**A**nother outcry after an “impossible” lottery result that “must” be fraudulous! Obtaining the sequence 5,6,7,8,9,10 on the Tuesday December 1, 2020, draw of the Souht-African Powerball is indeed a low probability event. Just like obtaining any fixed sequence on a specific day for a specific lottery system. As I am unsure the last number has to differ from the others or not, consider the approximation where the 6 numbers are drawn uniformly without replacement from the first fifty integers. The number of outcomes is then approximately 16 millions, making any fixed outcome having a chance of 6 10⁻⁸ of happening for one draw. However, the psychological impact of an “impossible” lottery result would have been the same for any sequence of 6 consecutive numbers, which makes the event happening with a probability of approximately one chance in 400,000. Not so staggering then! And considering the repetition of lotteries, space- and time-wise, it takes roughly 40,000 draws for a consecutive sequence to be drawn with probability 10%. Which means 16 years if considering each US State having a draw every week…

## Archive for lottery

## (im)possible lottery outcome

Posted in Kids, Statistics with tags coincidences, lottery, Powerball, South Africa on December 27, 2020 by xi'an## off to Vancouver

Posted in Mountains, pictures, Running, Statistics, Travel, University life with tags ABC, ABC-Gibbs, approximate Bayesian inference, British Columbia, colloquium, Institute of Applied Mathematics, lottery, NeurIPS 2019, Pacifics Institute for the Mathematical Sciences, PIMS, Squamish, The Chief, UBC, University of British Columbia, workshop on December 7, 2019 by xi'an**T**oday I am flying to Vancouver for an ABC workshop, the second Symposium on Advances in Approximate Bayesian Inference, which is a pre-NeurIPS workshop following five earlier editions, to some of which I took part. With an intense and exciting programme. Not attending the following NeurIPS as I had not submitted any paper (and was not considering relying on a lottery!). Instead, I will give a talk at ~~ABC~~ UBC on Monday 4pm, as, coincidence, coincidence!, I was independently invited by UBC to the IAM-PIMS Distinguished Colloquium series. Speaking on ABC on a broader scale than in the workshop. Where I will focus on ABC-Gibbs. (With alas no time for climbing, missing an opportunity for a winter attempt at The Stawamus Chief!)

## NeurIPS without visa

Posted in pictures, Statistics, Travel, University life with tags Addis Abeba, Africa, Canada, conferences, Ethiopia, ethiopian food, Human Rights, LGBT rights, lottery, NeurIPS, Synced, USA, Vancouver, visa on September 22, 2019 by xi'an

**I** came by chance upon this 2018 entry in Synced that NeurIPS now takes place in Canada between Montréal and Vancouver primarily because visas to Canada are easier to get than visas to the USA, even though some researchers still get difficulties in securing theirs. Especially researchers from some African countries, which is exposed in the article as one of the reasons the next ICLR takes place in Addis Ababa. Which I wish I could attend! In the meanwhile, I will be taking part in an ABC workshop in Vancouver, December 08, prior to NeurIPS 2019, before visiting the Department of Statistics at UBC the day after. (My previous visit there was in 1990, I believe!) Incidentally but interestingly, the lottery entries for NeurIPS 2019 are **open till September 25**, to the public (those not contributing to the conference or any of its affiliated groups). This is certainly better than having bots buying all entries within 12 minutes of the opening time!

More globally, this entry makes me wonder how learned societies could invest in ensuring locations for their (international) meetings allow for a maximum inclusion in terms of these visa difficulties, but also ensuring freedom and safety for all members. Which may prove a *de facto* impossibility. For instance, Ethiopia has a rather poor record in terms of human rights and, in particular, homosexuality is criminalised there. An alternative would be to hold the conferences in parallel locations chosen to multiply the chances for this inclusion, but this could prove counter-productive [for inclusion] by creating groups that would never ever meet. An insolvable conundrum?

## Brad Carlin’s take on Warren Buffett’s $1 billion offer [guest post]

Posted in Kids, Statistics, University life with tags Brad Carlin, lottery, March Madness, NCAA, Warren Buffett on January 25, 2014 by xi'an*[This is a guest post from Brad Carlin, prepared for a news channel that never called back. If, like me, you have no idea of what March Madness means or of the meaning of brackets and seeds in this context, read the insert below first. Brad kindly added it upon my request…]*

In mid-March every year, the national champion in US college basketball is decided through a 6-round tournament called “March Madness”: 64 teams are seeded into the tournament based on their perceived strengths, with 1 seeds going to top top 4 teams and 16 seeds going to weakest teams. A couple years ago the tourney added a partial 7-round, with just 4 more teams added (winning one of those those 4 “play-in” games merely gives you the right to be one of the 64 — and probably to lose in the next round to a top seeded team).

Anyway, every year Americans fill out “their brackets”, which means once the tourney is announced, it’s very very common to participate in a pool (often at your office) where everybody throws in some small amount of money ($10?) and submits a prediction of how *all* 67 games are going to come out, with the guy whose sheet most accurately predicts the actual outcome winning the money. Pool sheets are typically scored in some systematic way, the most common being 1 point for the first round (or play-in game, if included; many poolmasters just give you the play-in game winners for free), 2 for the second round, 4 for the 3rd, 8 for the 4th, and so on (the exponential award system reflecting how hard it is to keep getting the predictions right as the tourney progresses). Office pools have become so popular that it’s estimated that March Madness is now the most wagered-upon event in the world, passing even the Super Bowl (American pro football championship). Strictly speaking, as a form of gambling office pools are illegal in most states, but the cops generally look the other way provided the poolmaster isn’t taking a cut of the pot as a fee; all moneys collected must be distributed in prizes.

