(Epistemic status: This is super trivial information)

(Note 2: there is a timely Culture war issue that triggered this post but I will not be mentioning any Culture war issues in this post)

Imagine you worked for the US mint, and somebody was betting that a coin you manufactured was unfair, now you work for the US mint and you know this coin is fair, it isn't weighted and the edge alignment is perfect. The person making the bet going to use a coin flipping robot to remove any human deception.

What odds would you have to be given to actually take the bet?

I'll be using American odds. So in theory you'd accept any odds above +100 right? Well in a world without taxes yes, but taxes are one sided, you don't pay negative taxes on gambling losses, but you do pay positive taxes on gambling winnings. As such we need odds that are better than +100/(100-T) where T is our marginal tax rate. Marginal tax rate means territory/state, local and Federal income taxes which gets complicated, however for now if we assume 33.3% as our marginal tax rate (California man making >100k/year) , we would need odds of +150 or better to be worth betting. (That's 60% or better in manifold terms)

I feel like this point is understated, for real money markets you need to do the following to get the "estimated odds"

Let market "probability" be = M (for these purposes the bid ask spread in most markets is trivial relative to the weight of taxes)

The actual probability that the event happens is at least

The probability it doesn't is at most

\frac{3 M}{M + 2}

all told those are pretty stark differences, if the market is saying that an event has a 63% chance of happening then the event has anywhere from a 53-72% chance of happening!

So if somebody says "the market is giving probability of 63% but my model says it has a 55% chance of happening, "why aren't you betting" is not a credible argument because If they were right they would still be unable to profit from their disagreement with the market.