Depends not only on how many picks, but on how high the win % is and what kind of vig you're paying.
If you're paying no vig and hitting %60 over 200 bets, over 99% chance you'll be profitable long term.
Hitting 55%, you could be 95% confident that you're above 53.5% after 5000 bets.
Quick formula to std deviation on binomial distrubtions....
SQRT ( ((ratio you are winning at)*(1 - that ratio)) / number of bets placed )
so for 60% over 1000 bets you'd take SQRT ( ((0.6)*(0.4)) / 1000)
this gives you 0.015, or 1.5%. This number is called your standard error (think that's right anyway, not going to look it up)
You can be 75% confident that your real win % is within 1X this number, so between 58.5 and 61.5. You can be 95% confident that you're within 2X this number. 99% confident that you're within 3X this number, or will win > 55.5% of the time.
Those aren't exact numbers, but it does show that you'd have to hit about %60 over 1000 bets to make any conclusions paying -110.