The success of Bitcoin has attracted much attention from both industry and academia. The Bitcoin network mainly comprises mining pools responsible for network security and performance. While many measurements are available for the Bitcoin network, more information is needed to understand the behavior of mining pools, such as their revenue and transaction collection strategies. This paper aims to explore some of Bitcoin's mining history and compare its performance. We use over 700, 000 blocks mined from 2009 to today, serving as the coin's foundation. We have extracted structured and explanatory information about the pools' work over the years by analyzing the blockchain data. It is worth noting that the number of blocks mined by some mining pools only sometimes guarantees significant gains. Miners' overall earnings have been significantly afected by the lfuctuation in Bitcoin's value over the years.
In this section, we present an overview of the Bitcoin consensus protocol, and we define transactions.
Bitcoin is a peer-to-peer asynchronous network whose nodes host a ledger recording economic transactions grouped into blocks. The ledgers are trees of blocks with a pointer (handle) to a leaf block at maximal depth; the blockchain is the sequence of blocks from the handle to the root block, (genesis block). Blocks are created by particular network nodes – the miners – and contain information, such as, for example, related to transactions and a pointer to the current handle of the miner’s ledger.
Once a block has been mined, the miner (i) adds the block to its ledger (therefore, the depth of the ledger increases and the handle is updated); and (ii) broadcasts it to all the connected nodes of the network. Every node receiving the new block updates its local copy of the ledger by inserting the block in the correct position, and, if necessary, it also updates its handle. If the block cannot be connected to the ledger (because, due to network delays, a previous block has not been delivered), it is added to the local set of the miner and will be inserted afterward (orphan blocks).
Because of asynchrony, it may happen that two nodes mine and broadcast a block almost
concurrently, yielding diferent ledgers with diferent handles (and, therefore, with other blockchains). This
phenomenon, called fork, is at the core of the inconsistencies of Bitcoin, and to overcome this problem,
the protocol uses a probabilistic algorithm. In particular, Bitcoin has a technique to regulate the mining
of blocks, called Proof of Work [
To further reduce the probability of inconsistencies, Bitcoin also uses the so-called eventual consistency
(also known as -consistency [
In the early stages, the competition among miners was low, so the computational energy required to create new blocks and obtain rewards could be quickly processed on CPU-equipped devices such as ordinary personal computers. However, as competition among miners increased, significant developments in Bitcoin mining hardware emerged: • Mining with GPUs: The first significant step in mining hardware innovation occurred in 2010.
Video cards were first used for Bitcoin mining because they are optimized for parallel mathematical calculations, making the mining process much more eficient than CPUs. This made Bitcoin mining about six times more eficient than with CPUs, even though GPUs cost only twice as much. • Mining with FPGAs: FPGA (Field-Programmable Gate Array) devices were used for Bitcoin mining in 2011. FPGAs could perform the calculations required for mining twice as fast as the best GPUs. However, the configuration of FPGAs required considerable efort at the software and hardware level. • Mining with ASICs: In 2013, ASIC (Application-Specific Integrated Circuit) technology was introduced. ASICs were designed and optimized for Bitcoin mining and led to a significant increase in computing power, outperforming CPUs, GPUs, and FPGAs.3
In Bitcoin mining, the hash rate is the standard measure of a miner’s computing power to solve the cryptographic hashes required by proof of work. The hash rate determines how quickly a miner can provide solutions based on a specific hash and is used to estimate the eficiency of the hardware used for mining cryptocurrencies. For example, an ordinary computer can solve a few mega hashes per second (MH/s). At the same time, FPGAs or ASICs can run from hundreds of MH/s to tens of tera hashes per second (trillions of hashes per second). The global hash rate of the Bitcoin network as of March 14, 2023, is 550.85 EH/s4.
