It's pretty damn hard to beat a team 3 times in one season. Cats by 12.
I would be willing to bet everything I own that if you look at every 3rd matchup between basketball teams in the same season in the last 20 years that where one team has won the first 2 games, that team will also win the 3rd game more than 50% of the time. I wouldn't be surprised at all if the team won the 3rd game more than 70% of the time. In reality, it's hard to beat a team that has already beaten you twice.
Cats win 72-60.
I did this earlier, I came up with 42-23 record that the team wins the 3rd game as well, based on Big 12 Tournament History:
1995 KU W Iowa St. 89-74
1995 KU L Missouri 68-63
1995 MU W Nebraska 70-61
1995 Tex L Texas Tech 92-81
1995 OU W Texas Tech 67-60
1996 KU W Iowa St. 89-74
1996 KU L Missouri 68-63
1996 MU W Nebraska 70-61
1996 Tex L Texas Tech 92-81
1996 OU W Texas Tech 67-60
1997 KU W Iowa St. 89-74
1997 KU L Missouri 68-63
1997 MU W Nebraska 70-61
1997 Tex L Texas Tech 92-81
1997 OU W Texas Tech 67-60
1998 KU W Iowa St. 89-74
1998 KU L Missouri 68-63
1998 MU W Nebraska 70-61
1998 Tex L Texas Tech 92-81
1998 OU W Texas Tech 67-60
1999 KU W Iowa St. 89-74
1999 KU L Missouri 68-63
1999 MU W Nebraska 70-61
1999 Tex L Texas Tech 92-81
1999 OU W Texas Tech 67-60
2000 KU W Iowa St. 89-74
2000 KU L Missouri 68-63
2000 MU W Nebraska 70-61
2000 Tex L Texas Tech 92-81
2000 OU W Texas Tech 67-60
2001 KU W Iowa St. 89-74
2001 KU L Missouri 68-63
2001 MU W Nebraska 70-61
2001 Tex L Texas Tech 92-81
2001 OU W Texas Tech 67-60
2002 KU W Iowa St. 89-74
2002 KU L Missouri 68-63
2002 MU W Nebraska 70-61
2002 Tex L Texas Tech 92-81
2002 OU W Texas Tech 67-60
2003 KU W Iowa St. 89-74
2003 KU L Missouri 68-63
2003 MU W Nebraska 70-61
2003 Tex L Texas Tech 92-81
2003 OU W Texas Tech 67-60
2004 KU W Missouri 94-69
2004 Tex W Oklahoma 66-63
2004 OSU W Texas 65-49
2005 KU W Kansas St. 80-67
2005 MU W Nebraska 70-67
2005 OSU W Texas Tech 72-68
2006 KU W Nebraska 79-65
2006 Tex W Texas Tech 77-70
2007 KU W Kansas St. 67-61
2007 Tex W Baylor 74-69
2007 A&M L Oklahoma St. 57-56
2008 KU W Nebraska 64-54
2008 Tex W Oklahoma St. 66-59
2008 Tex W Oklahoma 77-49
2009 Tex L Baylor 76-70
2009 A&M L Texas Tech 88-83
2009 OU L Oklahoma St. 71-70
2010 KU W Kansas St. 72-64
2010 MU L Nebraska 75-60
2010 Bay W Texas 86-67
(Used Kenpom for historical results)