Bill Gates and Mark Zuckerberg each dropped out of Harvard to focus on Microsoft and Facebook respectively. John D. Rockefeller doubled down on oil even as kerosene for lamps was being made obsolete by the electric lightbulb. After a business loan was denied, Fred Smith took FedEx’s last $5,000 to Las Vegas and ended up winning $27,000 playing blackjack in order to pay the company’s outstanding fuel bill. So many of the biggest success stories involve taking big risks that pay off. But what stories aren’t we hearing? This is the concept behind survivorship bias. Popularized by Abraham Wald’s analysis of aircraft damage during World War II, it highlights the mistakes of focusing on visible successes and ignoring unseen failures.
Does this mean that you should ignore the stories and lessons of successful people in order to avoid the pitfalls of survivorship bias? It all depends on what you are optimizing for.
Looking through the lens of board games, there are a few approaches for optimization. Optimizing for your highest average score is making choices that, over a long enough period of time, will result in your best score. On the other hand, focusing on your best chances of winning is making choices that, in any one particular game, will give you the best chances of being in first place. In many cases, these are going to result in similar decisions, but let's look at situations where this might not be the case.
In the simple push-your-luck game Pig, you roll a die—if the number is between 2 and 6, add its value to the running round total, and you can decide to roll again. If it is a 1, however, you score nothing for the round and your turn is over. Play continues until a player reaches 100 points.
If you are trying to maximize your score, the decision space is trivial: roll until your running total is 20 or above, and then stop. If you are playing to win, however, the math becomes fuzzier. If you have a solid lead, you'll want to bank your points earlier to avoid risking your lead. Conversely, if you are playing from behind you'll need to take bigger chances to have any chance of catching up.
Balancing risk and reward applies to real-life scenarios as well as games: there are times when you want to maximize your "score" and there are times when you want to win. Consider investing in the stock market: if you want to get your best average return, you'll likely want to put your money in a diversified portfolio such as an index fund. A high risk/high reward might give you a big payout, but investing isn't a race to first. Interviewing for a competitive job, however, is a race to first. Since there is no prize for second place, you should consider a high risk/high reward strategy.
In games and in life, there are times to play it safe and times to take risks. Learning to recognize the difference can be crucial in making the right decisions at the right time.
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