This is the 11th installment of my weekly poker column in the Economic Times, Range Rover.
A few days ago, a friend rang me up to tell me a bad-beat story. He called a preflop raise in a home game with 33. The flop came A83r. The initial raiser c-bet, my friend raised, villain overbet- shoved for 500bb, my friend called, villain showed ATo. The turn was an ace. The river was an 8. ‘He was 2% to win the hand,’ my friend moaned. ‘How unlikely is that?’ ‘It’s unlikely,’ I replied. ‘But it’s also inevitable.’
That sounds contradictory, but it’s true, once you account for the lens through which you view poker. From a short-term perspective, the beat that my friend got is unlikely: it will happen one in 50 times. But the long view is that over the millions of hands that my friend will play in his life, this beat will happen to him again and again and again. To understand this, allow me to introduce you to a term coined by the mathematician David J Hand: ‘The Improbability Principle.’
In an excellent book by the same name, Hand lays out the Improbability Principle: ‘Extremely improbable events are commonplace.’ This seems counter-intuitive, but Hand elaborates upon it with a series of mathematical laws. The first of them is the Law of Inevitability: ‘If you make a complete list of possible outcomes, then one of them must occur.’ Lotteries are an illustration of this. Let’s say you buy a lottery ticket, and stand a 1 in 10 million chance of winning it. Every single person who has bought a ticket to that lottery has the odds stacked against him – and yet, someone will win: improbably, but inevitably.
Millions of poker hands are played every day across the world, mostly online. At a conservative estimate, let’s assume that every week, 100,000 sets run into top pair. At 50-1 to lose,it’s likely that 2000 of these will be busted. Yours could be one of them.
The next law, the Law of Truly Large Numbers states: ‘With a large enough number of opportunities, any outrageous thing is likely to happen.’ If you play enough poker, you will run AA into a smaller pair repeatedly. You’re supposed to win around 80% of those, so if you play 10,000 such hands, you should expect to lose 2000 of those. And yet, I know people who whimper like a baby every time their AA is cracked by 88. In poker, everything that is unlikely in the short run is inevitable in the long run.
Also consider the Law of Selection: ‘You can make probabilities as high as you like after the event.’ Let’s go back to the previous example of AA being cracked by a smaller pair. Over a sample size of 10k iterations, not only will this happen to you 2k times, but it’s likely that somewhere in there, you will receive that beat 4 times in a row. It would be a mistake to ignore the other 9996 times, select that sequence of four in a row, and whine, ‘My aces got busted all 4 times that I got them today, there’s a 1 in 625 chance of that happening, this site is rigged.’
Hand’s book has more math laws that explain the Improbability Principle, and I’d recommend it strongly to all my readers, not just to poker players. We are pattern-seeking creatures, and tend to give too much significance to coincidences and improbable events. Conspiracy theories and pseudosciences feed upon our misunderstanding of probabilities. Indeed, I think belief in God also relies, to a large extent, on our innumeracy. Perhaps my heresy is responsible for all my bad beats?
Previously on Range Rover: