Yes, the probababilty of drawing an ace on any one draw is 1/13. The proability of drawing any card except an ace is 12/23. In order that "Karl wins on his third turn", karl must NOT draw an ace on his first two draws but draws an ace on the third: the probability of that is (12/23)(12/23)(1/13). Of course, Hanna must not draw an ace on the first or second draws. The probability of that is (12/23)(12/23). Therefore, the probability of Karl drawing an ace on the third draw of those is the product: