A 6 ft 4 in (193 cm) forward from San Francisco, California, Dallmar played collegiately at Stanford University.

He led Stanford to the 1942 NCAA Championship, earning Tournament Most Outstanding Player honors.

From 1946 to 1949, he played professionally for the Philadelphia Warriors of the Basketball Association of America (a forerunner to the NBA).

Dallmar was the third leading scorer (behind Joe Fulks and Angelo Musi) on the team which won the 1947 BAA Championship.

In the 1947–48 season, Dallmar led the BAA in total assists[1] and was named to the All-BAA First Team.