There are cards numbered $1,2,\ldots,2n$ where $n$ is odd. The deck is shuffled. The top two cards are drawn. If the sum is even the even player gets a point and if the sum is odd the odd player gets a point. The next two cards are drawn and if the sum is even the even player gets a point and if the sum is odd the odd player gets a point. The game continues until all the cards are drawn. Which player will get the most points? Now for one draw odd is favored because once a even card is drawn there are more odd cards in the deck so it would appear that odd is favored. Here are my results. (Possibly wrong because the math is complicated) $$ \begin{array}{|l|l l|} 6\text{ cards} & \text{even wins }\dfrac{3}{5} & \text{odd wins }\dfrac{2}{5}\\\hline 10\text{ cards} & \text{even wins }\dfrac{67}{315} & \text{odd wins }\dfrac{248}{315}\\\hline 14\text{ cards} & \text{even wins }\dfrac{597}{1001} & \text{odd wins }\dfrac{404}{1001}\\ \end{array} $$
Each of these results was a surprise to me. Is there a simple explanation. What happens as $n$ gets large?
from Hot Weekly Questions - Mathematics Stack Exchange
Bob Powers
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