Dhameystir weedha soo socota: wuxuu ugu dambeyntii lumiyay horyaalkiisii 1985 kii Garry Kasparov, oo qaabkiisa dagaal ee xeeladeysan uu aad uga duwanaa qaabka booska ee Karpov. Labadooduba waxay la dagaalameen shan ciyaarood oo aad u dhow oo horyaalnimada adduunka ah, Horyaalka Adduunka ee Chess 1984 (si muran leh ayaa loo joojiyay natiijo la'aan iyadoo Karpov uu hogaaminayo +5 −3 = 40), Horyaalka Adduunka ee Chess 1985 (oo uu Kasparov ku guuleystay horyaalka, 13<unk>11),
Horyaalka Adduunka ee Chess 1986 (oo uu ku guuleystay Kasparov, 121⁄2 <unk> 111⁄2), Horyaalka Adduunka ee Chess 1987 (oo la saxeexay 12 <unk> 12, Kasparov oo haysta horyaalka), iyo Horyaalka Adduunka ee Chess 1990 (mar kale oo uu ku guuleystay Kasparov, 121⁄2 <unk> 111⁄2).