Bitcoin Mining Allocation

As Bitcoin has exhibited spectacular price increases since its genesis block, the mining industry has rapidly professionalized, going from small home operations to large mining farms. During the course of this, several forks occurred over the years, with the most prominent leading to the creation of Bitcoin Cash in August 2017. The second was the Bitcoin Cash hard-fork, resulting in the (in)famous “hash-war” in November 2018.

Most of the coins resulting from forks share the same hashing function, making them interoperable from a mining perspective. Hence, this report analyzes whether miners are rational in how they allocate their mining resources (e.g., hashpower) across Bitcoin (BTC), Bitcoin Cash (BCH), and Bitcoin SV (BSV).

1. Overview of the world of Bitcoin mining

1.1 Bitcoin’s ASIC dominance

Since its genesis block, Bitcoin mining activities have first pivoted from CPUs to GPUs; since 2014, BTC has been mostly mined by Application-Specific Integrated Circuits (ASICs).

Chart 1 - Mining difficulty of Bitcoin (BTC) (log scale)

As illustrated by chart 1, the mining difficulty of Bitcoin has increased dramatically since 2010. Before 2010, the mining difficulty remained constant around 1 as Satoshi was likely “mining everything by himself”.

Regarding Bitcoin mining, there are four primary paradigm shifts (and five phases) in these ten years:

1. Satoshi “and his friends”: over the first few months of the blockchain, its mining difficulty remained constant, indicating that mining was either conducted by (1) a single individual or (2) a coordinated group of people.
2. CPU (Central Processing Unit): initially, Bitcoin was publicly mined by CPUs.
3. GPU (Graphics Processing Unit): afterward, BTC mining pivoted from CPUs to GPUs.
4. FGPA (Field Programmable Gate Array)¹: in late 2011, FPGA gained interest from miners. With FPGA, specialized chips were installed in precise sequences and patterns to improve the hash-guessing ability for a designated computer.
5. ASIC (Application-Specific Integrated Circuit): since 2014, Bitcoin has almost solely been dominated by ASIC miners. Within the mining war, the ASIC era is also divided into three core facets:
   
   
   • Expansion with many ASIC equipment providers joining the market.
   • Consolidation in the ASIC mining equipment industry toward an oligopoly dominated by Bitmain and Bitfury.
   • The growth of ASIC pool mining.

Recently, the ASIC oligopoly has started to erode with new entrants such as Ebang (e.g., Ebang E12+) and Innosilicon (e.g., Innosilicon T3+Pro) challenging the existing status quo.

Owing to the ASIC dominance, Bitcoin's dedicated hashpower increased exponentially, leading to enormous climbs of the difficulty of Bitcoin mining. The continuously rising Bitcoin price also led to ASICs becoming increasingly performant, with many new participants joining the block-mining race.

Chart 2 - Mining hashrate in the “ASIC era” (2015-2019) (in TH/sec)

On January 1st 2015, the estimated hashrate stood at 0.033 EH/sec (33PH/sec). From January 2015 to mid-2018, the hashrate grew almost exponentially to highs of 5.5 EH/sec (on August 10th 2018), an increase by more than +15,000%.

However, Bitcoin’s hashrate dropped in the second half of 2018, likely owing to the sustained bear market, which saw the price of BTC dropping from a peak at ~ $20,000 to ~ $3,000. Since January 2019, its hashrate has been steadily growing and is now at an all-time high with an estimated value reaching for its first time 10 EH/sec (on November 27th 2019).

1.2 Bitcoin and its forks

Forks are frequent events in the cryptoasset industry². They can be classified into two categories: soft forks and hard forks. Binance Academy defines a hard fork as:

“A hard fork is a change in a cryptocurrency protocol which is incompatible with the previous versions, meaning that nodes that do not update to the new version won’t be able to process transactions or push new blocks to the blockchain."

Hard forks are often utilized for substantial changes in a blockchain protocol, as these events force all node operators to upgrade to a new version.

