There are a few things you're going to need... with the most important of them all being a digital asset wallet. There are many wallets out there, but I use a mix of Jaxx and Exodus. Jaxx is available on virtually everything including Windows, Mac, iOS, Android, and more. I use Jaxx on both Windows and Android, and haven't had any issues with it so far (except for sending $3500 to the wrong ETH address... so don't be like me, and triple check everything you do).
The biggest benefits of using Jaxx or Exodus is that they have ShapeShift built-in. Some of you will know what ShapeShift is, but for those who don't, ShapeShift is an incredibly useful tool for those who aren't going to be day trading cryptocurrency.
PC + Lots of GPUs
You won't need to have 50 graphics cards to mine cryptocurrency, a single graphics card and hell, even a laptop will do (you can mine using only your CPU). You can mine with your CPU, HDD, and GPU - something we'll get into soon. For now, you'll need a PC that is running Windows and a graphics card.
AMD is definitely superior at mining especially when it comes to Ethereum, but even their new Radeon RX Vega graphics cards run ridiculously hot when mining. I'm not going to spend much time recommending NVIDIA or AMD over each other, but if you want cooler-operating cards, go for NVIDIA GeForce GTX 10 series cards. If you want brute performance that will see you tweaking for hours, AMD has the power.
Time. Time is the most important thing here. Don't think that you can spend 10 minutes doing this and it'll be up and running and you can walk away from your PC and start cashing it in and buying Lamborghini's all over the place.
If you're running a single PC with a single graphics card then it's going to be very simple: install Jaxx or Exodus and get your BTC wallet and address in order, run the mining software (like NiceHash), and that's it. Your PC will make you money. If you have multiple PCs with multiple graphics cards per machine (like I do), it's a time-consuming hobby that just so happens to make you money.
The more systems you're running, the more time it will take to maintain it all. Heating and cooling becomes a problem, so does noise and networking. They are all things we'll talk about, but you'll need to be prepared to spend lots of time tinkering and reading if you want to be serious about mining cryptocurrency.
You should also consider your power costs to determine if mining is profitable or not.
Thankfully, NiceHash has a handy tool on its website that allows you to input the kWh charge your electricity company charges you and select your hardware, and it will give you a rough idea of potential earnings per day, week, and month.
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