True there are lots of ways how to present house edge calculation some of it are:
House Edge = 100% - Payout Percentage
House Edge = (1 - (payout ratio / average bet)) x 100%
House Edge = (odds against winning - 1) / odds against winning
House Edge = (Probability of Losing x Loss per Loss) / (Probability of Winning x Payout per Win)
House Edge = (Probability of Losing x Loss per Loss) / (Probability of Winning x (Payout per Win - 1))
In addition it is also stated that each game has its own house edge formula for calculating house edge like for example:
Slot machines: House Edge = (100 - payout percentage) / 100
Blackjack: House Edge = (total number of decks x (0.5% - 0.8%)) / (number of decks remaining in the shoe)
Roulette: House Edge = (number of zero pockets on the wheel / total number of pockets on the wheel) x 100%
Baccarat: House Edge = (number of decks x (14.36% - 1.17%)) / (number of decks remaining in the shoe)
Craps: House Edge = (total number of bet possibilities x (1 - (payout ratio / average bet))) x 100%
Video Poker: House Edge = (100 - payout percentage) / 100
We can see more example in this link: https://easy.vegas/gambling/house-edge-calculation