Is there any reason to think that investing in a casino's bankroll is any more (or less) risky than having BTC deposited at, say, an exchange? (Genuine question - I've had money at exchanges plenty of times, but never invested in a bankroll).
Depends what exchange.
If it's like cryptsy or bter then its risky, but if its like coinbase or poloniex then its less risky.
I think most gambling sites, the big ones (satoshidice, primedice,etc.) are pretty safe and low risk.
If I`d have to give them a risk rating I`d give them B- (given that their support system is not that good + anonymous)
But if you are risk averse then just keep the coins in a cold wallet, you dont have to invest if you dont want to.