How many confirmations of a bitcoin transaction are enough

In a recent study, European mathematicians Cyril Grünspan and Ricardo Pérez-Marco, usingmathematical analysis and game theory showeddue to the high level of network security and the relatively high price of bitcoin, small transactions do not need six confirmations, which today are required by some exchanges, cryptocurrency services or participants in the OTC market.

The habit of waiting six confirmations is inheriteddirectly from Nakamoto - the classic Bitcoin client will display a transaction as “unconfirmed” until there are six confirmations (6 blocks found).

This figure was not chosen by chance: it is based on the theory that the likelihood that an attacker can take over more than 10% of the network hash is extremely small, and a slight risk (less than 0.1%) is acceptable. However, the calculations of mathematicians show that each participant in the network can, at his discretion, lower the threshold to two or three confirmations.

“Our new article combines two previous studies.”Perez-Marco said in a comment for Bitcoin Magazine.

“The first is an accurate calculation of probabilitydouble-spending attack success, and the second examines the profitability model in selfish mining strategies. ” A new study raises the question: “How profitable is double spending and how many network confirmations are enough with honest mining?”

According to the presented results,A potential attacker who owns 1% of the total hash will have to spend at least 50 coinbase transactions (currently 625 BTC and 312.5 BTC after reducing the mining reward in 2020) to cancel one confirmation. To cancel two confirmations, the attacker needs 1666 coinbase transactions.

“We compared the profitability of double spending and fair mining”- explained Perez-Marco.

“Any large miner with a high hashrate is notinterested in a minor double spend… Only a larger amount can justify double spending from a profitability perspective. For example, with a 1% hashrate and only 1 confirmation, the minimum spend is more than 49 coinbase transactions - today that’s 612 BTC.”

After accounting for several math scenarioscame to the conclusion that after two confirmations on the network, honest bitcoin mining is more profitable than double spending. This conclusion from game theory is applicable even in cases where the transaction value is equal to coinbase transactions.

“Six confirmations are not a protocol rule, but a transaction receiver requirement”- concluded Perez-Marco.

"Satoshi made a good assessment, but he did not have a theory of profitability."

However, it seems unlikely thatconservative cryptocurrency exchanges and companies will lower the confirmation threshold for user convenience, and this mathematical study has not yet received much community attention.

If and when it will be accepted wideby the community, it may happen that most agree to consider bitcoin transactions final after one or two confirmations. However, such a change can also attract the attention of economically irrational players who do not mind burning part of their profits just to destroy confidence in Bitcoin.

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