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Lou Gehrig had the most games with 4+ hits and when collecting 4+ RBI, with 20 games.

most career games with 4 or more h and 4 or more rbi by a batter
Interpreted as:
most career regular-season games with 4 or more h and 4 or more rbi by a batter
GehrigGehringerSimmonsCabreraCruzBichetteBettsPiazzaBagwellPalmeiroDickeyGoslinStargellMaysPujolsRodriguezAndersonMartinezWalkerBondsCarterMurray201515141212111111111111101099999999
NAMEGHRBIABR2B3BHRBBHBPSOSBCSPATBXBHSHSFIBBGIDPAVGOBPSLGOPS
Lou GehrigLou Gehrig208096103591733310152114202530.777.7981.9612.759
Charlie GehringerCharlie Gehringer1563738134183104013861173110.778.7881.4442.233
Al SimmonsAl Simmons156273823810219005082133310.756.7561.6222.378
Miguel CabreraMiguel Cabrera145764713290203030174126290020.803.8111.7752.585
Nelson CruzNelson Cruz1249686028101191032061118300000.817.8201.9672.786
Dante BichetteDante Bichette1250546424101130027164101240000.781.7811.5782.359
Mookie BettsMookie Betts1144585435100215122060117310000.815.8332.1673.000
Mike PiazzaMike Piazza1146515326100155010058101250010.868.8791.9062.785
Jeff BagwellJeff Bagwell114553563271163142060102240000.804.8171.8212.638
Rafael PalmeiroRafael Palmeiro114548512310014302105497240000.882.8891.9022.791
Bill DickeyBill Dickey1144495419419400158771400.815.8281.4262.254
Goose GoslinGoose Goslin114551561745910315786180.804.8071.5362.343
Willie StargellWillie Stargell1043494824151140031048102300000.896.8962.1253.021
Willie MaysWillie Mays104247502824176014256103230012.840.8572.0602.917
Albert PujolsAlbert Pujols9374142219011300004579200001.881.8891.8812.770
Alex RodriguezAlex Rodriguez9395346286016203104993220100.848.8372.0222.858
Garret AndersonGarret Anderson9364643176112100104480190001.837.8411.8602.701
Tino MartinezTino Martinez9384147285015301005088200000.809.8201.8722.692
Larry WalkerLarry Walker9364543243218303424697230000.837.8482.2563.104
Barry BondsBarry Bonds9364145216015003304587210000.800.8001.9332.733
Joe CarterJoe Carter9393847247113003404787210000.830.8301.8512.681
Eddie MurrayEddie Murray9364546206111402205077180001.783.8001.6742.474
Lee MayLee May9374149234016005004989200000.755.7551.8162.571
Joe DiMaggioJoe DiMaggio93852452882193000491072910.844.8542.3783.232
Phil CavarrettaPhil Cavarretta939404918561210152591200.796.8081.2042.012
Chuck KleinChuck Klein
Mickey CochraneMickey Cochrane
Baby Doll JacobsonBaby Doll Jacobson
Bob MeuselBob Meusel
Paul GoldschmidtPaul Goldschmidt
David OrtizDavid Ortiz
Mark TeixeiraMark Teixeira
Todd HeltonTodd Helton
Manny RamirezManny Ramirez
Moises AlouMoises Alou
Sammy SosaSammy Sosa
Fred McGriffFred McGriff
Chili DavisChili Davis
Paul MolitorPaul Molitor
Stan MusialStan Musial
Earl AverillEarl Averill
Bill TerryBill Terry
Harry HeilmannHarry Heilmann
Nick CastellanosNick Castellanos
Matt KempMatt Kemp
Joe MauerJoe Mauer
Aramis RamirezAramis Ramirez
Sean CaseySean Casey
Mike SweeneyMike Sweeney
Ivan RodriguezIvan Rodriguez
StatMuse has game-level data for RBIs going back to the 1920 season.
Some of the information used here was obtained free of charge from Retrosheet.

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