By the end of the twenties, Jacoby had achieved fame as a player at both auction and contract bridge, further gaining international recognition when chosen by Sidney Lenz to be his partner in the famous Culbertson–Lenz match of 1931. Jacoby's more aggressive bidding style confused Lenz and Jacoby withdrew after Lenz's criticism. Years later the analyst Terence Reese wrote, "That the Culbertsons did not win more easily ... was due to the fact that Jacoby was a player of quite different class from any of the others". Jacoby subsequently solidified his position as the most successful tournament player in the thirties as a member of the famous "Four Horsemen" from 1931 to 1933 and the "Four Aces" from 1933 to 1941, dominating tournament play. He is recognized by the American Contract Bridge League (ACBL) as Life Master #2, one of ten named in 1936. LM #1 is David Burnstine, his partner on the Four Horsemen and co-founder of the Four Aces.