Building rig vs. Asic

I am new to crypto mining and I would like to get into mining. I do not mind saving up money to buy an asic or to to build a rig.

On asic miner value I was looking up the different ASICS, what they producer and cost to buy. Do you think it would be cheaper to built a rig than it is to buy an asic and still get equal or better payout than the asic?


Antminer S19 Pro (110Th) $40 daily earnings before electricity

Cost to buy: 11k to 14k

If the rig equivalent is cheaper, what to you think the price for the rig would look like?