Brian Harman has the most career rounds, with 964 rounds.

who had the most bogey-free rounds at muirfield
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HarmanHowell IIIEnglishStreelmanBradleyHoffmanReedStuardHorschelKucharTringaleKokrakWoodlandJohnsonBrownKirkKnoxSnedekerLeishmanSimpsonStallingsJones964901891887887876867865860859856849847840832826822820811810808805
NAMEEVENTSROUNDSBOGEYSTOP 10WINSMONEY
Brian HarmanBrian Harman3729642,362422$21,778,454
Charles Howell IIICharles Howell III3399012,130401$19,236,370
Harris EnglishHarris English3458912,206384$22,239,040
Kevin StreelmanKevin Streelman3418872,207342$19,121,802
Keegan BradleyKeegan Bradley3358872,276452$27,008,600
Charley HoffmanCharley Hoffman3348762,302362$22,480,680
Patrick ReedPatrick Reed2488672,149559$36,321,768
Brian StuardBrian Stuard2808652,222231$11,223,183
Billy HorschelBilly Horschel3038602,091516$30,417,840
Matt KucharMatt Kuchar3098591,965716$37,450,032
Cameron TringaleCameron Tringale3348562,081260$15,034,324
Jason KokrakJason Kokrak3198492,067333$20,225,854
Gary WoodlandGary Woodland3048472,098443$26,720,316
Zach JohnsonZach Johnson3198402,081455$25,831,391
Scott BrownScott Brown3218322,149251$10,654,046
Chris KirkChris Kirk3218261,914313$18,769,187
Russell KnoxRussell Knox3098221,876252$16,388,808
Brandt SnedekerBrandt Snedeker3098202,076517$29,178,062
Marc LeishmanMarc Leishman3068112,115486$30,608,372
Webb SimpsonWebb Simpson2908101,904645$35,205,406
Scott StallingsScott Stallings3288082,123232$11,799,842
Matt JonesMatt Jones2948052,020202$13,964,652
Brendan SteeleBrendan Steele3078042,046302$17,034,956
Bill HaasBill Haas3108032,009353$18,926,379
Jimmy WalkerJimmy Walker3217992,168386$22,907,896
StatMuse has season-level data for bogeys going back to the 2011-12 season.