As hard forks are not compatible retroactively, they often result in the creation of side-chains that die out quickly once all nodes migrate to the new protocol. However, in some cases, hard forks are contentious, with miners not reaching an agreement on whether to accept changes in the protocol. As a result, hard forks can lead to two independent protocols, resulting in two blockchains competing for the same computing resources provided by miners.

The most prominent example was the fork between Bitcoin and Bitcoin Cash in August 2017 along with the Bitcoin Cash fork, resulting in the “hash-war” in November 2018.

The table below describes key similarities and differences between Bitcoin (BTC), Bitcoin Cash (BCH), and Bitcoin SV (BSV)³.

Table 1 - Comparison between Bitcoin, Bitcoin Cash, and Bitcoin SV

Chart 3 - Prices of BTC, BCH, and BSV (USD)

The table below describes the spot trading venues for these three “versions” of the Bitcoin protocol, as defined in the whitepaper written by Satoshi Nakamoto in 2009.

Table 2 - Spot trading venues for Bitcoin, Bitcoin Cash, and Bitcoin SV

Nearly all of the most significant exchanges support both Bitcoin and Bitcoin Cash for trading, usually against each other and against either USD or USD-pegged stablecoins (e.g., USDT, USDC). However, the support for Bitcoin SV (BSV) is not as wide-spread. For instance, some of the largest exchanges (e.g., Coinbase) have never listed any pair against BSV while other platforms have delisted BSV (Kraken, Binance).

Amongst the ten exchanges selected by Bitwise in its ETF proposal⁵, only Poloniex and Bittrex support BSV, and these pairs display low daily volumes (usually between $100,000 and $1,000,000 in November 2019).

1.3 Overview of existing mining pools

In this subsection, the most significant mining pools are discussed for Bitcoin (BTC), Bitcoin Cash (BCH), and Bitcoin SV (BSV).

Table 3 - Support for BTC, BCH, and BSV from the largest mining pools

Bitcoin SV blocks are mostly mined by small pools such as CoinGeek (BSV only), Mempool (BSV and BTC), SVPool (BSV), and Sigma Pool (BTC, BSV, and LTC). As of December 16th 2019, CoinGeek and SVPool accounted for more than 35% of the total hashpower⁷.

1.4. Breaking down the mining rewards

For any PoW blockchain, mining rewards can be broken down into two core ../components: block mining rewards (distributed in the coinbase transaction) and transaction fees.

Chart 4 - Contribution of transaction fees (%) to the total mining rewards for BTC since July 2017

The contribution of transaction fees relative to the total mining rewards (i.e., the sum of transaction fees and block mining rewards) fluctuated over time. It gradually increased to a peak in December 2017, when the network got congested and fees subsequently spiked (as high as 20 USD for a single transaction). During this period, transaction fees accounted for as much as 40% of the total rewards, i.e., nearly as high as the block mining rewards. However, since then, the contribution of transaction fees to the total mining rewards has remained between 3% to 7%.

In contrast, transaction fees of both Bitcoin Cash and Bitcoin SV, contribute to a much lesser extent to the total block rewards, as illustrated by the chart below.

Chart 5 - Contribution of transaction fees (%) to the total mining rewards for BCH & BSV since August 2017

For both BCH and BSV, miners received almost negligible rewards from transaction fees, compared to BTC. For instance, transactions often accounted for less than 0.1% of the total mining rewards for both BCH and BSV (with minor spikes from time to time).

2. Mining resources allocation

In this section, the mining resource allocation problem is discussed from an efficiency perspective. Furthermore, the two subsequent sections analyze the respective empirical relationships between:

1. Bitcoin (BTC) & Bitcoin Cash (BCH) (August 2017 - November 2018)
2. Bitcoin (BTC), Bitcoin Cash (BCH) & Bitcoin SV (BCH) (November 2018 - December 2019)

2.1 Efficient resource allocation theory

According to Binance Research, the mining allocation problem can be referred to as a problem of efficient resource allocation, from the perspective of participants in the Bitcoin mining industry: SHA-256 (ASIC) miners.

