I installed a 3000 watt inverter in Big Blue and ran #2 wire from the aux battery to it. That size was predicated on the length of the run and the fact that the inverter can actually pull 6000 watts when starting a load.
You can read about my installation
here. But note that I connected to the aux battery. That way I won't strand myself in the middle of nowhere by pulling the starting battery down too far.
Gary, AKA "Gary fellow":
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Dad's: '81 F150 Ranger XLT 4x4: Down for restomod: Full-roller "stroked 351M" w/Trick Flow heads & intake, EEC-V SEFI/E4OD/3.50 gears w/Kevlar clutches
Blue: 2015 F150 Platinum 4x4 SuperCrew wearing Blue Jeans & sporting a 3.5L EB & Max Tow
Big Blue: 1985 F250HD 4x4: 460/ZF5/3.55's, D60 w/Ox locker & 10.25 Sterling/Trutrac, Blue Top & Borgeson, & EEC-V MAF/SEFI