Derrick Henry and Adrian Peterson are tied for the most games by a running back with 200+ rushing yards and 3+ rushing touchdowns, with 2 games.

which rb has the most games with 200 yards and 3 tds
Interpreted as:
Which rb has the most regular-season games with 200 or more rushing yards and 3 or more rushing tds?
HenryPetersonBellGrayMorrisMartinFosterHarrisonBarberJohnsonPortisTomlinsonAlexanderAndersonTaylorJamesDillonSandersMorrisWarnerCollinsPruittJohnson22111111111111111111111
NAMEGPRUSH YDSRUSH TDATTRUSH AVGRUSH YDS/GREC YDSRECTRGREC AVGREC YDS/GREC TD
Derrick HenryDerrick Henry24497499.2224.50000.00
Adrian PetersonAdrian Peterson252065010.4260.0282414.014.00
Le'Veon BellLe'Veon Bell12363386.2236.0624515.562.00
Jonas GrayJonas Gray12014375.4201.00000.00
Alfred MorrisAlfred Morris12003336.1200.012226.012.00
Doug MartinDoug Martin125142510.0251.021455.321.00
Arian FosterArian Foster12313337.0231.07117.07.00
Jerome HarrisonJerome Harrison12863348.4286.012236.012.00
Tiki BarberTiki Barber123432310.2234.024348.024.00
Larry JohnsonLarry Johnson12013267.7201.0212210.521.00
Clinton PortisClinton Portis12185229.9218.0362318.036.00
LaDainian TomlinsonLaDainian Tomlinson12203375.9220.05111144.651.00
Shaun AlexanderShaun Alexander12663357.6266.07117.07.00
Mike AndersonMike Anderson12514376.8251.05115.05.00
Fred TaylorFred Taylor12343307.8234.014374.714.01
Edgerrin JamesEdgerrin James12193385.8219.09119.09.00
Corey DillonCorey Dillon12464396.3246.030215.030.00
Barry SandersBarry Sanders12204239.6220.03147.831.00
Joe MorrisJoe Morris12023365.6202.015115.015.00
Curt WarnerCurt Warner12073326.5207.0000.00
Tony CollinsTony Collins12123239.2212.0515.05.00
Greg PruittGreg Pruitt12143268.2214.02337.723.00
John Henry JohnsonJohn Henry Johnson12003306.7200.0414.04.00
Cookie GilchristCookie Gilchrist12435366.8243.0000.00
Billy CannonBilly Cannon12163258.6216.0114522.8114.02
StatMuse has game-level data for rushing touchdowns and rushing yards going back to the 1960 season.

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