There are websites to tell you how best to fill out your poolsheet; poologic is one that I’ve been involved with, at least in some small way; see my name on a paper on the bottom of the program’s info page. My university has allowed (nay, encouraged) me to speak to reporters about March Madness when it comes around every year, and this year the big story is that Omaha billionaire Warren Buffett is underwriting an ad campaign by Quicken Loans that will pay you $1B if you get the whole bracket completely right — all 67 games, even the play-in games. The odds against this are astronomical (even with 10 million players), so my initial reaction was it’s not a very interesting problem; as Jeff Rosenthal might say, you’re more likely to be struck by lightning on your way to handing in your pool sheet than you are to win the prize. But the part I did find interesting is speculating about how much Mr. Buffett (the 2nd or 3rd richest man in the nation, and a very shrewd investor) charged Quicken for his agreement to underwrite (ie pay off the best if by some miracle somebody actually won). The blog post below suggests he probably only needed to charge about $78k to make the bet “fair”, but in fact he probably charged much, much more than this — a fee he will in all likelihood keep and smile as he walks to the bank.

**Warren Buffett, Quicken Loans offer $1 billion for a perfect bracket during March Madness 2014**

Hey, want to win $1 billion? Well, of course you do! All you have to do is fill out a perfect bracket for the NCAA men’s basketball tournament otherwise known as March Madness, and billionaire businessman Warren Buffett and Quicken Loans will send you $25 million a year for 40 years.

No big deal, you say? Think again: there are roughly 148 *quintillion* ways to fill out your bracket, the result of having to make 67 picks (the 63 games in the tournament proper plus the 4 “play-in” games).

Even though some of these picks are easy to make (say, that a 16 seed will not defeat a 1 seed, since no 16 has ever won a game in the men’s tournament), the odds of successfully completing a perfect bracket are astronomically small — somewhere between 1 in a billion and 1 in *128* billion.

So you’re saying there’s a chance? Yes, but a very slim one at best.

Brad Carlin, Ph.D., is a professor of biostatistics in the School of Public Health at the University of Minnesota and has been following this story since it unfolded. “This is a fascinating case, especially for me as a statistician long interested in NCAA tournaments and wagering. Mr. Buffett is essentially acting as the insurance company for Quicken, and it’s fun to speculate on how much he charged Quicken for this ‘coverage’.”

Rules of the contest specify only the first 10 million participants who register will be allowed to submit brackets. Assuming independent players each submitting one entry, standard probability calculations reveal the probability that at least one of them will achieve perfection. Multiplying by $1 billion produces the “premium” Mr. Buffett would need to charge Quicken to exactly cover the risk.

However, this premium varies widely depending on how hard you assume a perfect bracket is to achieve. Prof. Ezra Miller of Duke University suggests a skilled player would have a 1 in a billion chance of perfection; there is about a 1% chance that at least one of 10,000,000 such players would end up perfect. This leads to a premium of $1B x .01 = $10,000,000, a tidy sum indeed. However, Prof. Jay Berger of DePaul University thinks even a skilled player would have at best a 1 in 128 billion chance of perfection. The chance of at least one of 10,000,000 such players beating Mr. Buffett is only 0.0078%, leading to an insurance premium of just $78,000 – a relative pittance. Neither Mr. Buffett nor Quicken will reveal the actual premium, but it seems likely to be much closer to $10M than $78K; Quicken is donating $3M for home loans and other charitable causes as part of the promotion regardless of whether anyone hits perfection or not.

Carlin adds Mr. Buffett’s risk is probably even lower than this due to the lack of independence among players. “The best way to beat Mr. Buffett here would be to enter the 10,000,000 most likely pool sheets, which can be computed from point spreads and team computer ratings once the brackets come out.” But instead, Carlin predicts the public will likely do as they always do: overvalue “conventional wisdom” and overbet the favorites (higher seeds) in the tournament, leading to many pool sheets that look largely – or perhaps even exactly – alike. “Positive dependence among the 10,000,000 entries makes it even easier for Warren to hang onto his billion.”

Regardless of how they make their picks, odds, participants are going to have to overcome monumental odds to rake in the prize. For those who decide to get involved anyway, Carlin counsels diversity: “Don’t be afraid to pick a few upsets; unlike most March Madness challenges, here the goal is perfection, not merely point accumulation. Take more than a few chances to make sure your sheet differs from the other 9,999,999.”

*For more from Carlin on picking March Madness winners, see this past Health Talk blog post.*

## Mr Meyrowitz’s glasses

Posted in Statistics, University life with tags blogging, coincidence, CollegeBoard, France Soir, Le Loto, lottery, Statistics, teaching on October 23, 2011 by xi'an**T**oday, I found a site entitled Mr Meyrowitz’s Class that links to my first post on coincidences in lotteries as an example of “fatal error”. This seems to be part of a student’s assignment, apparently for the CollegeBoard programme, with 10 minutes allocated to students to find my “fatal error with decimals and probabilities”… As there is no hint, I wonder where my fatal error stands: I could not find it after those 10 minutes of intense searching and recomputing. Maybe Mr Meyrowitz actually needs new glasses to spot the difference between a 1‰ chance and a 1% chance… (Which actually misled a few other readers of the post.)

**Q**uestion 6) in this assignment also sounds very much inspired from another of my posts on coincidences in lotteries *[although not acknowledged in the assignment]* since the question refers to the same original France Soir article in French. The question is however rather vague: “do you suspect him of cheating?” and it shows a lack of knowledge about French loto where cheating is [close to] impossible. It is certainly *not* recommended as an exercise for beginning students in probability or statistics. *[Actually, in my opinion, the whole assignment is poor, being either imprecise, e.g question 7), useless, as for question 4) “Pick one topic that you understand very well and one that you do not understand well” (!), or plain wrong, as for question 2)…]*