The hand you are dealt

A key lesson in strategy, probability and business from a poker hand

You and I are going to play a very short and very simple hand of Texas Hold’em poker. Don’t worry, no prior knowledge is required and no money will change hands!

In Texas Hold’em, the first thing that happens is that each of us is dealt 2 cards - those are private, so only you can see your 2 cards and only I can see mine.

If we let the game continue, what happens next is that 5 more cards will be dealt onto the table so that we can both see them. Ultimately your objective is to build the best hand of 5 cards that you can, picking some combination of the 5 on the table and the 2 in your hand.

But of course the real game is in the betting. At various points, after the first 2 private cards are dealt and at intervals as the next 5 are dealt, we will put money on the table reflecting our confidence at winning. The whole thing might play out in full, with us ultimately showing our cards and seeing who has the best hand, but more often than not it will end before that as one of us decides our hand is rubbish and folds, ceding the money on the table to our opponent to avoid putting good money after bad.

For the purposes of this thought experiment, though, we are going to focus just on that moment when we’ve been dealt our 2 private cards. We are about to commence the first round of betting, and all each of us knows is what we hold in our hands.

Here’s the rub, though. Little do I know it, but you’ve been dealt 2 Aces. That is the best hand you could be dealt - you already have the highest Pair it is possible to make before anything has been dealt onto the table. I, on the other hand, have been dealt a 2 and a 7 - a really poor hand and statistically, if the cards are also of different suits¹, the worst hand possible.

Now that’s not to say that you are bound to win. If we let the game roll on and the 5 cards dealt onto the table includes another three 7s, for example, then my best hand will be “Four of a Kind” and will probably beat you. But that seems unlikely, doesn’t it?

And it is. At this point in the game, with just our private cards dealt, your probability of winning if we let things go forward is about 85%, with mine therefore being only the remaining 15%. Probability is very much on your side.

In the normal run of things, with everyone playing rationally, what would happen now is that you’d put a big, confident bet on the table and I would instantly fold, because we are both smart enough to read the probabilities.

But what if I’m not that smart? What if I put lots of money on the table myself, either because I don’t understand what I’m doing or in some attempt to bluff you? Well, the hand will progress and, as the statistics gods have already decreed, 85% of the time you will win.

But, as we’ve seen, 85% is not 100%. Just under 1 time in 7, I will fluke a win against your better hand.

What will happen next (trust me, I’ve been there) is that you will spend the next half hour kicking yourself for playing that hand, and I will spend the next half hour congratulating myself on my own genius. And we’ll both be making the same mistake.

There is, it is clear to see from this example, a big difference between assessing the probability of something before it happens, and looking back on the same thing afterwards. You playing your AA hand strongly was completely the rational thing to do, and me playing my weak hand strongly was idiocy. The fact that the gods of probability worked in my favour that one time doesn’t change that.

Trying to re-litigate the right strategy when you are looking back from after the fact is illogical and unhelpful - it is like saying that you wasted your money on your car insurance this year because you weren’t in an accident.

So what does that tell us about how to run our businesses? It is a lesson I’ve had occasion to return to many times over the years, and here are some thoughts I take from it:

• If you follow a plan that everyone agrees is the smart call and it doesn’t work out, there is no point beating yourself up about it. It is possible to play the cards of business correctly but not win, and that’s just life.

• It is, though, important to understand in retrospect whether you were wrong in your assessment of the probabilities or were just unlucky - in the former case there is something to learn, but in the latter case there is not.

• All of this is particularly true because, as we saw in a recent post, business life is not a one-shot game - and over the long term, the rational strategy will win out over flukes.

• Be very careful about taking life lessons from a business guru who played a weak 2 7 hand and just happened to win. Their input might not be worth that much! Just because your lottery ticket came up doesn’t mean that ‘buy more lottery tickets’ is good business advice.

It is a mistake to try and draw too much from a simple game, but this point about the difference between evaluating a strategy ex-ante (before it happens) and ex-post (afterwards) is one I see people wrestling with all the time.

Play the smart hand confidently and in the end, even the fickle gods of probability will smile on you.

1. Why different suits? If a 2 7 hand is also of 2 different suits then once the other 5 cards are dealt then the cards in your hand cannot contribute to a flush (5 of the same suit), cannot make a straight (5 cards in a row) and will make only low value pairs - so they are about as unhelpful as any 2 cards could be.