Specifically, for two Proof-of-Work (PoW) blockchains with the same hashing function (e.g., SHA256), the profitability of both blockchains should not diverge in the long-term.

From a mathematical perspective, the following set of equations can be written as follows.

Fixed costs mostly include costs of purchasing ASICs and running a node, etc. While fixed costs are not negligible, these costs will be omitted for the rest of this analysis as they are exactly the same for BCH, BSV, and BTC; hence, this analysis only focuses on the profitability of coins with the same hashing function (e.g., SHA256).

Variable costs are thus more significant; they are a function of the price of electricity, multiplied by the total power used for “finding the hash”.

Despite mining costs not being directly estimable, block difficulty is a proxy of the required power to find the correct hash to add a block to the chain. Hence, the following equation can be posed to describe this relationship.

Assuming that miners do not own material information about the short-term price direction of the asset mined, the ratio of mining rewards divided by the difficulty should converge in the long-term, or at least, should not diverge significantly in the long-run.

2.2 Exploring Bitcoin and Bitcoin Cash (2017 - 2018)

In this subsection, we explore the first fork of Bitcoin, which resulted in the creation of Bitcoin Cash.

In early 2017, on-chain transaction fees were increasing and started to hinder opportunities for Bitcoin to be effectively used as digital cash. Hence, some Bitcoin prominent figures advocated for an increase in the blocksize, stating that Satoshi never intended the block reward to be set at 1MB forever. However, other parties rejected any deviation from the original proposal, such as increasing the maximum blocksize.

Meanwhile, alternatives like SegWit or other layer-2 solutions such as using Lightning Network were proposed as preferable solutions to scale Bitcoin.

This heated debate resulted in both sides failing to find an agreement on the future of Bitcoin. Eventually, it led to the creation of Bitcoin Cash (BCH) on August 1st 2017.

2.2.1 Summary of Bitcoin’s first contentious chain-split

Chart 6 - BTC/BCH hashrates from August 1st to December 31st 2017 (TH/sec)

Since August 1st 2017’s Bitcoin hard-fork, the hashrate of Bitcoin Cash has only exceeded the one of Bitcoin once: around mid-October 2017.

Furthermore, the differential between both hashrates increased, as did the price ratio between one unit of Bitcoin and one unit of Bitcoin Cash, as illustrated by charts 6 and 7.

Chart 7 - BTC/BCH daily close prices (August 1st - December 31st 2017) (USD)

Following the fork (August 1st 2017), Bitcoin Cash developers introduced the Emergency Difficulty Adjustment (EDA). Its primary purpose was to incentivize miners to process BCH's transactions instead of BTC.

However, owing to the wild fluctuations of its hashrate, Bitcoin Cash’s difficulty adjustment mechanism was updated on November 13th 2017⁸. Since then, the new algorithm is based (its still used, right) on a 144-block simple moving average that adjusts the difficulty every block. The parameters for the adjustment are the amount of work done and the elapsed time of the previous 144 blocks.

Chart 8 - BTC/BCH mining reward-to-difficulty ratios (August 1st - December 31st 2017)

Prior to the November 2017’s upgrade, the mining profitability (measured by the reward-to-difficulty ratio) of BCH fluctuated very quickly owing to its new mining difficulty algorithm, which led to drastic adjustments in the mining difficulty of BCH. After the upgrade, the volatility in BCH’s mining profitability decreased, leading to the mining reward-to-difficulty becoming less volatile.

However, BCH profitability remained lower than BTC for a few months.

This is potentially explained by the increasing contribution of transaction fees to the total rewards for Bitcoin over the period (pre-hashwar chart 4), leading to a higher Bitcoin mining profitability than Bitcoin Cash’s during this period.

