You can compete against other players by pressing the Compete! link in the navigation bar, choosing the player you’d like to compete with, and clicking the button.
Competing will the combine the Determination of all the Challenger’s tack, up to the amount of club members the Challenger has, and compare it to the Horsemanship skill of the Defender’s combined tack, up to the amount of club members the Defender has. The highest number wins. The winner will gain some experience and, if the loser has enough cash on them, take some of the loser’s cash.
Tip: You can not lose cash that is in the bank!