What is the mathematical formula for determining the value of a bet / odds?

[roulette]

Each bet has a value, which is the probability/odds that a certain event will occur.

Beyond the arbitrage that occurs on a bookmaker, regardless of the result of an event, they have always a profit...
what system can be a system to calculate the value of a bet?

Are there any resources, forms, notes that make it possible to derive the value of each bet / odds?

(topic moderated to avoid spam and off topics)

 

[bellagio]

To set the best possible odds, bookies have many inside sources of information. If an athlete or team is having personal problems or is unmotivated and not training up to their usual standards. Anything that might affect the performance of an athlete or team that is being bet on. Oddsmakers will know of it long before the general public does. Said sources of inside information are one of the biggest advantages oddsmakers have over the casual sports gambler.

Insider trading in wallstreet and cryptocurrencies is a real thing. If investors know an announcement is coming that will jack up the price of an asset, they'll often buy in early and reap the benefits of inside information. The same precedent is found in sports gambling. There were rumors of Francis Ngannou having a knee injury going into his fight with Ciryl Gane. Gamblers with inside sources could have tried to take advantage of this, which could explain the massive betting line shift in Ciryl Gane's favor.

The best mathematical formula for determining the value of a bet is to acknowledge that oddsmakers have better sources of information and the line is set in whatever way they believe will earn casinos and sportsbooks the largest profits.