I try to do the same, personally I find it challenging. Another aspect that can throw a wrench in things is that even bets with negative expected value can sometimes be good to take because their payoffs are anticorrelated with other multiplicative bets that you take. Hence if you take the negative EV bet, the Kelly bet size for the combination of the two becomes bigger than it would be with just the other bets alone and the growth rate increases too.
Thanks for this post! This seems like good advice to me.
I made an Anki card on your three "principles that stand out" so I can retain those ideas. (Mainly for potentially suggesting to people I manage or other people I know - I think I already have roughly the sort of mindset this post encourages, but I think many people don't and that me suggesting these techniques sometimes could be helpful.)
Just wanted to say that I'm grateful that you share your struggles with anxiety openly :) The post's ideas gave me something to think about, although personally my main struggle is often with things that although I rationally know are wrong already, my brain refuses to acknowledge correctly.
In many cases it is hard to tell whether something that had a bad outcome was actually a good bet.
You enthusiastically implemented a good-seeming plan, something went wrong, and a bad outcome resulted. Does it make sense to say 'this was a good bet, I should be rewarded in spite of the bad outcome'? The correct response might instead be 'actually plans that seem like good bets tend to lead to bad outcomes, I should be much less enthusiastic about doing that.'
I agree that this is a risk. But as I tried to address in the post, I think there are many cases where this is worth the risk. In particular, I think there's a fairly large class of bets where I expect many bad outcomes before an occasional good outcome (eg going on dates, applying for jobs),
There are two additional activities that can help:
Games are a great way to practice acting with uncertainty, and experiencing "I made the best decision and still lost" in a low-stakes environment. Poker is not ideal, since you often don't have all the information, even in hindsight, to know if you made the best play - look for games where you make choices, then have the random outcome / hidden information / simultaneous choice reveal. Any cooperative board game (eg Pandemic) is great for this, since they are specifically callibrated to not be always winnable, and they are simple enough to do hindsight analysis and know if you made the best possible choices (at least in the endgame).
Ask someone else "what would you do (or would have done) in this situation?" Especially for big decisions, an actual outside view is far better than attempting to take the outside view from within your own head.
For a more in-depth discussion, you can listen to this podcast episode: https://lrcast.com/limited-resources-226-rotty-and-application-of-tools/
(ROTTY stands for Results Oriented Thinking - learning too much from the result of a decision without considering the counterfactuals)
Interesting.
> (Though only if I think it actually was positive expected value, obviously - don’t reward people for bad bets and bad outcomes!)
Beware people with social anxieties who won't send you a good bet because they think you might think it's a bad bet. In my experience, this is more common than the simpler 'won't send you a good bet because it might fail' form. (Then again, that's anecdotal evidence.)
I suspect you'll end up selection-biasing out a lot of marginally-positive bets if you do this. Which, admittedly, is better than selection-biasing out a lot of non-certain bets.
Introduction
I am a very anxious person. One of the most damaging ways this manifests is that I am pretty risk-averse and afraid of failure. In situations of uncertainty, I often want to freeze up, and know I’ll feel safer doing nothing.
This is a really bad problem! If I let this dictate my life, I lose a ton of value. In particular, there are a lot of areas in my life that are hits-based, where the best way to be successful is to persevere through many failures and seek the upside risk of things occasionally going super well. I want to be someone who can be a great researcher, find really awesome friends, and generally be ambitious about all areas of my life going well. And to achieve this, it is important that I be the kind of person who can take actions with high expected value, and persevere through failures without feeling paralysed. The key thing going wrong here is that I beat myself up over bad outcomes even when I had no way of knowing it wouldn’t work out, given the information at the time. And anxiety gives me a negative prior and causes suboptimal outcomes to stick in my mind. Failures feel painful in a way that missed opportunities do not.
My solution to this is to think in bets, not outcomes. To clearly notice all of the good bets that I take, the actions that I endorse given what I knew at the time, and to be happy about each of those. And to think of my life in terms of this, rather than the concrete outcomes of the bet, and whether that was a success or failure. At the end of the day, the only thing I can control is the bets that I make, and the policies I follow, and there will always be uncertainty on the outcomes. And if I make a good bet with a bad outcome, I should be happy about this, not sad! I refuse to let my negative emotions be tied to things fundamentally outside my control.
My Underlying Model
I first formed this view when I did a trading internship a few years ago. In settings like financial trading or poker, the fundamental skill is about engaging well with uncertainty, and getting past anxieties is a key part of that! And noticing all of the expected value I was missing when I froze up did a lot for helping me notice this failure mode and learning how to solve it. And though the lessons generalise, real life is often a much harder learning environment than these settings - I make fewer bets and so get fewer data points, and it’s much harder to explicitly calculate what’s going on.
I find it easiest to understand what’s going on here and how to fix it when thinking of myself as having a reinforcement learning system inside my head, shaping my actions. I take actions in the world, get feedback from my environment, and use this to update the policies that I follow. Within this framing, there are two clear problems with learning to make good bets with high upside, while being anxious.
The first problem arises because reality is noisy! Even if I had zero anxiety, fundamentally reality has unknowns and I must make decisions under uncertainty. But, by default, I only learn about my actions from their outcomes. And this makes it really hard to learn strategies around pursuing occasional major upsides! It’s obviously worth it to go on 99 unsuccessful dates if the hundredth results in marriage. But by default, my reinforcement learner will likely be discouraged and stop after 99 failures. While, if I can reframe it as 99 successful bets, then I get much better!
