BOSTON — The man at the wake for the father of the future Boston University hockey coach Jack Parker quietly approached Parker’s mother to offer his condolences. He also offered something more: cash.

The money, the man explained, came from a bet that the elder Parker had made on a horse named Arts and Letters in the 1969 Belmont Stakes. The horse, which had finished second to Majestic Prince in both the Kentucky Derby and the Preakness Stakes, had won the Belmont.

The man, Parker said, was his father’s bookie.

Parker never forgot the story, probably because it speaks to what he epitomized in four decades as the coach of the Terriers: loyalty, commitment and dedication. He has never coached anywhere else at the college level, and his 895 victories at Boston University represent the most by a hockey coach at one college. He also played at Boston University for three years, including as captain of the 1967-68 team, and was an assistant coach for three more.

On Saturday night, Parker retold the bookie story after stepping away from a postgame news conference at Agganis Arena for the final time. He will coach at least one more game — a Hockey East semifinal Friday against Boston College at TD Garden. The Terriers are not certain to make the N.C.A.A. tournament, but one thing is sure: Parker will no longer coach in the arena he helped build and at the rink that bears his name.