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I have recently heard about a different type of March Madness pool where you get a group of 16 friends. Each of you draw a slip of paper, numbered 1-16, from 4 different cups. You now have 4 numbers (representing the seed of a team from each of the 4 regions). If one of your teams makes it to the Elite 8, you break even on the money you put into the pot and if any of your teams go farther, you get more money.

My question is this: What are the odds that I at least break even if I participate in a pool such as this?

Similar - Flipping coin - Perfect Bracket

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Pants
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In many cases it is easier to find the odds of not what you are interested in, and then subtract those from 1.

Here, we'll find the odds of not making the elite 8 in any of the 4 regions.

For each region there will be 2 elite 8 teams out of the 16. The odds of you randomly selecting one of those two are (2/16), still better than my historical odds of non-random selection... The probability of not choosing an elite 8 team in any of the 4 regions is $\frac{14}{16}$.

So to lose all 4, we raise $\frac{14}{16}$ to the 4th power. $\left(\frac{7}{8}\right) ^ 4 = \frac{2401}{4096}$ and $1-\frac{2401}{4096}=\frac{1695}{4096}\approx0.414$ or just over 41%.

MikeP
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    This is exactly what I was looking for! Thank you! I knew it was much simpler than the way I was thinking about it. – Pants Mar 16 '16 at 14:44