The second problem comes from anxiety, which causes me to over-update on negative feedback, and consider it way more important than positives. This is a fundamental issue with my learning algorithm that means I will learn systematically bad policies. By focusing on the action I took being good, this reduces the anxiety caused by unsuccessful outcomes. Note that negative feedback doesn’t just include stuff that may actually be a big deal, like a romantic rejection, or missing out on a job I really cared about. At least for me, my anxiety reacts badly to even minor negative outcomes with no real consequences, like making a joke that didn’t land, or recommending a book to someone that they’ve already read.
By default, I feel like I can solve these issues if I just try harder. Think harder about an issue, go through every consideration, analyse it more deeply, and only take the actions that will work out well. This is an illusion! Reality is not fully knowable. And thinking harder has costs. If I follow the strategy of “just try harder”, I will implicitly miss a lot of bets worth taking. The optimal strategy, given that I am an imperfect person in an uncertain world, is to take positive expected value bets. Finding ways to learn well in spite of anxiety is essential, because anxiety holds me back from so many bets worth taking.
How to Apply This?
The idea of thinking of my actions as bets and not focusing on their outcomes is a pretty core part of how I think about my life, and is useful in a wide range of areas in different ways. A quick brainstorm of different areas where my anxiety significantly holds me back from making the right bets:
Exercise: Set a 5 minute timer and brainstorm times in your life when this bias applies. How could you orient to these in terms of bets, not outcomes?
The exact way I try to think in bets not outcomes varies depending on context, but there are a few core principles that stand out:
Does This Reward Bad Bets Too?
One caveat worth addressing is whether this strategy could be dangerous? When I think about putting it into practice, this is the biggest flinch from my anxiety - maybe my bets are actually systematically bad and I am deluding myself, and the outcomes are the only way to get this feedback. This is obviously worth considering, and will sometimes happen! The ideal world is one where I evaluate each outcome for information that I’m missing, and take it as a slight negative update on whether the bet was worth making.
But there is no way of reaching that ideal world - my anxiety is a major bias, it pushes me towards risk-aversion, and it’s basically impossible to perfectly correct for a bias like this. My solution essentially introduces a counter-bias, towards ignoring the outcomes by default, which pushes me towards risk-seeking. In principle, there’s some risk of overshooting the ideal point and being too risk-seeking, but in practice I think this is really unlikely! Especially if I explicitly reflect on whether I could have known better. My anxiety creates a pretty big bias towards risk-aversion, and dealing with anxiety is hard, and nothing I do is likely to create as big a bias the other way. I’m not able to ignore the anxiety at particularly bad outcomes, or the creeping doubt of getting way more unsuccessful outcomes than expected. The sheer fact that I feel anxiety about overshooting is a sign that I am safe, and can trust myself to not go too far without needing to actively track it!
Rewarding Other People’s Bets
Many of my anxieties are social in nature, and I get way more anxious about bad outcomes involving other people. And it’s much easier for someone else to help me overcome a socially-related anxiety by giving reliable feedback, than trying to deal with it within the insecurities of my own head. I like to seek positive externalities, so a great (and sad) thing is that this works in reverse - social anxieties are super common, so if I can help other people reward themselves for good bets with bad outcomes, I can help them make much better bets!
Often I do this by being enthusiastic and positive when I see someone who made a good bet with a bad outcome - offering them sympathies about the outcome itself of course, but also congratulating them on putting themselves out there, and making a good bet! I think it’s reasonable to have some concern about insincerity or seeming mocking/insensitive, but in practice I find this often goes down well. Especially if I explain the framing of bets not outcomes, and get them to think about whether the bet was a bad idea given what they knew at the time.
This applies in all the settings I brainstormed above, but is particularly important if someone made a good bet towards me! Eg someone recommends I apply for a job that’s a bad fit, sends me an article I didn’t enjoy, a book recommendation I’ve already read, an introduction that didn’t work out, gave me advice I’d already tried or that didn’t work, etc. I know I find it super discouraging to be on the other end of that, so I always try to clearly say that what they did was positive expected value, and that I appreciate it and hope they do that kind of thing again! A lot of great things in my life have come from people sending me good opportunities, and it’s crazy to train people to not do that. (Though only if I think it actually was positive expected value, obviously - don’t reward people for bad bets and bad outcomes!)
Doing this also selfishly helps me - it creates a social context around me where other people will reward me for taking good bets, and helps build the association in my mind that eg ‘applying for jobs and getting rejected = good’, which helps me internalise it and apply this to myself.
Exercise: Set a 5 minute timer and brainstorm ways you can help reward people around you for making good bets with bad outcomes.
Conclusion
If you relate with the failure mode of fixating on failures and being risk-averse, I think it’s really worth trying to be on top of this, and focusing instead on the actions you took, given what you knew at the time! Anecdotally this seems super common - many of the smartest people I know are super insecure and risk averse. And this is a massive tragedy because the world is full of wasted motion - if you’re unable to be ambitious and take the opportunities that come your way, you’ll miss out on a lot.
So, as a final exercise, reflect on where this bias holds you back in your own life. What are the good bets you fail to make? What opportunities do you miss out on? Where do your anxieties unduly punish you? And what are you going to do about it?