Four card players were astonished to pick up identical straight run hands in a bizarre fluke calculated as a 61 billion-to-one chance.

So what are the odds of that happening then?

Actually, about one in two or thereabouts.

It\’s one of these little things I like about probabilities. Sure, the likelihood of any individual being hit by lightning is pretty low, but there\’s lots of people out there so there are some each year.

Even if the efficient markets hypothesis is, in its strictest form, correct (you absolutely cannot beat the market except by chance) there are enough people attempting to do so that Warren Buffet\’s success is just about explainable by chance (no, I don\’t believe so and do not believe the strictest form of the EMH).

And our card hands? Sure, any specific deal has this one in 61 billion chance (although I would be wary of that calculation myself, for it\’s conditional. By the time you\’ve dealth the 51 st card then the 52 nd is obviously known, when dealing the 51st you\’ve a 50/50 chance of completing the runs etc. Don\’t know whether they did the calculation that way or not.) but how many hands are dealt in a year?

Despite the unlikely outcome he calculates that an identical deal should happen somewhere in the world about once every year.

The calculation is based on an estimate of 10 million people playing cards around the world every day, with each game requiring 10 deals.

That means 36,500,000,000 deals take place each year.

A 60 billion chance has a one in two probability of happening in 30 billion events.

“a bizarre fluke calculated as a 61 billion-to-one chance”

Actually, of course, any deal has exactly the same likelihood as any other deal. The chance of next week’s lottery result being 1, 2, 3, 4, 5, 6 is the same as any other, and the chance of the following week’s also being 1, 2, 3, 4, 5, 6 is also the same as any other because they’re independent events. However, it’s very unlikely that two consecutive weeks’ results will be the same.

Odd stuff, probability.

Except all the card players are not playing the same game.

I know someone who was playing bridge and another player was dealt an entire suit. He had been to the bathroom while dealing and had just returned so he placed the cards on the table and demanding to know who was playing silly buggers.

Kicked himself after.

(Admittedly it sounds apocryphal but that is what I was told by a moderately credible source)

@So much for subtlety

You have to admit, though, that by far the most probable explanation is that somebody was indeed playing silly buggers.

“The chance of next week’s lottery result being 1, 2, 3, 4, 5, 6 is the same as any other”

Apparently though its not a very lucrative outcome as there (at least I remember this back in the early days of the lottery) are something like 20,000 people who choose it to make a point, and so if you win 6 million quid you’ll only get 3,000 each.

3oo each, even.

Er, no!

There’s about a 40% chance that the event will happen at least once and about a 30% chance that it will happen exactly once. The average number of occurrences (if you repeat the experiment a large number of times) will tend to a half.

The actual number of occurrences has (to within a gnat’s whisker) a Poisson(0.5) distribution.

Apologies for the mistaken use of angled brackets in my previous comment.