A Bitcoin wallet stores a collection of public/private key-pairs of a user, not directly bitcoins. A Bitcoin
address is an identifier of 26-35 alphanumeric characters, and it strictly derives from the hash of a
generated public key (pubkey in the following) [[
A "share" is a potential solution for a block but not necessarily a block solution itself. For instance, if a block solution is a number that ends with ten zeros, a share may be a number with only five zeros at the end. However, eventually, one of the shares will have not only 5 but 10 zeros at the end, and this will be the actual block solution5.
A common mistake among new miners is to think that they have found a block (or even two) when they see phrases like "Share Found" and "Share accepted" in their mining software. In reality, mining pools need shares to estimate the miner’s contribution to the work performed by the pool to find a block. Based on the shares a miner sends to the pool, the pool can plot a miner hash rate graph and determine whether a miner is online, among other things.
There are numerous reward systems, but the majority of mining pools operate with the PPS, FPPS, PPS+, and PPLNS payment models6: • Pay-Per-Share (PPS): in this payment method, a miner receives a fixed payment rate for each completed share. After paying mining pool fees, miners receive a fixed share each day. Therefore, in the PPS method, returns are relatively stable. • Pay-Per-Last-N-Shares (PPLNS): is closely related to the number of blocks mined. If the mining pool mines more blocks in a day, the miners get a higher profit, calculated according to each one’s share; if the mining pool fails to mine a block during the whole day, the miners’ profit is zero. The PPLNS model is highly correlated with a pool’s luck, the probability of mining a block. • Pay Per Share Plus (PPS+): combines the previously mentioned methods, PPS and PPLNS. The reward per block is settled according to the PPS model, while the pool and transaction fees are settled according to the PPLNS model. 3https://www.coindesk.com/tech/2020/04/26/the-rise-of-asics-a-step-by-step-history-of-bitcoin-mining/. 4https://academy.bit2me.com/it/que-es-el-hash-rate/. 5https://2miners.com/blog/what-is-share-and-the-share-dificulty-when-you-are-mining-at-the-pool/. 6https://minebest.com/blog/pps-vs-fpps-vs-pplns-vs-pps-mining-pool-payouts-explained.
• Full Pay Per Share (FPPS): in this model, the reward per block and the mining service fee are settled based on theoretical profit. A standard transaction fee is calculated within a certain period and distributed to miners based on their hash power contributions in the pool. With the FPPS method, one gets paid regardless of whether the pool finds a block. • Proportional: in the proportional method, miners earn shares until the pool finds a block. After that, each user receives a reward = × (/ ), where is the share amount, and is the total amount of all shares in the cycle. • Pooled mining (BPM): also known as Slush system because it was initially used in Slush’s pool, it uses a system in which the oldest shares from the beginning of a mining cycle have less weight than the newest shares. A new cycle begins when the pool resolves a block, and miners are rewarded proportionally to the quotas submitted. • Solo Mining Pool: in this case, the reward for the block is not distributed among all miners. The entire reward goes to the miner who finds the block. • Peer-to-Peer Mining Pool (P2Pool): It decentralizes the responsibilities of a pool server. Miners work on a share, mining at a lower dificulty at one share block every 30 seconds. A share block is transmitted and joined to the blockchain when it reaches the network target. Miners are rewarded proportionally to the shares sent before the target block. • Geometric method (GM): it is based on the same idea as the BPM method: the score assigned for each new share, relative to the existing score and the score of future shares, is always the same, so there is no advantage in mining earlier or later in the cycle. • Double Geometric method: generalized version of the Geometric and PPLNS methods. Introduces a new parameter: (cross-round leakage). When = 0, this method becomes the Geometric method. When = 1, it becomes a variant of PPLNS with an exponential decrement7. • Pay On Target (POT): it is a variant of the PPS model. In this model, payments to miners are not determined by the work provided by the pool but by the dificulty of the work completed by the miners and returned to the pool. This method introduces more significant variability in payments than the traditional PPS model. • Pay Per Last N Shifts/Groups (PPLNSG): this payment method is similar to PPLNS, but with the diference that dues are grouped into shifts (shifts or groups), and these shifts are paid as a whole. • Shared Maximum Pay Per Share (SMPPS): is a payment method similar to the Pay Per Share (PPS) model, but with a specific limitation: the reward of all miners is never more than what the mining pool earns. • Recent Shared Maximum Pay Per Share (RSMPPS): is a payment method similar to the SMPPS method, but gives payment priority to the most recent miners8.
