In a decentralized system, where no individual or group holds the majority of power, the only way to seize control is to gain a majority of like-minded individuals. This is the origin of the 51% attack - where the system needs a majority vote to reach consensus.
Although a 51% attack in a large distributed network, such as Bitcoin, Ethereum etc. is highly unlikely due to sheer size, smaller coins face a bigger risk simply because there are fewer participants, which makes it easier to manipulate.
This is why the website crypto51 was made: a collection of coins and the theoretical cost of a 51% attack on each network, it is not meant to encourage attacks, but to get people talking about the problem and potential solutions. As to how it works, the website explains: “Using the prices NiceHash [a Slovenian cryptocurrency cloud mining marketplace] lists for different algorithms we are able to calculate how much it would cost to rent enough hashing power to match the current network hashing power for an hour.”
Bytecoin is an example of 51% attack potential: with a market cap of around USD 1 billion, it can be 51% attacked for only USD 557, according to the website. While hackers targeting coins such as Bata, Startcoin, Halcyon and some others would require only a few bucks to attack these networks.
51% attack costs. Source: crypto51.app
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Since NiceHash doesn’t have the hashing power for larger coins, the website also lists the percentage of the needed hashing power that is available from Nicehash. The attack cost does not include the block rewards that the miner will receive for mining.
In either case, recently there have been a number of 51% attacks including attacks on Verge and Bitcoin Gold.
Also, there was in fact a moment, in 2014, when the mining pool Ghash.io came close to obtaining 51% of the whole Bitcoin network. But then some members of the pool voluntary left, decreasing its share. Still, Bitcoin experts believe a 51% attack is very unlikely as its cost would exceed the possible benefits and it would most likely hurt the very attacker. Moreover, such an attack can’t be used to steal bitcoins or change older transactions, as the attacker would be only able to double spend his/hers funds from a recent transaction. Also, any attack would only last for a short time before being quickly fixed by the Bitcoin community.
Bitcoin evangelist Andreas Antonopoulos on 51% Bitcoin attack: