You're reading: Columns
- The Evening Independent – Nov 27, 1929: Four Perfect Bridge Hands Held On The Same Deal In London Game
- The Montreal Gazette – Mar 15, 1935: Perfect Bridge Hands: Four of Them at One Table Break Up Party
- Toledo Blade – Jul 17, 1949: Perfect Bridge Hand Is Dealt At Party
- The Vancouver Sun – Mar 13, 1954: 4 Perfect Bridge Hands Dealt Simultaneously
- The Press-Courier – Apr 5, 1963: Four perfect bridge hands reported second time in less than a week
- The Milwaukee Journal – Jan 25, 1978: A Magnificent 4 in Bridge World
- BBC News – January 27, 1998 Card trick defies the odds
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Four perfect hands: An event never seen before (right?)
A couple of weeks ago there appeared several reports of an astonishing coincidence. Reports in the Daily Express, The Sun and the Daily Mail tell of a game of whist at the village hall at Kineton, Warwickshire. In whist, one deals 52 cards equally between four players. During this particular game, all four players were dealt one entire suit each.
All three reports refer to an analysis by Dr Alexander Mijatovic of Warwick University. It is always difficult to know how much of what is reported is faithful, but the fullest account of his words was given in The Sun:
The chances of this happening are so humongous that it is almost impossible.
The event can only be compared to natural occurrences.
It would be the same as a person having a tiny drop of water and then finding that same drop of water in the Pacific Ocean.
I would question whether the cards were shuffled the correct number of times but if they were, and the people involved are sure they were, then it is probably safe to say this is the first time this hand has ever been dealt in the history of the game.
It is this last sentence, in particular, that caught my eye: “it is probably safe to say this is the first time this hand has ever been dealt in the history of the game”. I took a quick look on Google News, which indexes old newspapers. I obeyed the following rules: I ignored results when only one perfect hand was dealt (hardly remarkable at all!); I didn’t pick a second result from the same decade (although there were plenty, particularly in the 1920s and 30s) and I didn’t spend very long at all on this. Here are a set of articles I found:
I was particularly taken with an account by Catherine Ford in The Calgary Herald of 29th November 1983, which contains,
Every bridge player fantasizes about the perfect hand – being dealt the 13 cards of one suit – and the perfect game, in which each of the four players receives all 13 cards of one suit. The odds of this happening are 2,235,197,406,895,366,368,301,559,999 to 1, which explains why a plain brown envelope, sealed in 1946, is among my mother’s prized possessions. It contains the cards which dealt one perfect suit to each player.
William Hartson, commenting in The Independent on one such incident in 1998, said:
There are about six billion people in the world. If they all played one hand of cards every five minutes, 12 hours a day, such a coincidence would happen about once every ten trillion years. On the other hand, there are a good few practical jokers around who would love to sneak a doctored pack of cards to four unsuspecting players to create the perfect whist hands when dealt. I know which possibility my money is on.
It is tempting to suggest that someone made these stories up, or stacked the deck as a joke. However, it turns out these assumptions aren’t needed to explain what is happening.
Essentially, Dr Mijatovic was right to question whether the cards were shuffled correctly (so I wonder if this was actually the main thrust of what he said). Basically, whist is a game in which the objective is to stack the deck. A card is played and the other players must follow suit if they can, meaning the cards at the end of the game are particularly well ordered into suits. If the shuffling does not completely randomise the deck (and it often doesn’t) then the probability of a perfect game occurring is increased greatly. There is a good summary of this on the MAA website at Ivars Peterson’s MathTrek.
Samuel Hansen pointed out on the Math/Maths Podcast when we spoke about this that this is still very unlikely and may even be worthy of note in a local newspaper, so we should let people have their fun. He’s right, of course – I am mostly just amused by the claims of just how unlikely this is and the way an event that happens every few years is set up as unlikely to happen during the lifetime of the human race.
Wooden QR code stool by Elena Belmann
Shifting decline of mathematical preparedness?
Last year I wrote On the Decline of Mathematical Studies, and ever was it so, which looked at several examples of people complaining that the new generation of mathematics students were not as well prepared as the current one, with quotes from the late 20th C, mid 20th C. and even from the early 19th C. I wondered whether the problem was one of perception, or whether mathematics teaching could really be in constant (or, as Tony Mann pointed out, cyclical) decline.
