Being the first to pick 1 of 2 cards out of a deck of 52 that will win you 1 million dollars.

• The first-in-line is the winner with probability $\frac2{52}$
• The second-in-line is the winner with probability $\frac{50}{52}×\frac2{51}$
• In general, the $n$th-in-line is the winner with probability $$f(n)=\frac2{53-n}\prod_{k=1}^{n-1}\frac{51-k}{53-k}$$

However, $f(n)$ is strictly decreasing because (as can be shown by manipulating the definition) $$f(n+1)=\frac{51-n}{52-n}f(n)$$ Hence you should ask to be first-in-line to have the highest probability of winning.

Think of it this way. If there were only one winning card, it would have equal probability to be in each place in the deck, and (equivalently) each person in line would be equally likely to receive the winning card. With multiple winning cards, it’s still the case that each person in line is equally likely to receive a winning card; but to win, you need to receive a winning card and be the first to do so. This is most likely if you’re first in line, since the second condition is then guaranteed.