I don't have a clue what any of that means. Lol. How many amp hour is the battery?
Battery life has a lot of factors and you won't really know how long it will run until you actually test it.
Watts=Amps X Volts
Amps=Watts/Volts
Amps=50w/12v
Amps=4.17A
So theoretically your lights draw 4.17A.
4.17A X 8lights = 33.36A
A battery capacity is measured in Amp Hours (Ah)
Generally an amp hour is described as how many continuous amps a battery will put out over a 20 hour period until the battery is completely dead. The time may vary from manufacturer or type of battery. So to keep it simple say your battery is a 200Ah battery tested over 20 hours. This battery will operate a 10A draw for 20 hours. Because you are drawing 3x the amps mathematically you will get a little less than 7 hours on the battery. But because you are exceeding the 10A rating for the battery you won't get the full potential out of the battery. Adding in lost power for resistance I would guess a 200Ah battery would run those lights for about 5 hours.
Sorry for the rambling. Hope this makes some sense.
