(Continued from “Horse-Race Betting and Rationality:  Part 1” published on February 21, 2018)

When Bob, who was making his first ever trip to a racetrack, heard the track announcer introduce the horses to the assembled audience, he immediately had his exacta picks.  As an avid ice hockey fan, he chose Power Play as soon as the announcer uttered the words.  He then selected Game Changer for the bottom of the ticket because that is the moniker of his favorite mobile app for keeping track of breaking sports news and scores.

Bob’s picks were certainly unscientific but they did not violate transivity for the simple reason that he had little or no confidence to begin with about the order in which the horses should finish the race.  Moreover, in Bob’s view, his actions in choosing horses to bet on were perfectly sensible; he was at the track for relaxation and entertainment and if he lost his budget of $5 per race so be it.  He was out for a good time and if he happened to hit some longshot bets that would be icing on the cake.

Alex, the experienced handicapper, felt strongly before the race that the order of finish was most likely to be White Lightening, Power Play, and Game Changer, in that order, and he agreed with the odds on the tote board.  Yet he bet a straight exacta with Power Play over Game Changer.  Even though he felt that Horse A was more likely to win than Horse B and that Horse B was likely to finish ahead of Horse C, he still bet a ticket in which he preferred both Horses B and C to Horse A.

Ask Alex for his reasoning and he might come back with the oft-heard answer from handicappers, “I was trying to beat the favorite.”  Alternatively, he could say, with credibility borne out by statistics, that putting a 4/5 favorite on top in an exacta is an underlay that likely will not be profitable over a long series of bets.  Or he may say, for example, he had non-public information (a tip) from an insider at the White Lightening stable that the horse was not training well and on a downward trajectory, and hence the owner was trying to get him claimed.

One or more reasons like these for not betting White Lightening could be true, which would make Alex’s bet rational in his own eyes.  However, when bettors decide to act counter to their own reasoned judgment about transivity (i.e., Horse A is better than Horse B and Horse B is better than Horse C), it is easy to come up ante-race or post-race with explanations why the illogic was justified.

Real people in real-life decision making routinely make choices that are contradictory.  The racetrack is no different.

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