The lottery concept: scanning random private keys to find addresses with balance.

I always had a stupid question in mind: What if someone decides to create a tool to randomly scan bitcoin private keys? It is a bit like playing the lottery, with the possibility to try 1 ticket every second, knowing right away if you won and, all of that for free (if we neglect electricity costs).

You just need to let the tool run, and, if the key is empty: next. If there is something: you get a notification. Could it be possible?

Let’s dig in.

To answer this question, I will consider the most popular crypto: Bitcoin.

Long story short: there are around 2²⁵⁶ possible BTC private keys. That's a little larger than a 1 followed by 77 zeroes (1×10⁷⁷). How big is that? As a comparison: A group of researchers at the University of Hawaii attempted to calculate the number of grains of sand on Earth. After careful estimates of the sand on all the beaches and deserts in the world, they predicted that there are 7.5 quintillion grains of sand on earth (7.5×10¹⁸ ). You can then envision that even with this huge number, we are still very far from the 1×10⁷⁷ possible private keys…

But, in order to accurately estimate the probability of hitting a private key with funds, we must also consider the number of private keys currently being used (there is not only 1 user on the Bitcoin network). It was monitored that in January 2021, more than 22.3 million unique addresses were active in the BTC network meaning that at best, 2.23×10⁷ private key were active and used for sending or receiving BTC.

At the end, it then means that you have a one in 5×10⁶⁹ chance of finding a private key with funds on it. And even if you succeed, there is no guarantee that the amount of BTC will be substantial. Once again, even by reducing 1×10⁷⁷ to 'only' 5×10⁶⁹, this final number is still billions and billions times bigger than the amount of grains of sand on earth.

Still not convinced? The odds of winning the lottery are around 1 in 2×10⁸ (1/200 millions) while you have one in 3,4 million chance of dying after coming into contact with a venomous animal or one in 10 million chance (1×10⁷) of being struck by falling airplane parts.

Chances of finding a BTC key versus chances of being hit by a reactor : 5×10⁶⁹ vs 1×10^7. You have around 500000000000000000000000000000000000000000000000000000000000000 more chances of being killed by a falling airplane reactor than finding a BTC private key!

And finally, even if you have all the time in the world and even if we simplify the process of scanning (i.e. neglecting some parameters that might affect the time required to test a given BTC key), a conservative estimate predicted that with our current technology, it will take around 0.65 billion years to break one single Bitcoin key. However, this could change with the advent of quantum computers. But this is another topic.

At the end, the answer to the question ‘is it worth trying to scan random BTC keys?’ is pretty obvious: No, it is absolutely not worth it.

But… apparently, not everyone thinks the same. A quick Google search allowed me to see that many websites/tools exist to perform such a task. Either we don’t do math the same way or those guys are very optimistic.

In both cases, I wish them good luck.

Websites used for my research : 1-Reference 1 (1) ; 2- Reference 2 (2) ; 3- Reference 3 (3) ; 4 – Reference 4 (4) ;5- Reference 5 (5) ;6- Reference 6 (6) ;7- Reference 7 (7)

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TL:DR : You will die struck by lighting while being bitten by a cobra and hit by an airplane reactor before randomly cracking someone's BTC private key.