How unlikely is it to hack Bitcoin? An attempt to do some math.

Over the years, Bitcoin established itself as the most secure network in the world, due to its amazingly programmed characteristics. The biggest risk for Bitcoin would be facing a serious hack, due for example to a 51% attack.

A 51% attack on a blockchain occurs when a group of malicious miners gains control of over half of the network's mining power. This control theoretically allows them to manipulate the blockchain by preventing or reversing transactions, basically giving them the power to decide the destiny of the chain.

We often hear that a 51% attack against the Bitcoin network would be incredibly expensive but do you know exactly how much would it cost?

Currently, the best mining machine is the Bitmain Antminer S19 XP Hydro which provides an average hash rate of 255 Terahash per second (Th/s). I've looked online and you can purchase this machine for 8500$. Currently, Bitcoin hash equals 450 Exahash per second (Eh/s). Let's do some math: 51% of the current hash rate is approximately 230 Eh/s, equal to 230 million Th/s. If a single Hydro provides 255 Th/s, you would need 901960 mining machines, which you can afford if you have 7.66 billion dollars to invest.

In theory, the top 3 mining pools in the world, if they joined forces, could attempt to do a 51% attack but they would need to coordinate the attack with incredibly precise timing, creating a malicious block before the "honest" chain creates one itself and that's really difficult.

While smaller cryptocurrencies with lower participation rates are more vulnerable, larger networks like Bitcoin have robust security measures in place. So, even if an attack were attempted, the consensus mechanism and the great decentralization would easily prevent it.

What about Ethereum? Since its transition to proof of stake, Ethereum has become more resilient to these kinds of attacks. Currently, there are 27 million ETH staked and to try a 51% attack you would need to control 13.8 million ETH, equal to 43 billion $. Again, theoretically possible but highly unlikely. Also, the consensus mechanism would likely recognize the attack and immediately slash the staked ETH, costing the attacker an extraordinary amount of money.

I've always trusted the "attack's impossibility axiom" but I've never really looked into it, now I did and I thought it would have been interesting to share it, hope you appreciated it. Thank you for reading.