Codewars Kata: Shell Game (Clojure)

shell-game.clj

(ns the-shell-game)

;;https://www.codewars.com/kata/the-shell-game/clojure

(defn switch [location swap]
  (cond (= location (first swap))
           (last swap)
        (= location (last swap))
           (first swap)
        :else
          location))

(defn find-the-ball [start swaps]
  "Given the starting position and a list of swaps, find the final position"
  (if (nil? (first swaps))
    start 
    (find-the-ball
      (switch start (first swaps)) 
      (rest swaps))))

Maybe I'm restating what you just said.
Line 18 and 19 are the new values (the new state) in the recursive call.

(switch start (first swaps)) ;; calculates the new location based on the first swap.
(rest swaps) ;; first swap was processed in previous line, only process remaining swaps.