We all know that bookmakers will add an overhead to their probability percentage in order to protect their profit margins, i.e., an option that has a $70\%$ chance of winning might be given odds that imply a probability of winning of $85\%$.

For non-favourites, would the implied probability be lower than the true probability in order to entice more bets?

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    $\begingroup$ I am unsure to what extent issues concerning gambling odds are on-topic on CrossValidated. Clearly the fact that gambling odds do not match "true" odds (and therefore implied probabilities do not match real ones) due to overround is on-topic. But to what extent overround depends on e.g. the odds offered, seems to venture into economic theory (particularly behavioural economics). Corone's answer is excellent, and would be completely at home on Economics. I think this might merit migration. $\endgroup$
    – Silverfish
    Feb 23, 2016 at 12:24
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    $\begingroup$ They put overhead on all bets (otherwise the underpriced options will be heavily bet on) but the options with long odds tend to have relatively more overhead. $\endgroup$
    – Glen_b
    Feb 23, 2016 at 20:42
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    $\begingroup$ @Glen_b there are small rare exception to this. The book maker will construct a "tissue" of what it believes the true odds are, and attempt to put on overround an each of these. However, in some cases the betting volumes are uneven enough to encourage them to "pay" to remove the risk on certain outcomes. At that point a small bookmaker will offload the risk with a bigger bookmaker (an consequently be under-round on those names), or a bigger bookmaker will offer odds better than they believe - willing to pay to get rid of the risk. This is one of the ways professional gamblers profit. $\endgroup$
    – Corvus
    Feb 24, 2016 at 8:38
  • $\begingroup$ @Corone is correct, my brief comment oversimplifies. For example, once you set an initial book (set of odds), your actual offered odds will adjust to fit what is bet with you and to what odds others offer (the aim being that no matter which outcome occurs you shouldn't lose out), and you'll attempt to lay off some of the heavier betting that would tend to distort things too much for you -- but sometimes some particular outcomes (e.g. a heavily-bet favourite winning) may result in some losses because you couldn't lay enough off at the price you'd need. $\endgroup$
    – Glen_b
    Feb 24, 2016 at 20:24

1 Answer 1


Usually the opposite in fact. It tends to be the case that when gambling people are attracted to the small probability of a large win, rather than a higher probability of a moderate win. This effect can be neatly modelled by Prospect Theory.

This results in a Favourite-longshot bias that has been studied many times (Google Scholar). Roughly summarised the implied probability on a long shot is actually most wrong. Of course it doesn't often look like this because an implied probability of 2% for a real probability of 0.2% only looks like an over-round of 1.8%, but of course in log odds ratio, that is a massive difference.

You will often observe that 100-1 becomes a sort of catch all odds for anything very rare (unlikely teams winning leagues etc.).

Repeated betting on the favourite will lose you money much slower in the long run that betting on the outsider.

A related issue are "accumulators", in these bets people stack together multiple bets one after the other to create outlandish odds from multiple fairly low odds events. Here the over-round is even worse, and bookmakers can often afford to offer bonuses to attract people to these bets.

To see the issue, imagine betting on 5 events each with a real probability of 20% and implied probability of 25%. On an single bets your expected return is 80% of your stake (you win £4 when you "should" have won £5). By the time you stack them together the real probability of winning is $0.2^5 = 0.00032$ but your implied probability is $0.25^5 = 0.0009765$ - in other words you expect to win back only a third of your stake! This is why a bookmaker can happily offer to "double" your win on an accumulator.


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