To analyze the content of the Blockchain, a sample of 700, 000 blocks of it, mined from January 2009
to March 2023, was saved in a MongoDB database [
The first attempt to extract a graph that would allow an overview of the number of blocks mined by all the miners in the database over the years, shown in Figure 1, produced a dificult-to-read result because the presence of almost 100 diferent mining pools. So, we decided to focus the analysis on some selected miners. The first step is to use the top ten mining pools for the number of mined blocks. The result is shown in Figure 2. At the beginning of Bitcoin, the first mining pool was BTC Guild, which was overtaken in late 2013 by GHash.IO, lasting less than a year to benefit F2Pool. In 2016, the one that mines the most blocks became AntPool, overtaken in late 2017 by BTC.com. In 2019, F2Pool returned to the top, which was then overtaken in mid-2021 by Foundry USA. We can also see that the most long-lived mining pool is the Braiins pool, followed by F2Pool.
Notice that the greater number of mined blocks does not necessarily correspond to the higher gain; this is due to the significant increase in the value of Bitcoin over the years, e.g., the ViaBTC pool has mined fewer blocks than the BTC Guild pool but having mined them more recently it has earned more: the gain is calculated by multiplying the number of bitcoins received from mining the block by the value of Bitcoin in dollars on the date it was mined.
Figure 3 represents the top ten mining pools by total earned through mining. Here, it is clear how the miners who have made the most money have all thickened in recent years, thanks to a significantly higher value of Bitcoin. First is F2pool, thanks partly to its longevity, followed by AntPool. Note the significant growth of FoundryUSA in a few years, which is currently the highest-earning mining pool. We can also notice that the top ten miners by number of blocks are diferent for the aforementioned reason. In particular, BTC.Guild, GHash.IO, and BitFury are replaced by miners who worked in earlier periods: Binance Pool, BTC.TOP, and Huobi.pool.
Table 1 shows all the information about top mining pools. F2Pool is the one that mined more blocks, but AntPool earned more money. Instead, BTC.com is the second by mined block. On the other hand,
F2Pool is the second for gained dollar.
Mining pool earned fees($) earned fees(BTC) AntPool 374,798,304 36,499 F2Pool 352,529,741 30,602 BTC.com 323,100,643 27,127 ViaBTC 242,439,264 17,891 Poolin 212,224,122 9,921 BTC.TOP 156,725,336 18,033 Braiins Pool 154,238,694 21,324 Binance Pool 154,103,289 4,752 Huobi.pool 98,228,061 4,662
Foundry USA 74,769,139 2,360
In addition to the base Bitcoin reward, recognized by the protocol itself and set at 6.25 Bitcoin per mined block, a miner currently chooses the transactions to be validated by looking at the relative fees users ofer to be processed. Calculating each reward’s fee value was necessary to determine which mining pool has the most eficient block selection algorithm. This was done by subtracting the value of a reward on the day it was mined from the total reward in Bitcoin received by the miner. The results can be found in the table 2. Also, the mining pool that earned the most money was AntPool, and the second was F2Pool. Considering instead the number of bitcoins, the result is the same.
AntPool has been around for long, so it consistently comes out on top. To account for this, we have normalized the results based on the days each mining pool has been active. This helps provide a clearer understanding of which pools have superior algorithms for selecting transactions and fees. For the number of mined blocks and gains, we also use the number of days of each mining pool’s life for normalization. Instead, for the fees gained, we use the number of mined blocks to normalize. Table 3 shows the mined blocks and gain per day of the most important mining pools. According to the mined blocks, the most eficient pool is GHash.IO, followed by BTC Guild. On the other hand, the Binance Pool is the one that gains more per day of activity. The second is Foundry USA.