As transaction fees are not fully predictable in advance, this component of mining rewards may not have been properly anticipated by miners when deciding whether to allocate computing resources to mine BTC or BCH.

2.2.2 Aftermath analysis (December 2017 - November 2018)

Chart 9 - BTC/BCH mining reward-to-difficulty ratios (December 31st 2017 - November 14th 2018)

Since early 2018, mining profitabilities of Bitcoin and Bitcoin Cash have converged substantially, and since March 2018, these have been nearly equal, potentially owing to the reduction in the contribution of transaction fees of BTC’s total mining rewards. The decrease in the mining profitabilities of both cryptocurrencies, expressed by daily total mining rewards divided by difficulty, is mainly explained by the increasing progress of available ASIC mining machinery. Meanwhile, June-July 2018’s higher mining reward-to-difficulty could be explained by a sudden spike in transaction fees on the Bitcoin blockchain (see chart 3), which led to a more significant contribution to its total mining rewards.

Chart 10 - BTC/BCH hashrates (December 31st 2017 - November 14th 2018) in TH/sec

Chart 11 - BTC/BCH daily close prices (December 31st 2017 - November 14th 2018) in USD

2.3 Exploring Bitcoin, Bitcoin Cash and Bitcoin SV (2018-2019)

2.3.1 Immediate post-fork aftermath: the Bitcoin Cash “hash-war”

The hard fork of Bitcoin Cash, which occurred at block 609,136¹⁰, led to a hashrate competition (referred to as “hash-war”) to determine what “Bitcoin Cash version” was the most legitimate one.

This war was costly and mostly non-economical as it resulted in an estimated loss of around USD 278,000 for BCH miners and USD 439,000 for BSV miners in the span of only 24 hours¹¹.

According to Jiang Zhuoer (CEO of BTC.TOP), this hash-war between ABC and SV was built upon a game theory model, which is summarized in his excellent article.

In his model, which was defined before “hash-war”, there were four likely scenarios that would lead to two potential outcomes: (1) BCH not splitting; (2) BCH splitting into BCH/BSV.

Chart 12 - BCH/BSV hashrates (November 15th 2018 - November 30th 2019) in TH/sec

Ultimately, the second scenario took place, and BCH split into "BCHABC" (BCH) and "BCHSV" (BSV). BTC.TOP subsequently discontinued its support for Bitcoin SV, a few months after¹².

2.3.2 “Post-war” analysis

Since the “end of the war”, both chains have persisted, and BCH took the lead over BSV both from a price and hashrate perspective, as illustrated by the chart below.

Chart 13 - BCH/BSV hashrates (November 30th 2018 - December 15th 2019) in TH/sec

As illustrated by the above chart, Bitcoin Cash (BCH)'s hashrate has been consistently higher than the hashrate of Bitcoin SV since mid-December 2018. However, this finding mostly relates to the evolution in BCH and BSV prices. Indeed, the price of Bitcoin Cash remained higher than BSV over this study period.

Chart 14 - BCH/BSV prices (November 15th 2018 - December 15th 2019) in USD

Hence, correlations between hashrate and price remain extremely high, as miners can exploit arbitrage opportunities and point their hashpower to another blockchain, as long as the hashing function remains the same (e.g., SHA256, ETHash).

As a result, we can include BSV in the (previous) 2-asset model, which compares BCH and BTC respective mining profitabilities.

Chart 15 - BTC/BCH/BSV reward-to-difficulty ratios (November 15th 2018 - December 15th 2019)

As illustrated by the above chart, the reward-to-difficulty for BSV remained below the respective figures for BTC between November 2018 and August 2019. Nonetheless, BSV’s mining profitability sometimes caught up with the numbers of the two other assets, after respective substantial BSV prices.

Since August 2019, its mining profitability has been in line with Bitcoin.

Interestingly, during the first half of 2019, its reward-to-difficulty ratio never remained significantly higher than the two other cryptocurrencies. This could imply that rational miners were always “arbitraging” whenever the profitability of one of these forks went higher (relative to others).

