On... Coin Flips

I first came across the coin flip discussion in Nick Maggiulli’s blog post. Here is my simplified and slightly different take on the subject. Assume I offer you a coin flip bet, in which, you earn 60$ if the coin lands on head and you pay 50$ if the coin lands on tail, would you play? Of course you would. How can you lose money in such a game? 

I simulated 10 scenarios of  10 consecutive flips; and Scenario 4 (worst case scenario) came out as follows:- HEADS, HEADS, TAILS, TAILS, TAILS, TAILS, TAILS, TAILS, TAILS, TAILS.Only 2 flips out of 10 came out heads, which is a probability of 20%. Whats happening? Is the coin rigged? Isn’t a coin flip supposed to have 50% probability?

The chart above shows the results of all 10 simulated scenarios (chart showing probability of flipping heads); and it apparently isn’t 50%??!!!. In fact, the range is quite wide with scenarios ranging from 20% to 60%. The chart below  shows the money lost/gained for each corresponding scenario.

How is it possible to lose money in such a game? Well…… how about if we increase it to a 100 consecutive flips instead of just 10?

As the chart above shows, the range of outcomes is getting tighter and hovers around the 50% probability mark (which is the probability of a coin flip). And the chart below shows the corresponding money lost/gained.

In this case, all 10 scenarios show positive cash flow (Hooray!). 10 flips was actually too few to capture the true probability of a coin flip, therefore resulting in very random results. Therefore, the game was not rigged but the small sample size made it seem so.

Investing in the stock market can actually be quite similar. Even if you have the perfect strategy, you can still under perform in the short run. But in the long run, IF you execute the right strategy, you will be handsomely rewarded. And that is why investing is hard - because in the short run, even the right strategy can seem like the wrong strategy.