It’s a Coin Flip!

By Dr. J. David Ashby, CPA, CFP® professional

You may be familiar with the concept of a “fair” coin being used in a flip.  If the coin is “fair,” there is an equal chance of a heads or tails outcome.  If you flipped 100 times, you would expect roughly 50 heads and 50 tails as the outcome.  Certainly, it’s possible to get multiple heads in a row or vice versa.  But over many flips, the heads and tails should equal out. Suppose you and a friend engage in a game of betting money on coin flips, \$1 per flip. Neither you nor your friend should expect to come out ahead. The gains would cancel out the losses.

But what if you had the opportunity to play the game with a biased coin, one that comes up heads 60 percent of the time?  After a hundred flips, you would expect 60 heads and 40 tails.  So if you bet on heads, you should be up a net of \$20. You would no doubt prefer those odds and readily engage in the game.  How could you lose, right? Well, let’s check out an actual experiment.

Instead of using an actual coin, 61 participants were seated at a computer with a coin flip game in front of them.  Participants were told up front the odds: 60 percent of the time the coin would come up heads.  They were given \$25 of real money and told they could bet as much or as little as they wanted on each flip. They had to agree to play for 30 minutes.  The designers of the experiment, Victor Haghani and Rich Dewey, thought the average player could do 300 flips in 30 minutes. The maximum payout was \$250, though that was not disclosed on the front end.  If a participant got close, they were then told about the \$250 maximum.

So how did they do?  You might expect that most of them maxed out at \$250, given the biased odds.  The designers of the experiment thought so. But, in fact, only 21 percent reached the \$250 max, despite the odds in their favor!  The average payout was only \$91.  Roughly a third of the players ended with less than \$25!

So what happened? Well, several things.  Despite the 60-40 odds in favor of heads, 67 percent of the participants bet on tails at some point.  Surely if you have gotten 5 or 6 heads in a row, the next one must be tails, right? Not necessarily.  18 of the 61 bet their entire account on a single flip.  If it came up tails, they were busted. I should also add that the participants were mostly college-age students majoring in economics and finance, with a few young finance professionals sprinkled in.

Now, you might think, “Well, it was money given to them, not hard-earned money.”  As such, that caused players to be careless and take excessive risk.  However, in a previous column, I wrote about The Missing Billionaires by authors Victor Haghani and James White.  The descendants of wealthy U.S. families of over a century ago failed to maintain that wealth.  The most logical explanation for the loss of wealth: taking concentrated bets on a single investment, or only a couple of investments. The results of the coin flip game simulate the real-world results of how wealthy families lost wealth!

Your takeaway here: 60 percent odds don’t exist with a fair coin.  But they do exist with the stock market. According to Morgan Housel, author of The Psychology of Money, investing in the stock market a single day produces 50-50 odds of a gain or loss.  But stay invested for a year and your odds of a gain are 68 percent.  Stay invested 10 years and you’re up to 88% odds of success! Those are excellent odds, but they require patience, a trait many investors lack.

Just for kicks, you might want to play the coin flip game yourself. You can find it at elmwealth.com/coin-flip/. Happy flipping!