In summary, the Bitcoin SV reward-to-difficulty pattern implies that a significant portion of its hashpower might not have emanated from economically-driven actors until August 2019¹³.

Chart 16 - Difference (%) between BSV and BTC reward-to-difficulty ratios (November 15th 2018 - December 15th 2019)

Similarly, the difference between reward-to-difficulty ratios can also be computed with BTC and BCH.

Chart 17 - Difference (%) between BCH and BTC reward-to-difficulty ratios (November 15th 2018 - December 15th 2019)

As the opportunity cost to mine BSV/BCH (instead of BTC) adds up over time, we can calculate the aggregated opportunity costs of mining BCH/BSV, instead of BTC.

For BSV, if the absolute difference between the BSV reward-to-difficulty is superior to 5%, the following methodology is used:

1. Calculate the appropriate optimal difficulty for BSV mining to even the mining reward-to-difficulty of BSV with BTC’s.
2. Calculate the difference between optimal mining difficulty of BSV and actual mining difficulty of BSV.
3. Add this difference to the actual difficulty of BTC and calculate its new contribution to the new difficulty of BTC.
4. Calculate the daily opportunity cost, defined as the potential contribution (in %) multiplied by the daily mining rewards of BTC (in USD).
5. Compute the cumulative opportunity cost and plot it.

The same methodology is also applied for BCH (instead of BSV). Furthermore, if the mining profitability for BSV/BCH is higher than BTC, it would reduce the opportunity cost.

Chart 18 - Cumulative estimated cost of opportunity to mine BSV (instead of BTC) in USD

In less than a year, an estimated $12-13 million could have potentially been collected by Bitcoin SV miners, if they were acting rationally in their mining resource allocation (as discussed in section 2.1).

In comparison, BSV total mining rewards (assuming miners selling BSV coins at the end of each business day) were around $75 million over the same period. As a result, this potential opportunity cost represents around 16-17% of the total BSV mining revenue over the period.

Furthermore, Bitcoin Cash's reward-to-difficulty ratio also remained inferior to Bitcoin's ratio between June 2019 and August 2019. Hence, we can also calculate the cumulative estimated cost of opportunity to mine BCH since November 15th 2019.

Chart 19 - Cumulative estimated cost of opportunity to mine BCH (instead of BTC) in USD

BCH's estimated cost of opportunity is around $7.7 million. It could have potentially been collected by Bitcoin Cash miners, if these were fully rational in the allocation of their computing resources.

In comparison, BCH total mining rewards (assuming miners selling BCH at the end of each business day) were around $179 million over the same period. Hence, this potential opportunity cost represents only 4% of BCH's total mining revenue over the period.

The next section explores potential explanations, which can impact the efficient resource allocation theory discussed in section 2.1.

3. Exploring possible explanations

There are several reasons that may explain why the hashpower allocation may not be in line with our efficient resource allocation theory developed in section 2.1.

We broke down these potential explanations in four core groups:

• Liquidity and markets (subsection 3.1)
• Aggregated expectations (subsection 3.2)
• Intrinsic differences and game theory (subsection 3.3)
• Other factors (subsection 3.4)

3.1 Liquidity and markets

First and foremost, liquidity and product offerings are likely affecting the attractiveness of mining owing to implicit cost.

