Checking a round takes a few steps. After rotating the seeds, the player copies the revealed server seed, confirms that its hash matches the one shown earlier, and enters it with the client seed and nonce into a calculator. The calculator should reproduce the recorded result digit for digit. Casinos provide their own verification page, and independent calculators run the same formula, which removes the need to trust the casino's own page.
The client seed is the player's contribution, a value set by the browser or typed in by hand, and changing it at any time is part of the design. A counter called the nonce rises by one with every bet made under the same pair of seeds, so each round gets a fresh input. Because the player controls the client seed, the casino cannot pick a server seed that favours the house for a value it cannot see.
Each result comes from combining the server seed, the client seed and the nonce into a new hash, then turning part of that hash into a number the game can use: a dice roll, a card or a multiplier. The formula is published by the casino, often with sample code. Different games use different conversions, so a verification tool has to match the game in question, and the published formula is what makes an independent check possible.