I will see odds on people winning elections as 5/1 etc, but have no idea how to figure out if that means they are likely to win or not, other than through context. I have looked it up but never quite ‘get’ it. Please explain to me how it works in a way so simply that a child would understand!
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Mathematically, this is linked together by Bayesian probability. In Bayesian probability, probability is subjective: what the person believe to be the probability something will happen. The subjective odd is the payout:stake ratio you accept to be fair (ie. neither is at an advantage). In other word, if you’re a rational self-interest person (who only want to gain money and not care about anything else when making the decision to make a bet), there is a critical ratio, in which if the payout:stake is higher you will accept, and if the payout:stake is higher you will reject. That critical ratio is the fair point.
The idea that these follows the usual rule of probability is done through the Dutch book argument: if your belief in fair bet is inconsistent with the rule of probability, someone can make money off you by tricking you into making bad bets.
In other word, if you think that a betting scheme with payout:stake is 1:1, then your (Bayesian) odd in believing it happen is also 1:1.
This is why betting behaviors of people can be a very useful metric to find their subjective judgment of how likely something is to happen. The aggregation of that behavior give you the community’s aggregate opinion on what is the winning probability.
Note that this is the *subject* judgment of probability. Under the right circumstances, community’s aggregated subjective judgment is very good.
If you’re doing sport betting though, your bookie won’t give you a fair odd, because they want to make money. The odd would be in such a way that they rake in money no matter what the outcome is.
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