• Liquidity differences: as discussed in section 1.2 of this report, the liquidity is far from being the same among Bitcoin, Bitcoin Cash, and Bitcoin SV. Thereby, lower liquidity may negatively influence the profitability of each of these assets. Specifically, liquidity include factors such as:

  • Trading volume: the larger its trading volume, the more liquid an asset is. In general, volumes are a good measure of the overall market interest for large cryptoassets by marketcap. In normal trading environments, sustained high volumes illustrate continuous interest from market participants. However, volume numbers typically require to be put in perspective with other liquidity metrics, as described after.
  • Number of pairs & exchanges: in general, an asset with more spot pairs across many exchanges, likely has greater liquidity than an asset with a single trading venue.
  • Depth of the orderbooks: the higher the depth of the orderbooks, the larger are the quantities that can be traded without slippage.
  • Fee structure on the exchanges offering trading services for the asset. Some exchanges have a lower fee structure than others, which can ultimately impact the liquidity profile of an asset depending on the critical markets it is traded on.
  • Other costs, such as bid-ask spread or slippage costs (owing to low orderbook depth), also impact the liquidity profile of the cryptoasset.

  Regarding liquidity profiles, Bitcoin has the deepest liquidity of all three versions of the bitcoin protocol, followed by Bitcoin Cash, and ultimately Bitcoin SV (as seen as table 2 in subsection 1.2).

• Difficulty in shorting the spot asset: unlike BTC, many cryptoassets are not available for margin trading. Meanwhile, many large exchanges (e.g., Kraken, Binance) offer convenient access to borrowing and shorting BTC.

• Lack of derivatives market: BTC is the asset with, by far, the most significant number of derivatives products. There have been new offerings such as options markets (e.g., Deribit, CME, and Bakkt options), perpetual swaps (e.g., BitMEX and Binance Futures), and futures products that are either cash-settled (e.g., CME) or physically-settled (e.g., Bakkt futures).

3.2 Aggregated expectations

Expectations from the perspective of miners are also a critical element that can potentially impact the attractiveness of an asset. Some of these reasons include:

• Future price expectations: SHA-256 miners may have different price expectations for each asset they could mine. As a result, they might potentially prefer to mine less profitable assets instead of other assets. However, a rational miner should rather:

1. Mine the coin that provides the highest return on investment, measured by the reward-to-difficulty ratio.
2. Sell the coin to match personal future price expectations. For instance, if BSV were perceived as “too expensive-to-mine” compared to BCH and BTC, the miner could mine BCH and sell it to BSV.
   
   However, transaction fees, short-term volatility, and liquidity profiles (such as discussed in subsection 3.1) should be considered by rational miners. Hence, if the difference in the reward-to-risk ratio across two blockchains was meager, rational miners should not necessarily mine the most profitable.

• Different expectations about future transaction fees: similarly to the previous point, each miner may have unique views on the future usage of the blockchain. As seen in subsection 2.1 of this report, total mining revenue is the sum of block mining rewards and transaction fees, which is a function of the on-chain usage. If a miner expects the number of transactions and transaction fees to spike, it could be incorporated in the expected reward-to-difficulty ratio of a blockchain.

3.3 Intrinsic differences with game theory elements

Furthermore, other intrinsic differences are explained by the respective source-code implementation. Some of these differences are related to game theory, where all miners play a role. For instance, it includes factors such as:

• Alternative rules for the mining difficulty adjustment: for example, Bitcoin Cash and Bitcoin SV rely on DDA for the mining adjustment, while BTC relies on the original difficulty adjustment (every 2016 blocks).
• Different times for blockchain mining adjustment: for instance, the BTC mining difficulty is re-evaluated every 2016 blocks (which targets approximately 2 weeks in human-measurable time). However, it remains influenced by the consistency of the hashpower dedicated to finding the 64-digit hexadecimal number (i.e., hash) inferior or equal to the target hash. Over time, the mining difficulty does not re-evaluate at similar times for all three blockchains. These fluctuations in the hashpower compound and explain why mining difficulty adjustments do not co-occur for all three.

This also relates to game theory elements. For instance, if a miner expects other competitors to opt-out and starts mining another asset, he could decide whether it is worth staying on the same blockchain or mining a different coin. This essentially results in a Nash equilibrium with multiple parties¹⁴.

