it was possible to know, out of all the people who entered the lottery, how many different possible winning numbers were chosen by at least one person and that number was n, and the total possible winning combinations was N, then the odds of *someone* winning would be n/N.  The odds that you would be one of them, if you put in only a single ticket, would be 1/n.  The actual odds of you being the winner would then be (1/n) * (n/N).  Notice that ends up being 1/N, which is also the odds of winning the lottery computed directly: you put in one entry, and the odds of that one entry matching the winning combination is 1/N.

You math is still correctly calculated but misapplied.  Somehow, you are invoking the set n, the total nunber of *different* combinations entered out of all the people who enter P.  That quantity has nothing to do with the discussion at hand, but its an improperly defined value in your calculation assumptions.

Arcana, I already spotted my own error.  Of course I multiplied the factors. The percent chance OF a winning draw is applied to the chance OF a given person being the one to draw it. The word "of" indicates multiplication.

There is a number games played, G.
In each game the players act to create a pool of possible winning numbers of size V each game. For the sake of simplification I will treat this as a constant and it will be the same value each game.
In each pool there will be a certain percentage of duplicates, D. Also being treated as a constant for the same reasons as above.
The pool of unique numbers, U is equal to V*(1-D).
p is the percent chance of a specific number sequence being generated in the game drawing.
The chance of a player having picked a specific entry in the pool is 1/V for each game.
The chance of one of the numbers in the pool being drawn is 1-(1-p)^(U*G)

I'm not going to compute the odds of one of the duplicate values being drawn. This is complicated enough as is.

Let's recap. The chance of a given pool producing a wining entry is random with a binomial distribution, meaning the chances of a winning entry being produced increases with each game.
The chance of a given player having that winning entry is random with a flat distribution.
Both random selections are independent of each other.
The odds of two random selections occurring together is the product of their individual probabilities. R=(1-(1-p)^(U*G))/V

The odds of a random individual winning the lottery is 1-((1-(1-p)^(U*G))/V)^G if the same people play each game. The odds of an individual winning changes from game to game within these constraints.

[Aggelakis]

The odds of an individual winning changes from game to game within these constraints.

The odds of an individual ticket winning is 1/V, no matter what. No matter how many games are played, and no matter how many tickets are sold. That number combination has one chance to come up in a set of V numbers. It always has one chance to come up. Every draw, it has one chance to come up. One time.

If it's a drawing out of two tickets, A and B, you'd win statistically half the time if you pick either letter. No matter how many tickets are sold. No matter how many games are played.
** If 600 million people played once, you'd split the winnings approximately down the center, 300 million ish people would win.
** If two people played 600 million times, you'd split the winnings approximately down the center, both individuals winning approximately 300 million times.

This chance of one individual = one ticket = one chance does not change with the number of tickets sold or the potential number pool.

It only changes if one individual purchases more than one ticket. Then their chances go up. Statistically insignificantly after about 4 tickets, but up nonetheless.

[HEATSTROKE]

 YIKES giant walls of text and math!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

[avelworldcreator]

To recap: you didn't know who Arcana was, as a self-confessed numbers hobbyist, in a CoH-related forum, in a thread were darn near every other post is a numbers post by Arcana.  There's nothing wrong with that at all but as I said I was a "little surprised" of that being the case and asked "If you don't mind my asking, do you have any experience with CoH?" 

And *that* makes you angry and is considered an insult?  As you admitted in the next post there actually are a couple of CoT developers who never played CoH.  You honestly do not see how that could have possibly have been a valid question?  And I'm at a complete loss of how a question specifically for you somehow become an insult to "people [you're] close to"? 

I'll offer this, no insult was intended.  But I won't offer up an apology for imagined slights.

To recap: I just started back on these forums after a long hiatus and that was AFTER following a link from elsewhere to this topic and I did so because the topic was potentially relevant to my own work. I read the beginning entry. Skimmed past a number of other entries and focused on the last few pages of more than a thousand such that happened within the last few weeks. I paid attention more to the conversations than the posters even then. This is not enough to evaluate the statistical frequency of a given individual poster or to become familiar with that person or her self-descriptions. Arcana's level of posting in these forums does not relate in any manner or form to the any other person's experience with the City of Heroes game. Your "surprise" was based on overdrawn and egocentric assumptions. You said and asked more in that post than "If you don't mind me asking...". You related my experience, or the potential lack thereof, to the possibility that I and the people involved with the project would have no insight or understanding of the game we are trying to capture the spirit of.  You made an accusation BEFORE you presented that question. Your question was to shift the burden of proof from yourself to me. THAT is what was the basis of insult. If the question had been presented by itself I would not likely have been insulted. But that was not the case and your attempt to compartmentalize your question from the rest of your statements is disingenuous. You accused me of possibly being deceitful or incompetent and they you have the gall to say my insult is imagined?  Take that question and convert it to a statement of what you believed about me and my circumstances at the time. Consider what action were you trying to justify in relation to me or my associates based on my reply. That's right, you were demanding >>I<< take responsibility for your future conduct.

