If “best” means which one gives you the best odds of winning, then the Mega Millions lottery would be the better bet. The odds of winning the lottery are 1 in 258,890,850 (1 in 258.9 million). That’s downright fantastic when compared to the Billion Dollar Bracket challenge which comes with odds of 1 in 9,223,372,036,854,775,808 (1 in 9.2 quintillion) if you picked your bracket at random. If you use a little bit of NCAA basketball tournament knowledge, you can increase the odds of picking a perfect bracket to 1 in 128,000,000,000 (1 in 128 billion). Still, as far as pure odds go, 259 million to 1 is much better than 128 billion to 1, meaning that playing Mega Millions would be the “best” to enter in this scenario.
Looking strictly at the odds, however, leaves out a few important factors which can have a significant impact on which of the two would be considered “best” to enter. For example, in order to play Mega Millions, you need to pay, whereas you can play the Billion Dollar Bracket challenge for free. As mentioned above, both contests come with odds that are so large that it isn’t likely that you would win either of them. If you look at which contest is “best” from the point of view of “Is it better to lose no money or lose some money?” the Billion Dollar Brackets is the best choice since you don’t have to risk any of your own money to play.
It’s important to remember that the grand prize isn’t the only monetary prize available in both contests. The second prize for Mega Millions is $1 million which comes with odds of 1 in 18,492,204 (1 in 18.5 million). The second prize for the perfect bracket challenge is $100,000 and comes with odds of 20 in 15,000,000 (20 in 15 million). While the prize is less for the bracket challenge than the lottery, the odds of winning are much greater.
In fact, the odds for the $1 Billion Bracket challenge are likely even better that 20 in 15 million. First, those odds assume that all the 15 million entries for the contest will be filled. Secondly, it assumes that everyone who participates will know previous NCAA tournament history to have a better chance of picking a quality bracket which isn’t likely to be the case. Since it’s the best 20 brackets that win if there isn’t a $1 billion winner, and if winning a major prize is the criteria for “best,” then the Billion Dollar Bracket Challenge would win.
Another way to look at it would be which contest gives the best chance to win something. If this is what would be considered “best,” then the lottery would win hands down. The odds of winning something would be just under 1 in 15 (see chart below), although in many cases, the prize would be quite small.