For the 2 to 1 bets, the largest sample size in which this is a good bet is 14 games. Picking randomly you would have a 39.5264% chance of picking 57% or better, or 8 or more right. You need to have better than a 33.3333% probability for it to be a good bet. 21 is close to fair, but the probability is slightly too small at 33.1812%. The larger the number of picks required the lower the required percentage should be. For example, if 1000 picks were required the greatest number required to have more than a 1/3 chance of winning would be 507. The probability of getting 507 or more right in 1000 picks is 34.05%.