You could draw a winner as soon as the newest Bitcoin block hash contains a certain sequence.
That would be my thinking; however the blockchain doesn't provide a statistically constant rate of blocks, because mining isn't constant. If the goal is to generate on average one "event" per day or per week, it will still take manual intervention if the Bitcoin hashrate is increasing or decreasing, or above or below the difficulty; the actual hashrate cannot be determined to make it fair.
In addition, a criteria that may happen on average once per week (such as block hash mod 1008 = 0) has a not-insignificant chance of taking over a month, which may make players restless.
A better solution would be a satoshi-dice style provable, where the random choosing method for transactions sent into the jackpot pool is transaction hash plus site's secret which is pre-published as a hash. For example, if one in 16 bets may win the whole jackpot, etc... If I need to explain more, you shouldn't be running a gambling site.
