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Frontlines of the Non-digital: Hedging Our Bets

So I’m in a bit of an interesting quagmire: remember my post a few weeks back about the NCAA tourney pools? Well, low and behold, I’m in 4th place in a 250 person pool with quite a bit of *cough* pride on the line (enough for the IRS to be interested, let’s say). It’s an interesting dilemma that might be best phrased in this way: if someone walked up to you on the street and offered you a month’s rent but you had to flip of a coin to get it, would you risk that OR take half of a month’s rent guaranteed without having to flip the coin? This is basically what hedging a bet is all about, because only fools would flip the coin.

So here’s my situation fully explained: there are 3 games to be played (the round of 4 and then the round of 2, aka the championship) and I need to correctly predict all 3 games. If I do so, let’s say for the sake of argument that I will finish in 2nd place and win $1500. Now here’s where it gets interesting: I want to hedge my bets and after a bit of analysis I’ve figured out that if team A wins the match-up between team A and B in the final four game, and then Team A goes on to win the championship over teams C or D, I’m guaranteed 2nd or 3rd ($750). In other words, if Team A beats Team C in championship, I win 2nd; if Team A beats Team D in championship, I win 3rd. My problem is simple if Team A reaches the final: just hedge half the $ at stake by betting on either Team C (for $750) or Team D (for $375). Then no matter what happens, I’m guaranteed the $750 or $375 (instead of gambling all or nothing for the $1500 or $750).

But what do I do about Team B, the team that could ruin everything? How do I hedge against this? The question now becomes do you want to flip for a month’s rent, or do you want a quarter of it guaranteed? And now I’m beginning to feel a bit more foolish. IF I were to hedge against team B, I could lay $375 on them and guarantee myself exactly that much (no more, no less) no matter how the tourney played out. Seems pretty boring compared for the chance to win $1500. Hedging usually is. Thoughts?

10 Comments

  1. Frank wrote:

    Hi Charles, I think you might be confused.

    >> if someone walked up to you on the street and offered you a month’s rent but you had to flip of a coin to get it, would you risk that OR take half of a month’s rent guaranteed without having to flip the coin? This is basically what hedging a bet is all about, because only fools would flip the coin.

    I don’t understand why it would be foolish to take the flip. You might have a point if you were risking a significant portion of your overall bankroll, but in the case you describe you are risking nothing.

    Lets say your monthly rent is $1,000. I offer you $500 or a 50% chance at $1,000. There is no rational reason to prefer not flipping to flipping (or vice versa). From a purely rational perspective, you shouldn’t care which one you get, because they are “worth” the same amount.

    Of course it’s more complex than that. There may be some reason that $500 is worth more to you than half of $1,000 (ie. if you already have half of your rent and are about to be evicted.) But its clearer and more useful to assume that there aren’t any special considerations like that (since you can always construct examples that don’t have them, and thereby get at the underlying principles that we’re talking about.)

    I think what you might be talking about is reducing variance. Not flipping has zero variance, the outcome is certain. Flipping has high variance, the outcome is very uncertain. But variance in and of itself is not a negative value. The role of variance in gambling is extremely important, but mainly in relationship to the critical importance of bankroll management. Assuming that the $500 and $1,000 amounts in question are *not* a significant portion of your gambling bankroll, there is, again, no rational reason to prefer flipping to not flipping.

    You might simply prefer avoiding variance. You might just like “sure things” and dislike uncertain outcomes. That’s fine, but it isn’t rational, it’s emotional. It’s a very natural and widespread emotion, it’s difficult *not* to prefer $500 to %50 of $1,000, but you have to consider: do you prefer $500 to %50 of $1,001? What price are you willing to pay for the emotional comfort of reduced variance? For a rational, profitable gambler that cost comes directly out of their profits, it’s money they are *throwing away*.

    Instead, the rational decision is to manage variance through serious and disciplined bankroll management, which strictly determines the size of wagers you should allow, and then to maximize your profit within those limits, without worrying about variance.

    I didn’t really understand the details of the rest of your situation, but I don’t think that the “hedging” you describe is profitable.

    For more insight on the mathematics of sports betting you could check out

    - Sharp Sports Betting, by Stanford Wong
    - Weighing the Odds in Sports Betting, by King Yao
    - Getting the Best of It, by David Sklansky

    Go Team!

    Saturday, April 5, 2008 at 3:57 pm | Permalink
  2. Thanks, Frank.

