I'd say that your bankroll should be at least 10 million times greater than your bet.

So for a "safe" long run betting system with a 1 satoshi bet you need 0.1 btc.

Just don't be greedy and don't look at the bets because it's fucking boring and you'll be tempted to make higher risk bets. I know this from experience. 

I only lost money when I was greedy and stupid to think I may do better than the boring strategy. Stick to the boring plan and you'll make a small profit everyday but a huge profit in the long run.