As shown in Table 4, Houbi.pool is the most eficient for selecting transactions with high fees when it creates a block. Binance is the second, followed by Braiins Pool. AntPool and F2Pool, the ones with the highest total amount, are now the last. When considering the block fees in bitcoins, one mining pool stands out from the rest: BTC.TOP. According to the data, BTC.TOP leads the pack with a block fee of nearly one bitcoin per block, making it the most profitable pool. Braiins Pool is the second-best option, with a competitive block fee significantly lower than BTC.TOP’s. This information identifies miners looking to maximize their profits.
The provided data in Table 5 shows the number of transactions each mining pool has mined. F2Pool is the leading miner as it has mined the most significant number of transactions so far, followed by AntPool, which is quite close behind. When considering the mean of transactions per block, Poolin is the best-performing mining pool, along with Binance Pool. These two mining pools have proven to be highly eficient regarding their block creation rates and the number of transactions processed. On the other hand, the last two mining pools on the list, GHash.IO and BTC Guild, have not been performing as well. However, it is essential to note that they were active before the massive activity of the Bitcoin network. Overall, these findings provide valuable insight into the performance of diferent mining pools.
The total hash rate and the number of participants in a pool do not afect the income of a miner who is part of it. In fact, being part of a pool twice as large as another means that the pool can mine double the blocks, so it has twice the frequency of distributing the rewards, but the miner’s share is half, as is the reward. In a smaller pool, the miner gets a higher payout but with a lower frequency, given the lower total hash rate and the longer time it takes to mine a block. The calculations vary slightly depending on the payment system ofered by the pool. However, the fee types (PPS, PPS+, FPPS) primarily keep the miners in the pool and disadvantage those miners hopping from one pool to another to try to make more money.
The higher gains are where there are lower fees, but it is important to note that a miner does not choose a pool only for maximizing earnings. Often, the quality of customer service, credibility, and nationality of a pool are crucial factors in the miner’s ultimate decision.
This section analyzes mining pool data by year, starting from January 2011 through March 2023.
In 2011, database miners mined 2, 104 blocks, earning a total of 220, 557$. Among the seven operating pools, BTC Guild, Eligius, and yourbtc.net mined and earned the most; despite this, all three stopped activity. In 2012, the pools mined 17, 310 blocks, with a total gain of 6, 751, 084$. Active pools have more than doubled from the previous year (15 total), and the BTC guild pool remains at the top of the list for gains and the number of blocks mined. OzCoin and EclipseMC also shut down. In 2013, the database’s miners mined 52, 481 blocks, gaining 259, 493, 456. The number of active pools increased to 25, and the pools that mined and earned the most were BTC Guild, 50BTC, and GHash.IO, which are now closed. In 2014, they mined 50, 549 blocks, gaining a total of 604, 950, 230$. There were 33 active miners, and the most eficient pools were GHash.IO, BTC Guild, and F2Pool, the latter of which is still alive. In 2015, pools mined 51, 041 blocks, with a total gain of 321, 385, 158$. The number of active miners reached 41, and the most eficient pools were F2Pool, Antpool, a leader in mining even today, and BTCC Pool, which closed in 2018. In 2016, they mined 54, 638 blocks, with a total gain of 556, 928, 279$. The number of active miners dropped to 39, probably due to halving, and the most eficient pools were again F2Pool, Antpool, and BTCC Pool. In 2017, the database’s miners mined 55,554 blocks, gaining a total of 3, 292, 676, 723$. The number of active miners increased to 40; the most eficient pools were AntPool, F2Pool, and BTC.top. In 2018, mining pools mined 53, 281 blocks, with a total gain of 5, 329, 510, 817$. The number of active miners reached 41, and the most eficient pools were BTC.com, which is still active today, Antpool, and BTC.top. In 2019, they mined 52, 121 blocks, with a total gain of 4, 993, 038, 036$. There were 41 active miners, and the most eficient pools were BTC.com, F2Pool, and Poolin, which are still active. In 2020, mining pools mined 51, 054 blocks, with a total gain of 4, 798, 331, 807$. The number of active miners dropped to 33, aided by halving