3.4 Other factors

Finally, other factors may also contribute to differences in the underlying profitability, such as:

• Merged mining: additional rewards stemming from merged mining could skew the analysis. As the reward-to-difficulty ratio uses the price of the parent blockchain (e.g., BTC price, BCH price) in the numerator, the entire revenue component may not be calculated correctly as additional profit sources may be disregarded. However, in the case of the BSV differential with BTC, it would mean that the reward-to-difficulty ratio of both BCH and BSV should be consistently higher than BTC as only Bitcoin (BTC) offers merged-mining additional rewards for no additional fixed cost (e.g., MyriadCoin, Elastos, RSK Network).

• Operating costs of running a node: the cost of running a node is a function of the blockchain size and the usage ratio of a blockchain. However, these operating costs are low and do not differ significantly among blockchains.

• Difference in mining pool structures: mining pools often have different fee structures, set of rules, or do not allow users to shift easily what asset they wish to mine.

3.5 Final thoughts

Bitcoin SV (BSV) has been mostly mined by pools that are BSV-centric, as described in subsection 1.3. Specifically, more than a third of its hashpower is still generated by pools (CoinGeek, SVPool) that are owned and backed by significant BSV stakeholders.

As the hashrate of BSV is much lower than BCH (by around 2 to 3 times) and BTC (by approximately 100 times), BSV miners may have attempted to maintain the SV network secure, regardless of (potential) opportunity costs, when its price dropped.

However, economic considerations must not be excluded either as the reward-to-difficulty ratio of BSV never remained consistently higher than BTC's. As a result, it is possible that rationally economic-driven miners maintain “passive-watch behavior” and would mine whichever asset becomes the most profitable to mine. If the price of BSV were to increase substantially, its hashrate (and the mining difficulty) would also increase, as a response from economically rational miners.

Furthermore, BSV miners were presumably not mining at a loss over the first six months of 2019, and their respective vested interests (i.e., owning a lot of BSV coins) probably outbalanced opportunity costs¹⁵. These vested interests would incentivize them to secure the BSV network to preserve a significant portion of their capital.

An alternative view might state that sustained price increases would always lead to greater hashrates, as seen in our proposed mining efficient allocation theory (see section 2.1). If so, large coin-holders could potentially find a cheaper alternative to secure the network in the short term than mining at an opportunity cost.

Since August 2019, Bitcoin SV reward-to-difficulty ratio has converged and is now in line with both BCH and BTC.

On the other hand, Bitcoin Cash (BCH)'s reward-to-difficulty remained in line with BTC's for most of the "post-war" period. However, between May and October 2019, its profitability (measured by the reward-to-difficulty ratio) was often lower than BTC's, possibly owing to its price decline over the summer of 2019. Once again, mining rewards, i.e., a function of the price of an asset, remain the main element to consider how computing resources are allocated to secure blockchains.

With halvings on schedule for all three cryptocurrencies in 2020, miners will likely pay closer attention to any potential imbalance in the USD rewards for a given difficulty.

4. Conclusion

Throughout this report, the efficient resource allocation theory for miners was introduced and applied to the three largest SHA-256 blockchains by marketcap: Bitcoin (BTC), Bitcoin Cash (BCH), and Bitcoin SV (BSV) for the period between August 2017 and December 2019.

At first, the profitability pattern of both Bitcoin and Bitcoin Cash was analyzed from the 2017’s chain-split to the end of 2018. Following a few weeks after Bitcoin’s first fork event, BTC and BCH miners were both economically rational. Most BCH miners were participating in both blockchains, switching back and forth between these two to mine whatever was the most profitable for a given difficulty, as illustrated by BTC and BCH reward-to-difficulty's convergence over the period.

Following the controversial Bitcoin Cash hard-fork, which occurred in late 2018, this analysis was then extended by including Bitcoin SV. However, the mining profitability (measured by the reward-to-difficulty ratio) of these three blockchains did not converge until recently. In the first eight months of 2019, Bitcoin SV appeared to be often mined at an opportunity cost, as illustrated by its lowest reward-to-difficulty ratio. On the other hand, BCH miners were more rational, but between June to September 2019, BCH miners mined at an opportunity cost.