[Aggelakis]

We're going to nip this in the bud... feel free to take this to PMs, but y'all getting dangerously close to personal at this point, so I suggest not even continuing this line of conversation at all. Just FYI I'll delete posts that further it, no matter who's posting.

[worldweary]

YIKES giant walls of text and math!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

If you would keep posting builds this would happen less.

[avelworldcreator]

The odds of an individual ticket winning is 1/V, no matter what. No matter how many games are played, and no matter how many tickets are sold. That number combination has one chance to come up in a set of V numbers. It always has one chance to come up. Every draw, it has one chance to come up. One time.

If it's a drawing out of two tickets, A and B, you'd win statistically half the time if you pick either letter. No matter how many tickets are sold. No matter how many games are played.
** If 600 million people played once, you'd split the winnings approximately down the center, 300 million ish people would win.
** If two people played 600 million times, you'd split the winnings approximately down the center, both individuals winning approximately 300 million times.

This chance of one individual = one ticket = one chance does not change with the number of tickets sold or the potential number pool.

It only changes if one individual purchases more than one ticket. Then their chances go up. Statistically insignificantly after about 4 tickets, but up nonetheless.

Again, I ask that you prove your assertion. You have stated my argument is in error by simply dismissing it as untrue. My analysis is directly based on an understanding of binomial distributions. Please show how a lottery is not a event that has two possible outcomes for a given trial and that each game is not instance of such a trial in a sequence of such.
Your first assertion is that the odds of an individual ticket winning is 1/V no matter what. The error here is that the chance any member of member of V must first be a winning number. The phrase "no matter what" means independent of outside influences but that is not the case. The outside influence in this case is the actual lottery drawing. You ARE correct that the odds of a person having one of the numbers in V is 1/V every time. But there is a chance that two or more people may choose the same set of numbers as well.

Where you get 600mil vs 300mil when the number of combinations of lottery numbers is barely over 200 mil is unexplained. But here is a shocker there is an actual chance of all 600million people all picking a losing number and there is also a chance (much lower but it still exists) that all 600 million people can pick the winning number. Crazy things like this happen I watched one joke about those very kind of odds with dice, throw something like 20 of them, and they ALL came up sixes! Trying figuring the odds of something like that. Not that they all came up with the same number but that it happened right after he did it to prove how unlikely it was to happen. It's something called the "Law of Large Numbers".

I just connected the 1/V chance to the chance that any number in V would be drawn BECAUSE that first chance was dependent on the second. The math of that second selection mechanism is a bit more messy. And it gets equally messy when you play more than once. "The more times you play the more likely you are to win" is a truism. It isn't limited to just four chances to be statistically significant.

[avelworldcreator]

They haven't even released a beta of the game yet, and already they are replicating the experience of communicating with the devs.  That's a good sign?

I hope so. 

[Vee]

Again, I ask that you prove your assertion.
Where you get 600mil vs 300mil when the number of combinations of lottery numbers is barely over 200 mil is unexplained.

ok now you're getting agge confused with me. The 600 i was saying yesterday was based on my faulty memory from the original conversation. I should have known never to not use google as my memory. my memory now tells me it's 1 in 292 million and change.

the 600 million agge just used was as far as i can tell just a large number out of a hat.

[avelworldcreator]

ok now you're getting agge confused with me. The 600 i was saying yesterday was based on my faulty memory from the original conversation. I should have known never to not use google as my memory. my memory now tells me it's 1 in 292 million and change.

the 600 million agge just used was as far as i can tell just a large number out of a hat.

Oh, didn't know that number had been used by you before. I'm actually surprised this conversation got so deep. I'm just a little confused by people saying "you are wrong because of this" just after I found my actual mistake and pointed it out.    I found my goof actually quite hillarious but I guess you have to be more of a math geek to catch it.

[Aggelakis]

Again,

That was the first time I've posted on this subject.

And this is the first time anyone's ever mistaken me for Arcanaville. lol

[Vee]

Except that the mistake we've all been talking about isn't a math mistake but a 'this is how this particular lottery works' mistake. Your catching your own math mistake is the only problem I recall anyone having with your math thus far. I refer you to Arcana's

The fact that you are doing math implies a problem.

[Aggelakis]

The error here is that the chance any member of member of V must first be a winning number.

The whole point of a lottery is at the end, you draw a number. So yes, a member of V must be a winner. Whether or not it is chosen by a player is completely irrelevant. A number is always chosen.

[avelworldcreator]

Except that the mistake we've all been talking about isn't a math mistake but a 'this is how this particular lottery works' mistake. Your catching your own math mistake is the only problem I recall anyone having with your math thus far. I refer you to Arcana's

I found her statement illogical. Statistical analysis without math? That seems akin to doing cooking without ingredients.

[avelworldcreator]

The whole point of a lottery is at the end, you draw a number. So yes, a member of V must be a winner.

At least we hope so!