26 January 2015

Poker & the laws of improbability

A fish taught me a poker lesson

The other day I was chatting to a friend of mine - who is a brilliant mathematician - about improbable things and he told me improbable things are happening around us at every moment; only we ignore their improbability.


He pointed out some amazing facts that I had never thought about – the kind of thoughts that only reside in the minds of numerical geniuses like him.

A fish taught me a poker lesson

I must confess that when he mentioned improbable, I figured he would lecture me on the lottery topic but, as it turns out, there are far more improbable things that happen in our daily lives than winning the lottery, only we don’t notice them.

But let me rewind:

I had just experienced a bad beat playing Poker and the very same guy, the mathematician, had taken all my chips.

I was cursing my luck repeating  ‘not in a million years’ after the river gives him a 7 and completes his inside straight flush.

I knew my full house was dominating the play up until the turn and I could not believe in his fish play as he calls my all-in bet, with absolutely nothing but hopes for a miracle.

Like winning the EuroMillions right? Wrong!

When the miracle happened - to my disbelief - he waved my protests with a smile, calmly grabbed the deck of cards and asked for a pen and a piece of paper.

After a good shuffle, he spread the cards in a neat line across the table, looked me in the eye and asked ‘What do you see?’, ‘Nothing special ‘ I replied. He smiled and said ‘this you are observing is way more improbable than winning the EuroMillions’.

As I gazed in disbelief, he paused, grabbed the pen and paper, wrote for a minute and then handed me a note.

As it was, the odds of a deck of 52 cards being shuffled and presented in that exact sequence were of: 

1 in 80658175170943878571660636856403766975289505440883277824000000000000!

In comparison, the odds of winning the EM jackpot are only 1 in 116,531,800!

The highly improbable had just happened yet I had never realised that event was so improbable.

He then explained that we only perceive the odds when they are presented to us ex ante - as it is with the lottery. When we don’t know the odds before the event our brain simply ignores the improbable occurrences that happen right before our eyes.

He went forward to argue that this perception of probability affects lottery winners that believe to be incredibly lucky, as well as the ones that refuse to play because they don’t realise the probability of their numbers is exactly the same as everyone else’s.

I have to say that, although I was convinced by his argument, I was still not impressed by his fishy Poker play because the odds were clearly against him there.

I voiced my discontent, ‘but how did you know?, You going to tell me that Paul the Octopus foresaw it for you?’.

He again smiled ‘You got your probabilities mixed up’ he replied.

If you remember, Paul’s the octopus in 2010 became world famous for predicting 6 world cup matches, favouring each time one of the sides to satisfy his ingestion needs.

While many deemed Paul a psychic we know he was no more than a hungry sea creature stuck inside an aquarium.

The odds of Paul doing what he did were only 1 in 256. He happened to be the one that did it.

I lost my chips but I learned a lesson and I’ll tell it to you quoting Han Solo in the classic 1979 Star Wars while navigating the Millennium Falcon through an asteroid field.

‘Never tell me the odds!’

The EuroMillions jackpot now sits at €21 million. 

May the probability be with you!