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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.

6 Responses to “Four perfect hands: An event never seen before (right?)”

  1. Avatar Peter Rowlett

    I should have acknowledged John Read sent me the original story. I forgot this because it was a while ago and I already had the story on my list for the podcast. John sent it with a note Tom Button had posted on Twitter about the talk we saw on card shuffling at the Maths Jam conference. Sam pointed this out on the podcast as well – one possible explanation could be that there was a new pack of cards and some accidentally perfect shuffling took place.

  2. Avatar Linda Squire

    Best bridge hand I ever picked up was 4 aces, 4 kings, 3 queens and 2 jacks and my partner had the other queen. I was about 10
    at the time, playing with my mother against my dad and sister!!

  3. Avatar Robert MacTavish

    In !965 my paternal grandmother, Katie MacTavish, and her three playing partners all received perfect hands. It occurred in Kitchener, Ontario, Canada.


    Fifty to sixty years ago I wrote a “Letter to the Editor” which was printed in The Star newspaper in Johannesburg, South Africa. The gist was as follows.
    As a hand is played, the cards are placed in tricks of four cards, mostly of one suit. These are placed in overlapping sets, for easy counting. At the end of the hand the next dealer pushes them together and picks them up. Assume the top half has several sets of four Spades, followed by sets of four hearts. The bottom has four sets of Diamonds followed by four Clubs. After the piles are divided at the intersection point, a perfect riffle results in Spade, Diamond, Spade, Diamond, …Heart, Club. A further perfect riffle gives the start of four perfect sets of one suit. The chance of four perfect hands is much improved.


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