and the dificulties triggered by the pandemic. The most eficient pools were F2Pool, Poolin, and BTC.com. In 2021, the database miners mined 49, 577 blocks, gaining 15, 749, 186, 536$. The number of active miners remained stable at 33; the most eficient pools were AntPool, F2Pool, and Poolin. In 2022, the database’s miners mined 53, 034 blocks, gaining a total of 9, 505, 458, 011. The number of active miners decreased to 31, and the most eficient pool was Foundry USA, which had the fastest growth among all those analyzed due to the absence of fees, AntPool, and F2Pool. In 2023 (data through March), they mined 10, 095 blocks, with a total gain of 932, 182, 558$. The number of active miners dropped to 20, and the most eficient pools were Foundry USA, AntPool, and F2Pool.
However, Figure 6 shows the number of mined blocks each year has always been stable at around 50,000 as the protocol increases or decreases the dificulty of mining to keep mining a block for about 10 minutes.
Given the decrease in miners over the halving years, we conducted a more detailed analysis to determine how many have closed because of this. The halving event occurs after every 210, 000 blocks mined, about once every four years. During halving, the bitcoin reward that miners receive is halved, which has a significant impact on the supply of new bitcoins and the work of the pools since only the miners with the most eficient hardware and the lowest operating costs can sustain this change while maintaining a gain on the resources spent.
The date of the first halving is November 28, 2012; the next ones were July 9, 2016, and May 11, 2020. The next halving is scheduled for 2024. In particular, in Figure 7, we can see the activity of the miners during the second halving, where 15 pools closed in a few weeks. During the third halving, 12 mining pools stopped working. Figure 8 shows their activity.
The Bitcoin mining and mining pools have been explored in several ways in the literature. In 2014,
[
In 2015, the authors of [
The year after, [
This 2017 paper [12] proposes an intelligent mining strategy to help a mining pool increase its chances of receiving rewards disproportionate to its computational power. The strategy involves deploying forwarding nodes based on the distribution of Bitcoin nodes. By doing so, the time delay for message propagation can be reduced, and the probability of a new block being appended to the longest blockchain can be increased.
In 2020, the authors of [13] developed an incentive mechanism called the Mining game, which uses a Stackelberg game. They have demonstrated that the Mining game is profitable, individually rational, and has a unique Stackelberg Equilibrium. They have formulated the Budget-feasible Reward Optimization (BFRO) problem for the private cost model to maximize the reward function under the budget constraint. They have also designed a budget-feasible reverse auction to solve the BFRO problem, which is computationally eficient, truthful, individually rational, budget feasible, and constant approximate.
In the last year, the authors of [14] proposed a new approach to decentralize Bitcoin mining pools by introducing an uncertain mining reward system based on transaction fees. The authors have presented a simple model demonstrating how risk-averse Bitcoin miners are more likely to distribute their computational power across multiple mining pools when transaction fees make up a significant portion of the mining reward. Their empirical study has shown a negative correlation between the proportion of transaction fees and the decentralization of Bitcoin mining pools.
The paper overviews mining pools activity and the mining process. We have analyzed the information contained within the Blockchain to derive structured and explanatory data about the pools’ work over the years and highlight factors that may influence it. In the history of cryptocurrency mining, we have seen a significant increase in the number of pools. This growth has occurred even though many of those established in the early years (2011-2014) have closed as a result of halving, i.e., the reduction in the reward for mining that occurs periodically in the Bitcoin blockchain, and the increase in the dificulty of mining with consequent hardware evolution. This phenomenon shows how dynamic and competitive the mining industry is, with new players constantly entering the market to get a share of the block rewards. Interestingly, some pools have mined many blocks, but this did not always translate into significant gains. The fluctuation in Bitcoin’s value over the years significantly afects the overall earnings of the miners.
