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A One Up On ‘Betting Your Beliefs’

Horse betting has been a crucial faction of American gambling for dozens of decades, and continues to make its financial mark, both good and bad, on hundreds of thousands of willing bettors every year. One caveat of the horse betting industry is figuring out a way to make the most money given the possible ways to win at the track, mainly by figuring out what the other bettors don’t know. In Fortune’s Formula: The Untold Story of the Scientific Betting System That Beat the Casinos and Wall Street, the author describes the benefits of “betting your beliefs,” that is, betting appropriately given some kind of outside information unbeknown to the other bettors in the market. One key note the book makes concerns the source of the outside information, know as a “wire” or other vague source of insider information that could highly alter your beliefs about the horse bound to win. Poundstone argues that when an outside source provides a bit of information that could give you a leg up on the other bettors, it is important to consider all aspects of the tip: how trustworthy is the wire, how has their information fared you in the past, is the information consistent with what you previously thought, etc. These distinctions will help you understand how the betting will unfold at the track, especially if the wire provides information that counters the public’s general beliefs (the Odds). Betting your beliefs can loosely be explained as allotting your money based on how the current market appears, once you have considered all of the information you can. for example, if your outside source tells you there is with out a doubt a 100% chance that a certain horse will win – and you believe him –  then the most appropriate course of action is to bet all of your money on that horse. Conversely, if there is a 50% chance of that horse winning (Odds of 2:1) then you should bet only half of your retainer on that horse.

Poundstone goes on in the next section to talk about a key point glossed over in lecture, the fact that all of a bettors money should be bet on at least one horse. His answer is quick, “. . . the horse most likely to win might not win,” but concise. Here, we realize that to better – really, best – your odds of winning something, it is most auspicious of you to bet all of your retainer, even if you are more willing to hold the extra 1 or 5% left over in your pocket. The betting market is not truly predictable, and there are plenty of ways for unexpected mishaps to arise.

One very interesting second idea Poundstone delves into is the idea of a formula to help one bet in a market where not all of the money (total wealth) of the bettors is returned to the bettors – i.e. a fraction of the winnings is cut off to give to the venue. Although this scenario was not  covered in class, it is interesting to consider a different approach rather than “betting your beliefs.” This ‘formula’ presents a fraction which represents how much of your bankroll should be bet on a particular horse:


We must define a few terms here. Edge is how much you expect to win, given the “board odds” or the public opinion about the race. The edge is calculated as your bankroll times the odds, times the chances of that horse winning based on your beliefs/outside knowledge. For example if the odds are 6:1, you are betting $100, and your outside information tells you there is a 1/3 chance of the horse winning, your profit is $100, then divided by your wager your edge is 1. since the odds are 6:1, you should bet 1/6 of your total bankroll on said horse. This idea is quite interesting, because if it weren’t considered you may have bet 1/3 of your wealth on the horse, as your beliefs told you was correct. This “adjusted” formula helps take into account small inaccuracies of the betting market. More interesting is how you should bet when you know nothing about the race: when you know nothing, your edge is zero, so you should bet nothing. These simple ideas presented are interesting to consider in different betting situations, especially when large sums of money are at stake.




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