Deposit enough so your balance can be worth at least the double of your total free-roll earnings.
This question has been answered multiple times in this forum thread, but here's the answer once again:
To remove the captcha you should deposit a Bitcoin amount equal to the amount of your free roll earnings. You can see your current free roll earnings by clicking "Stats" and then "Personal Stats". For example if you earned 0.001 BTC from free rolls, you should deposit 0.001 BTC to your FreeBitco.in BTC deposit address and the captcha will be removed. My advice is to deposit a bit more, because if you continue with free rolls, the earning from free rolls will soon become more than the deposited amount and the captcha may return. Please someone correct me if something in my answer is wrong.
Close enough to being correct. A simpler way of putting it is that you need a balance of double your total free roll earnings. You don't have to deposit it, you can win it from gambling or earn it from referrals as well.