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Finding Expected Value in Unusual Places: an example

One day, on a Sunday afternoon, I was sitting at a friends house watching and New England Patriots game. I’ll be the first person to admit that I know very little about football, and could care even less. And while I do fancy myself as an “unusual investor”, I am also not opposed to throwing down small five or $10 bets on a game just so I have somebody to cheer for.

But as fortune would have it, as I was looking around at some of the strange side bets, such as which player would score the first touchdown, or whether the first score would be a touchdown or field-goal, I came across something interesting.

The bet was this, would the game go to overtime? If so, you would be paid at 11 to 1 if you took the bet, and if you wanted to bet that the game would not go to overtime, you would have to put down $13 to win a single George Washington.

Now the thing about bookmakers is that they do not set the odds on bets on based on the likelihood that something will or will not happen, they set their odds based upon how much money is coming in on each side.  And I don’t know about you but putting down $13 to win one does not sound like a bet that is going to be really popular amongst the masses.

So, I spent the first half of the game on the website, checking the game results for the last three years. And sure enough, only about one in 17 games went into overtime. So on average, I could place this bet 17 times, win 16 times for $16, and lose once for 13.

So the next question was, how much was the maximum bet? And it turns out, that the maximum bet was around $1700. There were three games each Sunday where this that was available, and one game on Monday night.  And at that point in the season, there was probably something like 25 games left to bet on. Meaning if more than one game went to overtime in those 25 I would be taking a loss. On the other side, I could also go 25 for 25, and end up taking a straight up $2500. After determining using an Excel spreadsheet that going 25 for 25 was more likely than losing two or three (yikes!), I was ready to go. But, and this is a big but, you still have to be prepared to lose. Most likely $900, but possibly $2600, and a very, very outside (less than 1%) chance of losing over $4000!

So the question I had to ask myself is no longer whether this is a good bet, we have already determined that it is. The question is, can I afford to lose $4000?  This is the most important part of determining how much you should be placing on any given investment…  What if I lose?  Even if there is only a 1% chance I could lose everything, I have to take that into account. Therefore, I can only play with an amount of money that I can afford to lose every single dime. At that point in my life, $4000 was not a game stopper, so I decided to go ahead.  A 4/17 edge is much better than any mutual fund is going to get you.

Now here’s the strange part:  what happened after the point that I decided to move forward does not matter. If I won money, it was a good bet. And if I lost money, it was still a good bet.  If we decided that we had made a mistake if two games had gone to overtime, we would be in a mode of thought referred to as results – oriented thinking.  And results – oriented thinking is a mode of thought that gets human beings to believe all sorts of ridiculous things which are patently untrue.   After all, the games can’t possibly be rigged, the bookie can’t possibly know in advance who is going to overtime or when.

We just have to get used to the fact that, not just in investing, but in life, that we can do the right thing, make the most optimum decision, and still lose.  In fact, that is one of, if not the most difficult part of investing (as opposed to gambling).  The ability to emotionally handle losing, especially when you lose six, seven, 10 times in a row.  Which, statistically speaking, has to happen sometime.

Because those emotional roller coasters can lead us into bad decision-making, which lead us to make “investments”which aren’t really investments at all.  And that is the greatest enemy of every investor.

(fwiw, while I won’t tell you exactly how I did, the bookie did take down the wager at the conclusion of the second season of my playing that strategy.)


  1. Brígida says:

    great post.

  2. Edenira says:

    i like it…keep up.

  3. Cassandra says:

    thanks for the nice post.

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