    I was talking to a friend in a bar last night about this and he argued the same position as yours about variance and being consistent. Much of me now sees the situation differently. But when I say “only a fool would flip a coin,” I’m not speaking of the hardened gambler who no longer sees money as money but instead as chips (I think the gambler would be in agreement with you certainly). The fool I refer to is the one time non-gambler to whom the $ on the table is a significant amount for them. Personally I’m somewhere between the non-gambler and the harden gambler so I’m still not sure what I’m going to do tonight.

    Is there a gambler out there who is harden enough to turn down a guaranteed $500 million for a coin flip to win $1 billion?

    Saturday, April 5, 2008 at 4:59 pm | Permalink
  3. Frank wrote:

    >> The fool I refer to is the one time non-gambler to whom the $ on the table is a significant amount for them.

    I still maintain that calling the flipper “foolish” is wrong and misleading.

    Again, let’s assume that there isn’t some hidden reason to prefer the $500 (like another, highly-profitable wager that you can only take if you win the $500). And let’s look at a casual, naive, uninformed player and what might motivate them taking the flip:

    1. she misundertands the situation and believes that a 50% shot at $1,000 is worth MORE than $500 (foolish)
    2. she correctly intuits the truth of the situation and chooses at random (not foolish)
    3. she correctly intuits the truth of the situation and chooses the high variance choice because its suspenseful and exciting (not foolish)
    4. she misunderstands the situation and believes that a 50% shot at $1,000 is worth LESS than $500 but prefers the excitement of flipping anyway (foolish)

    You seem to feel 1 and 4 are the most likely explanations, but I’m not convinced that’s true.

    >> Is there a gambler out there who is harden enough to turn down a guaranteed $500 million for a coin flip to win $1 billion?

    This is a good example of a case where all dollars are not equal. For most people, in terms of *utility*, the second 500 million in a billion is worth far less than the first. Therefore not flipping is the rational choice.

    Saturday, April 5, 2008 at 6:03 pm | Permalink
  4. I understand your rationale better with the 1-4 explanation. I suppose for me, the second $500 is not worth as much as the first and therefore I consider it foolish for me to flip… but I stand corrected that not everyone would be a fool to flip the coin.

    It would be an interesting survey to pinpoint everyone’s “flipping point.” What would be the amount where you wouldn’t flip?

    Saturday, April 5, 2008 at 7:06 pm | Permalink
  5. Frank wrote:

    I am particularly fascinated by this topic, hence the highly pedantic response to your original post. More coolness about these kinds of decision can be found here: http://en.wikipedia.org/wiki/Prospect_theory

    Sunday, April 6, 2008 at 2:48 am | Permalink
  6. Dan wrote:

    Also fascinated by this topic, in particular how it relates to delusional decision making on the show DEAL OR NO DEAL. There have been some interesting studies that show how previous outcomes affect decision making. . .

    http://papers.ssrn.com/sol3/papers.cfm?abstract_id=636508

    and some neurosciency explanations of behavior:

    http://www.sciencedaily.com/releases/2006/12/061219201947.htm

    Me, I always flip (reason #3).

    Sunday, April 6, 2008 at 6:00 pm | Permalink
  7. Wow, Dan Shiffman watches Deal or No Deal!

    I once invested in a mutual fund that studied behavioral investing and used their research to maximize profits. Seems the one behavior that is certain is the irrational behavior of investors. The fund really never did much for me.

    I’m about to take a look at these papers you listed Dan… I’m wondering if either will touch on “beginner’s luck.” There really is such a thing but it has nothing to do with luck (obviously): it has to do with the fact that a player new to a game has no previous outcomes and therefore often uses better judgment in decision making than someone who has more experience and has learned bad habits.

    Monday, April 7, 2008 at 3:57 am | Permalink
  8. Charles Joseph wrote:

    I’m glad that someone else thinks that the contestants on Deal or No Deal are delusional.

    Monday, April 7, 2008 at 4:11 pm | Permalink
  9. I’m sure everyone will be relieved to know that i did NOT hedge any bets and my team did in fact win. So I flipped and flipped well.

    Tuesday, April 8, 2008 at 4:49 am | Permalink
  10. Frank wrote:

    > I’m sure everyone will be relieved to know that i did NOT hedge any bets and my team did in fact win. So I flipped and flipped well.

    Nicely done.

    Wednesday, April 9, 2008 at 11:13 pm | Permalink

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