Bitcoin Mining versus Lottery

Mining Bitcoin on CPU or GPU is no longer profitable, for a while now. But what if you just keep your computer mining, by itself, without joining a mining pool? After all, it’s your ticket to the 12.5 BTC (~$75,000) lottery award, given out every 10 minutes. What is the probability to win this award? How does it compare with probability of winning an old fashioned lottery? Let’s see the numbers.

Bitcoin mining at its core, is a search for a solution to a math problem. Anyone can participate by allocating computing power and the chances to find the solution are proportional to your share of of the entire network computing power (or hash rate).

Current total hash rate is ~11,000,000 TH/s. A good ASIC miner has 13.5 TH/s while a GPU has, let’s say, 700 MH/s and a CPU has 20 MH/s. I’ve picked rather the high end hardware, so your results may differ.

Thus the probability of mining one block (and getting the award) is:

p1 = 13.5/11,000,000 = 0.00000122 for ASIC

p2 = 700/1000/1000/11,000,000 = 0.0000000000063 for GPU

p3 = 20/1000/1000/11,000,000 = 0.00000000000018 for CPU

Not a great probability! Now, in a month, there are N=6*24*30 mined blocks. To find the probability of winning one award in a month, we use the Bernoulli trial formula:

N*p1*(1-p1)^(N-1) = 0.0026 for ASIC

0.000000137 for GPU

0.0000000039 for CPU

So with $1400 specialized ASIC, mining without joining a pool, for a full month, only gives us a 0.26% chance of winning a $75,000 award with electricity cost about $40.

Let’s see how it compares with a traditional lottery.

At 6/59 Lotto program in UK the probability of winning with a 2GBP ticket is:

1/45,057,474 = 0.000000022

This is pretty close to our CPU probability but the award is much greater, up to 1M GBP. So, maybe not surprisingly, it’s better to play lottery than to mine Bitcoin with a CPU or even a GPU. If you wanna try your luck you can mine with an ASIC on your own, or just go for the sure thing and join a mining pool where you convert your chances into an actual percentage of reward (that is, you may receive 0.0026 * $75,000 = $195 in the first month). Note that mining performance depends on many variables, where total hash power and Bitcoin price are the most important (and also quite volatile).