Pool | Harder, Better, Faster, Stronger

On Hockey Pools

18/10/2011

If you have ever played in Hockey pools (or any other kind of pools) you know that if you do not get a good drawing rank, your chances of winning anything are greatly diminished. So, here’s how a typical pool works. There are $n$ pool players that will form “teams” with $k$ league players (usually real players from the real leagues, with their standardized scores) from a total of $m$ league players.

To form the $n$ teams, the $n$ players put their numbers $1,2,\ldots,n$ in a hat, and the numbers are drawn one by one, determining in which order, in each round, pool players will get to choose their next pick in the remaining league players. That is, if the order drawn is, say, 5, 3, 4, 2, 1, then pool player number 5 gets to choose first, picking one league player, then goes pool player 3, and so on, until all pool players picked a league player, thus completing one round. There are $k$ of those rounds so that each pool player has his team of $k$ league players.