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Since the merger of the AFL and the NFL in 1970, the Chiefs have a long history of losing strange divisional playoff games, particularly ones in which they are playing at home and favored in.
In 1971, the Chiefs lost the longest game in NFL history in double overtime to the Miami Dolphins ...... in spite of Ed Podolak's 350 all-purpose yards, which remain a post-season record to this day. Also, the first pure place-kicker to ever be elected to the Hall-of-Fame (Jan Stenerud) missed a chip-shot field goal with less than a minute remaining in the 4th quarter, which would have won the game for the Chiefs.
In 1995 the Chiefs were the #1 seed in the AFC with a record of 13-3, and were heavily favored against Jim Harbaugh's Indianapolis Colts ...... but lost by a score of 10-7.
In 1997 they again were 13-3 and the #2 seed in the AFC, but lost in the divisional playoffs to John Elway's Broncos, who would go on to beat the defending world champion Green Bay Packers in the Super Bowl.
In 2003 it was again the Indianapolis Colts haunting the heavily favored, #2 seeded Chiefs again. This time the Colts beat the Chiefs in a 38-31 shootout
IN A GAME IN WHICH NEITHER TEAM PUNTED. ) 
In 2016 the Chiefs lost yet another divisional playoff game on their home field in a game in which they outscored their opponents, 2 touchdowns to 0.
They did manage to win one divisional playoff game in 1993, when Joe Montana and company took down the Houston Oilers in the Astrodome ........ but that was on the road, and (unlike the numerous other heartbreaking divisional losses which they have sustained), they were not the favorites to win that game.
The Kansas City Chiefs ...... a strange (and painful), but true divisional playoff history.
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