Decisions + expected value: part 1
When you see the world in terms of expected value, you will become a better decision maker.
There was this popular tweet from a few weeks ago, challenging people to choose between two buttons, one with a guarantee of $1m, and one with a 50% chance of $50m.
The responses quickly concluded that if $1m matters a lot to you, you should press the red button. Bird in hand, if you will. But the more interesting deconstruction of this problem would be if the money didn’t matter, which should you press?
The expected value of pressing the green button is $25m (50% of $50m). This does not mean the button guarantees you $25m. It also doesn’t mean that if you could press the button twice and miss the first time, the second button press would guarantee you $25m. Also, the button will either give you $0 or $50m, not $25m. So what does expected value even mean?
A better way to explain: if that button awards you $50m when you press it and win, but nets you $0 when you press it and “lose”, and you pressed that button hundreds of thousands of times, you would be approaching a net reward close to $25m. Over millions of button presses, you would be very very close to $25m, which is the expectation of that button press. Expected value is the your average result over a long run.
A good point of view for the lesson here: if over your lifetime you are given a 50% chance of a great outcome, but a 100% chance of an outcome that is 1/50th of the value of the great outcome, you should keep taking the 50% chance, even if it causes some short term pain.
Another example of this lands in my domain of expertise: poker.
AK is one of the best hands you can start with in poker. 72 offsuit is the literal worst hand. But 72 still wins 30.7% of the time against AK. In betting, if you ever get to be a 70% favorite at winning something at even money, you should instantly take that bet. But even though AK is a 70% favorite to win, you could lose 10 times in a row to 72. Or even many more times than that if you’re unlucky enough. But over hundreds of thousands of times playing these two hands, you will get very close to that 70% win percentage with AK. Which is the expectation of this particular hand scenario over the long run.
So why does this matter for decision making?
What poker has taught me is to focus on the correct decision over short term results. It’s because I will lose to the worst hand in poker a whopping 30% of the time when I play AK. But if I can keep getting my opponents to commit a lot of chips when they are way behind, and I can do that consistently over the long run, I will emerge as a big winner as the results even out. The only disaster would be me changing my correct decision making due to a short term unlucky outcome. I made this handy quadrant to illustrate the point:
The upper quadrants represent good outcomes and decisions you want to repeat. The lower quadrants represent things you need to stop doing ASAP, no matter the outcome.
The easiest of the group to execute are good processes that lead to immediate good outcomes, and bad processes that lead to immediate bad outcomes. The former provides strong, immediate incentive to keep repeating what you’re doing. The latter on the other hand will give strong, often painful reinforcement to not try that again.
The most difficult quadrants to be disciplined with are the ones we need to focus on. Get these wrong and you will be in trouble.
Good processes leading to bad outcomes may discourage you from trying again. No one wants to keep facing setbacks and bad outcomes. But if you have done your research and practiced strong critical thinking followed with good processes, likely you are just getting unlucky and need to grit your teeth and keep going. Discipline in repeating good processes will show compounding, long term benefits.
Bad processes leading to good outcomes however is the most dangerous quadrant. These outcomes will strongly encourage you to continue to execute bad decisions, especially when you don’t recognize you’re just getting lucky. This will lead to disaster in the long term if you don’t course correct. Bad decisions leading to good outcomes is the core issue with being overly results oriented: you become incentivized to chase bad decisions over and over again.
The takeaway here is to be process oriented, and take a long view on your goals. Embrace the research, critical thinking, and discipline it takes to make good decisions. And stick to them even if you’re encountering short term setbacks. If you made a huge mistake and got lucky, laugh it off and have the discipline to not make a bad gamble again.
So how can you identify good decisions from bad decisions, if you can’t just count on the outcomes?
A good framework involves just taking the time to think critically through things. What are the second and third order effects of a decision? Will you fix one problem and cause two more problems? Train yourself to follow decisions to their logical conclusions.
Also think of your outcomes in terms of expected value. If I were to make this same decision 10,000 times, what would happen? Would I get good outcomes 80%? 20%? 80% feels like a pretty good decision. 20% feels like it’s time to get back to the drawing board.
Losing 10 times in a row with AK may make you think you should play the hand more passively, but that would be a huge mistake. Launching a product that doesn’t catch on immediately may make you panic and want to abandon ship, but often some patience and a little iteration is all you need to get back on the right track.
But another factor to consider is the speed in which you need to make decisions. You can’t suffer from analysis paralysis just to arrive at the perfect decision every time.
To be continued in our next newsletter, where we’ll cover fast vs slow decisions.
Part 2 is here: https://owngrowth.substack.com/p/decisions-expected-value-part-2
edits: thanks to Chris Smith for pointing out the ev calc should be 50*.5 + 0*.5 rather then -50 for the latter part, corrected in post. Also added more extrapolated example of ev to drive the point home 👍
The laughs
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