I'm quite tempted to just give up on this whole thing. It looks like the site is simply at nakowa's mercy. He's promised me in the past that he won't play any more, but never sticks to his word. So what do I do? Continue to let the investors take these horrific losses?
Firstly, I want to compliment you on your brilliant ideas for just-dice.com. I discovered it only a few days ago, and have been thinking about it ever since. I really appreciated the analysis you did for SatoshiDice and I can tell this has given you a great deal of respect in the quickly-growing bitcoin community.
In regards to taking the site down, well, you are a statistics expert: Lets make the null hypothesis Nakowa is not cheating and see what the p-value is when we test it. Obviously, Nakowa is lucky, but if the p-value is, say, no smaller than p = 0.05, then I dont think we can conclude that he is cheating. The investors signed up knowing that there were risks involved, and shutting down the site would not be fair.
Lastly, while I have no doubt that you and your team are completely honest and trustworthy, I suspect that if you take the site down without strong evidence that there is a real problem, it would sort of make you look guilty as per Lohoriss insight while I don't think [Nakowa is] cheating, it is worth noticing that if he was cheating, then pretending to be victim of a gambler's fallacy (like he is doing) is actually a great tactic to go unnoticed.
Personally, I hope Nakowa comes back again soon...