This is even cheaper than Screwy's, but you might need a BIOS update to run kaby lake CPU's.
You can go with a B250(will add a bit to the price), as there is no H210 chipset.
Removed fan, swapped GPU for less expensive one, G4560 is same as i3-6100, added dual channel RAM, cheaper case, cheaper motherboard, cheaper HDD. Don't worry about the cheaper components, everything will work the same.
I am pretty sure that Pentium can run Battle Field, because it performs almost the same as i3-6100. It's not a normal pentium, it's hyperthreaded, same as the i3, it has 2 threads for each core.
Cut $200 from the price.
PCPartPicker part list /
Price breakdown by merchant
CPU: Intel Pentium G4560 3.5GHz Dual-Core Processor ($94.00 @ shopRBC)
Motherboard: Gigabyte GA-H110M-A Micro ATX LGA1151 Motherboard ($63.98 @ DirectCanada)
Memory: Corsair Vengeance LPX 8GB (2 x 4GB) DDR4-2400 Memory ($67.00 @ shopRBC)
Storage: Western Digital Caviar Blue 1TB 3.5" 7200RPM Internal Hard Drive ($62.85 @ Vuugo)
Video Card: Gigabyte GeForce GTX 1050 Ti 4GB Video Card ($181.50 @ Vuugo)
Case: Xion XON-350_BK ATX Mid Tower Case ($34.99 @ Newegg Canada)
Power Supply: Corsair CXM 450W 80+ Bronze Certified Semi-Modular ATX Power Supply ($59.99 @ Memory Express)
Total: $564.31
Prices include shipping, taxes, and discounts when available
Generated by PCPartPicker 2017-01-29 14:32 EST-0500