Unexpectedly Intriguing!
23 July 2021

Suppose for a minute that you just wagered 25 cents on the outcome of a coin flip with a friend. The coin flip happens, you call "heads" while it's in the air, but after it falls, it comes up "tails". You've lost.

Your friend offers you the chance to go again. You take it, but you double the size of your bet to 50 cents. The coin is flipped and you call "tails", but it comes up "heads" and you lose again. Now, you're down 75 cents. Your friend offers you another chance to play.

Once again, you take it. But once again, you double the size of your bet, raising it to one dollar (or 100 cents, if you prefer). This time, the outcome of the coin toss matches your call, and you win. You've gone from 75 cents in hole to a net gain of 25 cents compared to when you started playing.

You may not realize it, but you've been using the martingale system (or strategy) in choosing the size of your bets. The strategy was first put forward by French mathematician Paul Lévy, who realized that one winning bet was all that was needed to turn around and fully reverse the outcome of a series of losing bets. Of course, the catch is that you have to have sufficient resources to weather the losses while you're racking up losing bets and realistic odds of eventually winning your wager to make it work for you, but if you want to learn more about the mathematical insight behind it, check out the following 19 minute Numberphile video featuring Tom Crawford.

If you're ready to head to the casino after seeing the video, you can rest assured you will not see any games where you have a 50% chance of winning or losing. There are some games that come close to those odds, but the potential rewards will be less.

With some modifications, you could apply the system to investing, but you'll find that approach has many of the same limitations:

### Drawbacks of the Martingale Strategy

• The amount spent on trading can reach huge proportions after just a few transactions.
• If the trader runs out of funds and exits the trade while using the strategy, the losses faced can be disastrous.
• There is a chance that the stocks stop trading at some point in time.
• The risk-to-reward ratio of the Martingale Strategy is not reasonable. While using the strategy, higher amounts are spent with every loss until a win, and the final profit is only equal to the initial bet size.
• The strategy ignores transaction costs associated with every trade.
• There are limits placed by exchanges on trade size. Therefore, a trader does not receive an infinite number of chances to double a bet.

Don't forget that time is one of the transaction costs you pay. So are opportunity costs, because you may have other, better things to do with your stake that you are passing up by trying to come out just slightly ahead in continuing to play the same game you started losing.

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