However, since September/October 2019, BCH and BSV have seen their respective reward-to-difficulty ratios converging with BTC's.

Finally, this report highlighted that prices remained the main driver of how much computing resource is allocated to secure a PoW blockchain and that coins with the same hashing function were essentially competing for resources to secure their network.

As halving events have never occurred on neither Bitcoin Cash nor Bitcoin SV, it remains to be seen how such an event might impact their respective mining profitability and to what extent it will test the sustainability of their underlying economic incentive reward schemes. Hence, a few questions should be raised:

• Can competing PoW blockchains remain secure?
• Will some miners remain political after the halving events?

This report greatly contributed from discussions and feedback from Dan McArdle (CTO of Messari), Nate Maddrey (Research Analyst at Coin Metrics), Huyette Spring (Chief Product Officer at Coin Metrics), Antoine Le Calvez (Data Engineer at Coin Metrics), Jacob Franek (COO at Coin Metrics), and many other contributors who wished to remain anonymous.

For more information about them, please visit Messari and Coin Metrics.

5. References

• Aggarwal, V. and Tan, Y. (2019). A Structural Analysis of Bitcoin Cash's Emergency Difficulty Adjustment Algorithm. http://dx.doi.org/10.2139/ssrn.3383739
• Antonopoulos, A. M. (2014). Mastering Bitcoin: unlocking digital cryptocurrencies. " O'Reilly Media, Inc.".
• Bissias, G., Thibodeau, D., & Levine, B. N. (2019). Bonded Mining: Difficulty Adjustment by Miner Commitment. In Data Privacy Management, Cryptocurrencies and Blockchain Technology (pp. 372-390). Springer, Cham. https://arxiv.org/pdf/1907.00302
• BitInfoCharts. Website. https://bitinfocharts.com/
• Coin Dance. Website. https://coin.dance/
• Coin Metrics (2018). What should we expect from Bitcoin’s block size in the coming years? https://coinmetrics.io/what-should-we-expect-from-bitcoins-block-size-in-the-coming-years/
• Coin Metrics (2019). A Comparative Analysis of Bitcoin Forks. https://coinmetrics.io/a-comparative-analysis-of-bitcoin-forks/
• Courtois, N.T., Grajek, M., and Naik, R. (2014). Optimizing SHA256 in Bitcoin Mining. Proc. Int’l Conf. Cryptography and Security Systems (CCSS 14) pp. 131–144.
• Iyidogan, E (2018). An Equilibrium Model of Blockchain-Based Cryptocurrencies . https://www.aeaweb.org/conference/2019/preliminary/paper/kGyRnYKk
• Kwon, Y., Kim, H., Shin, J., Kim, Y. (2019). Bitcoin vs. Bitcoin Cash: Coexistence or Downfall of Bitcoin Cash? In: Proceedings of the IEEE Symposium Security and Privacy
• Nakamoto, S. (2008). Bitcoin: A Peer to-Peer Electronic Cash System https://bitcoin.org/bitcoin.pdf
• Noda, K., Shunya, H., and Okumura, Y. (2019). A Lucas Critique to the Difficulty Adjustment Algorithm of the Bitcoin System. https://ssrn.com/abstract=3410460
• Ozisik, A.P., Bissias, G. and Levine, B. (2017). Estimation of Miner Hash Rates and Consensus on Blockchains (Draft). https://arxiv.org/abs/1707.00082
• Song, J (2017). Bitcoin Cash Difficulty Adjustments. https://medium.com/@jimmysong/bitcoin-cash-difficulty-adjustments-2ec589099a8e
• Zhuoer, J (2018). ABC vs BSV Hash War (Part III) — The War of The Hash Power. https://medium.com/@jiangzhuoer/abc-vs-bsv-hash-war-part-iii-the-war-of-the-hash-power-45fef8010467