I have just read ‘Mathematics at the Transition to University: A Multi-Stage Problem?‘, an essay by Michael Grove (of the National HE STEM Programme, which supports my project) which offers an interesting view on this question. Though the complaint, that students are not prepared for university courses, sounds the same, Michael suggests the root cause and manner in which this problem manifests itself has changed. He backs up his argument with findings from several recent reports. His essay is worth a read if you are interested in this issue.
Having identified a possible root cause for the current situation, Michael also makes recommendations for what can be done to address this and points to relevant work the Programme is doing.
XYZT, Les paysages abstraits by Adrien M / Claire B
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My Erdős number?
People ask, from time to time, what is your Erdős number? For a long time I’ve said I haven’t got one because I haven’t published a mathematical research paper. When I gave this answer to Samuel Hansen last year he told me that any research paper counts, not just those in mathematics. This left me idly wondering and today, having listened to Samuel discussing social network theory on the Big Science FM podcast, I finally decided to have a go. There are a few possibilities, none of which seem, to me, entirely satisfactory.
Short answer: At most 4. Probably.
Long answer:
My list of publications is on my website. I do not appear on MathSciNet.
MathSciNet tells me Edmund Harriss wrote ‘Flattening functions on flowers‘ with Oliver Jenkinson, who wrote ‘Zero temperature limits of Gibbs-equilibrium states for countable alphabet subshifts of finite type‘ with R. Daniel Mauldin , who wrote ‘The nonexistence of certain invariant measures‘ with Paul Erdős. This gives Edmund an Erdős number of 3. Edmund and I are both authors on the paper ‘The unplanned impact of mathematics‘ in Nature, which would make my number at most 4. However, this was a strange piece and although it is listed as one paper on the Nature website it was actually a series of seven short pieces under a common title and introduction. It is difficult to say whether this counts as a collaboration.
From the same root article, MathSciNet tells me Mark McCartney has an Erdős number of 5, Graham Hoare has 4 (although this is via a biography ‘Stefan Banach (1892–1945). A commemoration of his life and work’ in Mathematics Today which may not count (see below)), Juan Parrondo has 5, Julia Collins has 5 and Chris Linton has 4. These all have the same problem as Edmund above and are all greater numbers than Edmund’s anyway.
For another route, MathSciNet tells me Joel Feinstein wrote ‘A fixed-point theorem for holomorphic maps‘ with Richard Timoney, who wrote ‘An extremal property of the Bloch space‘ with Lee Rubel, who wrote ‘Tauberian theorems for sum sets‘ with Paul Erdős. This makes Joel’s Erdős number 3. Joel and I have a paper ‘Media Enhanced Teaching and Learning‘, in the new issue of MSOR Connections. This would make my number 4. MSOR Connections is a mathematics education practitioner journal and I am not sure if this counts.
Stephen Hibberd and Cliff Litton, with whom I collaborated on some of my first articles, including ‘MELEES – Managing Mayhem?’ (Proc. Mathematical Education of Engineers IV), both have an Erdős number of 4. Going this route, mine would be 5. Being a paper in conference proceedings, this seems the most ‘real’ route.
So what are the rules? The Erdős Number Project says:
Our criterion for inclusion of an edge between vertices u and v is some research collaboration between them resulting in a published work. Any number of additional coauthors is permitted. Not normally included are joint editorships, introductions to books written by others, technical reports, problem sessions, problems posed or solved in problem sections of journals, seminars, very elementary textbooks, books on history, memorial or other tributes, biography, translations, bibliographies, or popular works.
The Nature article perhaps doesn’t count then, even if it counts as a collaboration, as it is a history or perhaps even popular article (exposition rather than original research). By this definition, the article with Joel Feinstein does seem to count. We’ve collaborated for a couple of years on using tablet PCs to deliver mathematics lectures, both while I was at Nottingham and since then, and have run several workshops on this topic. This collaboration led to this paper on Joel’s use of this technology in his lectures. So I suppose that would make my Erdős number 4.
Of course, like any social network analysis, the members of a network may not be able to find the shortest path through it. For example, I co-authored with Claire Chambers who has a healthy number of co-authors but as her work now is in education around geography they are not included in MathSciNet. I have other co-authors on my list of publications that don’t appear in MathSciNet but may, as I appear to, have a number. Indeed, any of the authors listed above could have a shorter route found by leaving MathSciNet’s database. So I should say my Erdős number is “at most 4”.
I find you can only go so far down this rabbit hole before it all seems far too preposterous to go on, so I will stop.