I’m not an expert so take this with a grain of salt,
ps4 roughly 100watts
tv roughly 150 watts (could be 400 depending on size/type)
= 250 watts / 110v = 2.27 amps
(watts / volts = amps)
Then plug that in here (if the calculator works correctly): https://www.batterystuff.com/kb/tools/dc-to-ac-amperage-conversion-run-through-an-inverter.html
so ~ 23 amps an hour, so for 3 hours ~ 70 amps. This really doesn’t take into consideration a lot of factors such as how efficient your inverter is at converting power. From looking at this 110/120 dc seems to be about 10x the amps. 70 amps is more power than we typically pull in three days, but we don’t have a TV or playstation 4 hooked up in our van. Maybe look at a tablet. We honestly use our ipad pro for everything, tv, games, movies, work. Beyond our phones, it’s the only electric device we use that isn’t life sustaining.
Also if you have standart lead acid batteries, you only can take 50% of the power from them before they start to sulfate and lose overall capacity. So for 3 hours you essentially would need two 70ah batteries. Again, I could be way off base here as we don’t convert 110 for anything in our build.