Each bet can be verified using the day's secret and the last deposit's TXID. To produce a stream of numbers a nonce is appended which is incremented by 1 on every bet. The nonce is reset to 0 on every deposit.
The lucky number is computed by the first 4 hex digits of hmac_sha512(secret, lastdeposittxid:nonce)
For more information on how to verify a bet enter its ID at the top of the page. (Example)