Coin Flips and Investing
3 simple but fundamental lessons this coin flip game will teach you about investing.
Let's start with the rules of the game:
You begin with $25.
The coin is biased. There is a 60% chance it will land heads and a 40% chance it will land tails.
You can bet any amount of money in your balance on either heads or tails.
You lose if you reach $0.
You can try playing this game here. Alternatively, search “Elm Coin Flip” on your browser.
If you have the time, I encourage you to play this game for a couple minutes before continuing to the rest of the article. Take the game seriously. It might help to pretend that $1 in this game is equivalent to $100,000.
Note that there is actually a correct way of playing the game with 0% chance of reaching $0.
How did you do? Luckily for us, we have a good comparison. The founder of Elm and the creator of this game, Victor Hagahni, asked investment experts at a MBA conference to play the game for 30 mins. If you did badly, I hope these results make you feel a little better.
Out of the people who played, 28% went bust (here, going bust was defined differently – having less than $2 by the end). Around ⅓ ended up with less than what they had started with. Only 21% ended up winning (defined as having more than $200 after 30 minutes). The average result was around $91.
What’s even more shocking is that almost 30% of the participants went “all in” at least once. 67% bet on tails (CLEARLY the wrong decision) at least once. 21% of the participants bet on tails more than 25% of the time.
What is the right way to play the game?
The right way is to implement constant fractional betting. This means to bet a set percentage of what you have remaining each time. For example, if you decide for your set percentage to be 20%, you bet $5 if you have $25, $4 if you have $20, and $20 if you have $100.
Oh, and if it wasn’t obvious, always bet on the higher probability — heads.
Here is a table of simulated results after 300 iterations. As you can see, constant fractional betting results in better outcomes compared to other methods. More importantly, the chance of going bust is always 0%.
“Constant Absolute” is betting a set amount each time, regardless of the amount of money you have left.
“Doubling Down” means starting with a certain sized bet and doubling that amount every time you lose.
Expected Outcome can be thought of as the average money people have after 300 iterations assuming a large number of people played.
Enough about the best strategy. What does this simple game teach us about investing? Here is my list of three key takeaways. If you can think of more, share your insights by commenting below.
Lesson 1: You first have to stay alive to win.
It doesn’t matter how much money you have accumulated or how many tosses you guessed correctly in a row so far. If you go “all in” in the next toss and lose all your money, it’s over. Once you go bust, you can’t bet again. When you find a game that is tilted in your favor (i.e. you can win 60% of the time), the worst decision you can make is to put yourself in a position where you can get kicked out.
The same goes for investing. To accumulate wealth, you should avoid exposing yourself to the risk of permanent capital loss. No matter how good you are at investing, you cannot recover if you lose all your money.
Let’s say you find an investment proposition with a 90% chance of tripling and a 10% chance of going bankrupt. This is an enticing deal, and it’s probably a good idea to invest part of your money in a deal like this. But why not go all in?
Going all in in this situation means you have a 10% chance of losing all your money, and that is never a good bet. Your goal should be to accumulate wealth over time, and if you want to do that you first have to stay alive.
I think this is partly what Warren Buffett meant when he said there are only two rules to investing:
Never lose money.
Never forget rule No.1
Lesson 2: Bet on the right probability.
This one is pretty obvious. But clearly, 67% of the investment experts surveyed didn’t follow this rule.
This phenomenon is amplified in the real world, where there is no exact probability specified in advance. Investing would be a lot easier if every stock displayed its probability distribution – but then again, this would make markets completely efficient.
Since there is no clear probability distribution, we have to come up with a rough estimate ourselves – What is the probability that we are right? What is the probability we are wrong? How much will we win if we are right? How much will we lose if we are wrong?
Even still, it is impossible to check whether our probability estimates were right. Howard Marks explains why that is so perfectly.
“Think of the weatherman. He says there’s a 70 percent chance of rain tomorrow. It rains; was he right or wrong? Or it doesn’t rain; was he right or wrong? It’s impossible to assess the accuracy of probability estimates other than 0 and 100 except over a very large number of trials.”
The important thing is that we at least attempt to come up with an approximate probability distribution. More on this topic in this article, where we talk about Oda Nobunaga, a Japanese warlord and one of the greatest strategists in history.
Unfortunately, investors often bet on the unfavorable probability, or even worse, don’t even consider a probability distribution.
A good example of this would be investing in companies with incredible yet highly unlikely goals. People are often mesmerized by the rosy prospects of a company that they fail to realize the probability of its dreams materializing is close to zero.
This is similar to buying a lottery ticket. If you win, you earn a lot of money. But, you lose money on average and the expected outcome is negative. It’s a losing bet.
Lesson 3: The truth only reveals itself when you give it time. Accept short term failures as inevitabilities.
In the coin game, your expected return is positive assuming you bet on heads. You also have a bet sizing strategy that prevents you from going bust. The perfect process for success. But this process does not guarantee wins in the short term.
The odds might go against you, and you may land tails ten times in a row. Even if you have skill (favorable probability + correct bet sizing), you can still lose in the short run due to bad luck.
In the short run, luck has a larger influence on the outcome than skill. However, as time passes, the influence luck has on the outcome decreases and the influence skill has on the outcome increases. This is because luck is a random variable and skill is not.
Bad decisions can lead to good outcomes and good decisions can lead to bad outcomes. Do not be overjoyed by short-term success and discouraged by short-term failure. The truth only reveals itself when you give it time.
The same goes for investing. Let's assume we have an investing competition between an unskilled investor and Warren Buffet. They both start with the same amount of money. The chances of an unskilled investor beating Buffet in the span of 6 months is probably not that low. But what if we increase the time span to 5 years? To 10 years? To 60? I think not.
Randomness has a great influence on the outcome of events. Thus, the focus should never be on short term performance. Instead, track long term performance and focus on the process. Are you betting on heads?
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