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Betting and Statistics

Betting and Statistics

Betting has had a long and close relationship with the science of probability and statistics.  In the mid-1600’s, the French intellectual and gambler Antoine Gombaud, who called himself Chevalier de Méré, enlisted the help of the mathematician Blaise Pascal to solve several puzzles involving dice games.  Pascal’s ensuing work is regarded as the foundation of probability theory.

Games involving dice, cards and balls in an urn have long been staples of statistics instruction. In our own course Introductory Statistics, we rely on these devices to make clear the probabilistic mechanism we are studying.  In creating these courses, I was inspired by Julian Simon, early pioneer of the bootstrap and my colleague in developing and promoting Resampling Stats software.   

Simon’s main fame came from his study in demography and natural resource economics – he was an opponent of the “gloom and doom” school of thought, which held that the earth was running out of resources and was overpopulated.  In the 1980’s, this was a lonely position, and Simon, frustrated at not being taken seriously in either academia or the media, turned to the device of a public bet with a primary antagonist, Paul Ehrlich. They bet on the prices of copper and four other metals.  Ehrlich, banking on resource scarcity, bet that their prices would rise. Simon, banking on technological innovation and substitution, bet that they would fall. Simon won – the prices of all five metals fell. For Simon, the simple bet cut through volumes of academic debate and statistical argument, and crystallized the issue with a simple binary choice.

The Simon-Ehrlich bet was an early incarnation of betting as a quantitative approach to public policy-making, but it was not alien to economists.  Financial markets are, in reality, a system of “betting at scale” that provides useful information about the economy in general and its constituent parts in detail.  The impending initial public offering (IPO) of Aramco offers a chance to bet on the outcome of multiple moving parts – global economic growth, the potential for Iranian attacks on Saudi facilities, and the progress of fracking – to name three.  The financial writer Aaron C. Brown points to gambling games, rather than early financial institutions, as the antecedents of modern financial derivatives.  Brown himself was a professional poker player in his college years, and went on to serve as Risk Manager at major financial institutions such as Morgan Stanley and J. P. Morgan Chase.

Financial markets are a pure example of crowd-sourcing, and taking advantage of “the wisdom of the crowd.”  Las Vegas odds makers are another. However, true crowd-sources odds in Las Vegas (i.e. resulting from bets) are limited almost entirely to sports – you’ll see odds on political races but they are simply estimates, since institutionalized betting on elections is prohibited in the U.S.

Except at  Betting on most topics is legal at, up to a limit of $850, under a special exemption.  According to its web site, it is “an experimental project operated for academic purposes [by the University of Victoria, Wellington, New Zealand] under permission from the CFTC (Commodity Futures Trading Commission).”  As of this writing,for $0.76 per “share,” you can place a bet that President Trump will be impeached before the end of his first term by the US House of Representatives, with shares redeemable for $1.00 if you are a winner at that time.

US Government Funded Betting Venues

Betting on election outcomes is an interesting parlor game, but contributes only marginally to the extensive polling information available on most elections worldwide.  What about events outside of sports and politics? On several occasions, U.S. defense funding has been made available to develop betting markets on the future course of events in areas of interest.  An early one, FutureMAP (Future Markets Applied to Prediction) dated from 2001, and was designed to test “whether whether prediction markets, markets in which people bet on the likelihood of future events, could be used to improve upon existing approaches to preparing strategic intelligence” (in the words of an article posted on the CIA web site).   

FutureMAP was cast as an effort to develop a “futures market” in which people could purchase futures contracts on potential events (e.g. a terrorist attack in the Arabian peninsula), but it really amounted to a fancy betting parlor (as do all futures markets).  The idea was to leverage the “wisdom of the crowd” to gain intelligence insight on security threats and issues. FutureMAP, however, never launched, due to concerns that it was unseemly to be hosting a forum where individuals (including, possibly, terrorists) could place bets on terrorist acts.

A similar effort funded by the U.S. intelligence community in 2014 was  It crowdsourced an international search for Malaysia Airlines Flight 370, but has been inactive since 2016, when it lost funding.  (Another forecasting effort funded by the US intelligence community, The Good Judgment Project, relied on curated opinions of “superforecasters,” and was not an open betting venue.)

Validating Research

Yet another initiative funded by the U.S. intelligence community is  This site serves as a venue where participating forecasters can place bets on whether specific claims made in research papers will replicate.  The emphasis is on social and behavioral research, with claims like:

  • Will narcissists be unwilling to apologize for their interpersonal transgressions?
  • In a set of dynamic decision-making tasks in which reward values were dependent on the sequence of previous choices, would older adults made more optimal choices than younger adults?

It is difficult to imagine what replication would look like in many cases:

  • Is a perceptually completed whole less than the sum of its parts?

Thus, the site’s caution that “most markets will not resolve, so you may wish to diversify.”  Only time will tell whether betting is a useful guide to the validity of research, but a brief review of the topics on offer made me wonder what utility they will have to the CIA or any other part of the intelligence community.