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16 May

Making sense of "long-term thinking"


The quality of your decision depends on what time horizon you're considering while making it.

All long-term thinking is actually strategizing around playing repeated games versus one-off games.

The strategy you use to continue playing the game over a longer period of time is very different from the strategy you use to play one or two games and then quit.


"Pace yourself, do not burn out."
"Live to see another day."
"Don't put all your eggs in one basket."

All of these utterances are examples of a mathematical phenomenon called 'ergodicity'.

Technically, an ergodic system is a system that has the same outcomes when one instance is averaged across 100 iterations or one hundred instances are averaged across one iteration.

Don't feel intimidated, here's a simple example.

Imagine a single person tossing a fair coin 1000 times. The person, on average, will get ~500 heads as the probability of getting heads in every coin toss is 0.5. Now imagine 1000 persons tossing a coin once. Again, on average, we will get ~500 heads.

We say that a coin tossing game is "ergodic." The average expected number of heads in either scenario is the same.

In contrast, consider this scenario:

Say you're investing in 10 stocks once, where each stock's probability of going to zero is 10%. What is the probability of your entire portfolio going to zero? It would be 0.1^10, i.e. 0.00000001%. For your entire portfolio to go to zero, every stock must go to zero at once.

But, say you're investing in the same stock 10 times. Now, the probability of your entire portfolio, statistically speaking, is ~100%, as every event has a 10% chance of reducing your portfolio to zero. Over 10 events, it is very likely that you will lose your entire principal amount invested up until that point, post which you cannot invest anymore. You're out of the game.

Investing in stocks is non-ergodic. Your average outcomes when investing in 10 different stocks once look very different than your average outcomes when investing in just 1 stock 10 times.

Let's take a more down-to-earth example.

Imagine two world-class mountain bikers participating in a world championship. The first one has a 25% chance of winning each race and a 10% chance of getting injured and dropping out of the competition in every race. The second has a lower risk appetite; she has a 15% chance of winning each race, but only a 1% chance of getting injured.

Who do you bet your money on to win the competition?

Well, the answer entirely depends on how many races there are in the competition.

If the competition has only a single race, the first biker has a higher chance of winning the competition (25% vs. 15%). But the more number of races the competition has, the higher the chances that the first biker gets injured (there's a 10% probability of getting injured in every race) and has to drop out of the competition. If the competition has more than 20 races, it is statistically likely that this person will get injured around race 10 or 11 and will have to forfeit the rest of the races.

Sports is a non-ergodic domain.

100 people climbing Mt. Everest at once will have different success rate versus one person climbing Mt. Everest 100 times — especially because with each expedition, there comes significant risk of career-ending injury.

In the former scenario, 85 out of 100 people may summit Everest and return safely without getting injured (85% success rate). In the latter, you might get injured (or die!) in attempt no. 6, and not be able to summit Everest ever again (5% success rate).

A car crashing into a pole at 1 km/hr 150 times is not equivalent to the same car crashing into a pole once at 150 km/hour. In the former case, you will probably escape without a scratch. The latter is life-threatening.

Likewise, if you have $10 mn, burning all of it on a single experiment is very different from burning $1 mn on 10 different experiments. The former means you cannot learn from future experiments if this one fails. And in startups, learnings take multiple experiments and iterations to accrue.

Habit-formation is non-ergodic.

Doing something once every day for 20 days builds a habit, but doing something once a month for 20 months does not.

In the second scenario, you will likely drop the activity post a month or two. Because to build a habit, frequency/unit-time matters, not simply the total number of iterations.

All good decision-making in risky domains boils down to what time horizon you're optimizing for.

If you're transacting with a person just once, never to see them again, the best strategy according to game theory is to cheat them to maximize your own outcomes.

But if you're planning on transacting multiple times and building a relationship with them, cheating them might not be such a good idea. Because once you do that, you will not get to play with them in the future.

The difference between short-term thinking and long-term thinking is this: the former optimizes for one-off games, while the latter optimizes for repeated games.

And in the long run, your ability to survive and keep playing matters much more than your performance in every game. Because the upsides of maximizing outcomes or performance also come with the significant downsides of burning out, getting injured, or destroying a relationship.

If a biker's probability of winning a race is 20%, over 10 races, you might say that she is statistically expected to win 2 races. But reality is more complicated than simple expectation value. If she has a 25% probability of getting injured in every race, she probably get injured around race 4 or 5 and not be able to participate in the remaining races at all.

Injuries are irreversible events. You cannot recover from them. Once you're injured, you're out of the game.

When it comes to brands, trust is non-ergodic.

Trust, once broken, is damaged irreversibly. That is why reputations are hard to build and easy to lose.

If you're a salesperson, optimizing for maximum deals this quarter at the expense of fooling customers means you will probably lose your job and reputation and not be able to sell anything in the future.

This is also why resorting to clickbait is such a bad long-term strategy. 100 brands using clickbait once is very different from 1 brand resorting to clickbait 100 times. Your audience will stop trusting you after the first few betrayals.

In general, we can say that in any repeated activity, irreversibility matters much more than performance in the current game.

You cannot simply calculate expected future gains without accounting for irreversible decisions that can end the game for you.

Keep this in mind the next time you decide to throw all caution to the wind. You might not be able to play the game again, because success is a result of 10000 iterations, but irreversible failure is a result of only 1.

P.S. — To understand why co-operation is such a good strategy for long-term success, play this interactive game on your desktop browser.

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