Probability and decision-making – with Annie Duke

This time last year, here on The Value Perspective, we enjoyed an extended chat with Annie Duke, the professional poker player turned business consultant, whose 2018 book Thinking in Bets we have referenced in articles such as How to have no regrets as an investor and Lessons from the controversial 2015 Super Bowl. Her next book, How to Decide: Simple Tools for Making Better Choices, is due out this September.

More recently, we have been running a series of podcasts looking at how people from walks of life beyond investment approach decision-making in uncertain and complex environments. While our conversation with Duke was not originally intended to feature among these podcasts, we hope you will agree its discussion of probabilistic thinking, base rates and a focus on outcomes makes it an excellent addition to the series.

We will also explore the main points of our conversation with Duke over a trio of written articles. Our second and third instalments will look at, respectively, the importance of base rates and how to counter being ‘on tilt’, and outcomes and timeframes in the context of decision-making. For starters, though, we will focus on the benefits of thinking in terms of probabilities – particularly from an investment perspective.

After all, those earlier pieces of ours contain our own impressions of some of Duke’s ideas but how would she herself sum up why thinking ‘probabilistically’ – that is, in terms of probabilities – can be so helpful to the decision-making process? “That is a very big question,” she replies, after what feels like a very big pause. “But really, at its base, every single decision you make is a prediction or a forecast.

Opportunity cost involved

“Or you can think about it as a bet, where you are investing limited resources – you don’t have unlimited time, you don’t have unlimited money and you cannot exercise every single option available to you – so there is opportunity cost involved in any choice you make.” Further complicating matters, she points out, is that it is very rarely the case that a decision will have only a single possible outcome.

As such, Duke argues, any decision is essentially defining “the set of possibilities and how likely each of those possibilities is to occur” – that option A creates one set of possibilities, option B another set and so on.

To her mind, then, thinking probabilistically is the best way to approach life and thus: “The more we can recognise that, when we make a decision, the outcome is always probabilistic, the better off we are.”

Here on The Value Perspective, we do like this idea –  it’s why we have highlighted it in other articles – but we cannot miss the opportunity to push back a little. We can see probabilistic thinking working very well in the context of poker, say, where there are a set number of players and a finite, albeit large, number of card permutations but what about more complex environments with far more unknowns such as, well, investing?

Duke readily concedes the decisions facing a tableful of poker players are going to be simpler than those facing a marketful of investors but goes on to argues the key issue here is not the number of people interacting with each other but the particular problem that must be addressed. “You are trying to figure out, as best as you can, what the probabilities are in terms of what the set of outcomes are,” she explains.

Narrowing the range

So when people – and often they will be investors – tell her they are in competitively tough situations when it comes to decision-making because they are operating in a world where the probabilities are unknown, Duke counters that it is very rare to know the exact probability in any situation. “That’s also true in poker,” she adds. “In almost 90% of the hands you play, the cards don’t actually get turned face-up for you at the end.

“So while the probabilities are theoretically known – as they are when you are investing – you generally don’t find out the answer. That being said, that is not really what your job is at a poker table or in investing – what you are trying to do is get better at narrowing down the range of possibilities, which could literally be somewhere between zero and 100%.”

The more complicated the problem at a poker table – the more people in a hand, say – then, short of picking up a pair of aces, the harder it will be to work out a probability to help decide the appropriate course of action. “What I am trying to do instead is to get down to a range,” Duke says. “I know I can do better than ‘anywhere between zero and 100%’ so how much I can get this down?

“So I start thinking about situations like mine. I am looking for reference classes, for base rates, for information that will help me along. I am looking for feedback from other people, I am looking for things I particularly know about the position I am in and I am trying to merge ‘inside-view’ and ‘outside-view’ information – all to try to get some sense of what the probabilities are here.”

Driver of mistake

The aim, Duke says, is to go from ‘I have no idea’ to a position where you have confidence the probability of something is, say, between 30% and 60% or that you might win 70% of the time or that the odds are maybe two-and-a-half to one in your favour. “Obviously there is still a lot of uncertainty in there,” she says. “You are not anywhere close to 100%.

“But the fact you are really making this commitment to try to get as close as possible to an answer – that helps you with the biggest problem we have. It is not so much that the probabilities are unknown – because they are somewhat known – but the fact the incomplete information we are working with is actually the driver of most of our mistakes.”

As Duke goes on to explain, incomplete information falls into two categories. “There are things you don’t know – that would be on the ‘information asymmetry’ side,” she continues. “But then, within the things you do know, your own understanding of how good that knowledge is – how biased it might be, for example or how confident you should be in it – is actually incomplete as well.”

This knowledge of our incomplete knowledge should fire us up in two ways, Duke strongly believes – to carry out a “really good internal auditing” of what we do know, and to become more efficient at working out what we don’t. “One of the drivers here has to be a total unwillingness to accept that a probability is unknown,” adds Duke.

“As soon as you do not accept a probability is unknown, that puts the quest for better knowledge in the forefront, because it is the better knowledge that will allow you to start narrowing down those probabilities. You just have to be comfortable with the fact – and this is true in poker as well – that there is almost never going to be a precise probability, that it is still going to be a range.”

It could also be the range you end up identifying is actually polarised – that, as Duke puts it, you could be “a really big favourite to win, or a really big favourite to lose, and nothing in between” – but, whatever you conclude, the key here is you are thinking in terms of probabilities. “That desire to uncover what most people are perfectly happy to leave hidden,” she concludes, “is what actually allows the more important piece – that is, the piece about what you do know – to really start to improve.”

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