Decentralization of mining pools is essential for the health and security of the Bitcoin network. A high concentration of power in the hands of a few pools can pose security risks to the network. Therefore, miners should choose diferent pools to avoid centralization and contribute to greater network security. In addition to protocol rewards, mining pools receive commissions from the blocks they process. Huobi.pool has proven to be the best at choosing blocks, followed by Binance Pool and Braiins Pool. When the last Bitcoin is mined, which is expected to happen in just over a hundred years, miners will stop receiving block rewards upon completion of each block. Despite this, mining operations should remain profitable in the future, considering that transaction fees will replace block rewards as a source of revenue. Our plan for the future is to expand our analysis of miner eficiency by considering various factors, such as the block and transaction dimensions. By doing so, we can provide a more comprehensive and accurate analysis of the eficiency of miners in selecting and validating blocks. Examining the block and transaction dimensions will provide insights into the miner’s ability to handle complex transactions.
Furthermore, it would be valuable to include a discussion on the computational power of each mining pool and its gains. Such an analysis would help us understand how much computational power each mining pool contributes to the network and how much it earns.
S. Bistarelli, I. Mercanti and F. Santini are members of the Gruppo Nazionale Calcolo Scientifico-Istituto Nazionale di Alta Matematica (GNCS-INdAM). This work has been partially supported by: • GNCS-INdAM, CUP_E53C23001670001; • European Union - Next Generation EU PNRR MUR PRIN - Project J53D23007220006 EPICA: “Empowering Public Interest Communication with Argumentation”; • University of Perugia - Fondo Ricerca di Ateneo (2020, 2021, 2022) - Projects
BLOCKCHAIN4FOODCHAIN, FICO, AIDMIX, “Civil Safety and Security for Society”; • European Union - Next Generation EU NRRP-MUR - Project J97G22000170005 VITALITY: “Innovation, digitalisation and sustainability for the difused economy in Central Italy”; • Piano di Sviluppo e Coesione del Ministero della Salute 2014-2020 - Project I83C22001350001 LIFE: “the itaLian system Wide Frailty nEtwork” (Linea di azione 2.1 “Creazione di una rete nazionale per le malattie ad alto impatto” - Traiettoria 2 “E-Health, diagnostica avanzata, medical devices e mini invasività”). • Project “SERICS” (PE00000014) under the MUR National Recovery and Resilience Plan funded by the European Union - NextGenerationEU; Selected Papers, volume 9603 of Lecture Notes in Computer Science, Springer, 2016, pp. 477–498.
URL: https://doi.org/10.1007/978-3-662-54970-4_28. doi:10.1007/978-3-662-54970-4. [12] Y. Liu, X. Chen, L. Zhang, C. Tang, H. Kang, An intelligent strategy to gain profit for bitcoin mining pools, in: 10th International Symposium on Computational Intelligence and Design, ISCID 2017, Hangzhou, China, December 9-10, 2017 - Volume 2, IEEE, 2017, pp. 427–430. URL: https://doi.org/10.1109/ISCID.2017.184. [13] G. Xue, J. Xu, H. Wu, W. Lu, L. Xu, Incentive mechanism for rational miners in bitcoin mining pool, Inf. Syst. Frontiers 23 (2021) 317–327. doi:10.1007/S10796-020-10019-2. [14] Z. Li, J. Li, K. Zhou, Bitcoin transaction fees and the decentralization of bitcoin mining pools, Finance Research Letters 58 (2023) 104347. URL: https://www.sciencedirect.com/science/article/ pii/S1544612323007195.