Wikipedia:Reference desk/Archives/Mathematics/2022 July 1

Welcome to the Wikipedia Mathematics Reference Desk Archives
The page you are currently viewing is a transcluded archive page. While you can leave answers for any questions shown below, please ask new questions on one of the current reference desk pages.

July 1

Balance between betting odds in sports betting (and similar games)

In the case of non-fixed odds betting like sports betting, horse racing, political market, etc, assuming the game is not rigged, and has many players that have equal access to loads of information:

would the game have a tendency towards a balance? That is, chances of winning 10x are approx. 1/10?

This is more a psychology than a mathematical question, but could betting for the underdog have a consistent positive expected earnings? That is, most people prefer to bet for teams that win more often, even if they get lower betting odds. It just feel like a winning move, even if the math tells us the expected earning are lower. There's also a feeling of reward getting more results right and some punters won't keep track of losses. Bumptump (talk) 18:30, 1 July 2022 (UTC)

I don't know how bookmakers decide the odds, but they can do it in such a way that they make the same profit percentage regardless of the outcome. Suppose there is a match between A and B, and 60% of bettors bet on A while 40% bet on B. If the bookmaker sets the odds for A to 8/5 and for B to 12/5, they will always make 4%. If a bettor happens to know that actually A and B are a more even match than suggested by the ratio 3 : 2 – specifically, the likelihood of B winning exceeds 5/12 ≈ 42% – their expected outcome when placing a bet on B is positive. If a substantial number of bettors are not rational actors but severely underbet when it comes to underdogs, betting on underdogs may be rational, but whether this is actually so depends on the messy mindset of the mass of gamblers and is not a mathematically resolvable issue. If you have data about a large number of matches with betting odds and actual match outcomes, this can be examined for these data, but note that the results may depend on the type of event, the time period, and the locality.  --Lambiam 19:56, 1 July 2022 (UTC)

Look up parimutuel betting. Basically the bookmaker calculates the odds according to the bets received so far, and almost always gets a profit that way. 2601:648:8202:350:0:0:0:FD2B (talk) 06:21, 2 July 2022 (UTC)

Thanks; the hypothetical example I presented fits with the formulas in Parimutuel betting § Algebraic summary, using n = 2, W₁ = 60, W₂ = 40, and r = 0.04. The bettors of the question may be placing their bets with betting houses that use different systems, though. In any case, knowing the system used by the house does not help to answer the question whether bettors tend to underbet on underdogs.  --Lambiam 10:06, 2 July 2022 (UTC)