Before you take a single spin, the server generates a secret seed and publishes its SHA-256 hash. You choose the client seed. A nonce counts up by one for every spin, and the database refuses to record two spins under the same seed and nonce.
Reel positions come from HMAC-SHA256 of your client seed and nonce, keyed with the server seed. Because the hash was published first, the server cannot have picked a seed to suit the outcome. Rotate your seed and the old one is revealed, at which point every spin you took under it can be recomputed here — by you, or by anyone you show it to.