# Luck of the Mining Pool: How Luck Impacts Bitcoin Miner Success

## In this article, we dive into how luck variability plays into the Bitcoin mining process — specifically in mining pools.

*Authored by Senior Manager of Financial Analysis Collin Bourke and Senior Manager of Business Development Charles Chong.*

Bitcoin mining is the process of adding new transactions to the Bitcoin blockchain by performing computationally intensive work using powerful computer hardware. The first miner to solve the equation receives a reward in the form of new bitcoin. However, mining Bitcoin is more than just being the fastest or having the most powerful hardware. Luck also plays a significant role in the process, especially with mining pools.

**Luck in Mining**

Bitcoin mining is probabilistic by nature, and your chance of mining a block depends on your hashrate relative to the global network. A common analogy used to explain the impact of luck in mining is the lottery. You can think of each computation as buying a lottery ticket.

For example, if your hash power represents 10% of the network, you would purchase 1 out of 10 tickets. Over time, you would be expected to find 1 out of every 10 blocks mined. However, in the short term, you will experience variance — for example, there is a 35% chance you would not mine a single block out of 10. Joining a mining pool may increase these odds.

**Mining Pools**

A mining pool is a group of miners who combine their computing power to solve the mathematical equations required to add new blocks to the blockchain. Using mining pools can significantly increase a miner’s chance of successfully mining a block as a group and receiving a reward.

For example, with a network hashrate of 300 EH/s, a single 100Th S19j Pro has a 0.0048% chance of mining a block in a day. Put another way; it can be expected to mine a block only once every 57 years. By joining a pool, the miner aggregates their hashrate with others to earn rewards more consistently. Using the lottery analogy, you are pooling together with others to purchase more lottery tickets, and the rewards would be shared among everyone. However, although the increased computing power of a mining pool reduces the luck variance, it doesn’t eliminate it altogether.

Let’s use an example to illustrate the concept of pool luck. Bitcoin has an average block time of 10 minutes — on average, 144 blocks are found daily. A pool with a 50 EH/s hashrate represents 16.67% of the global network (300 EH/s) and would be expected to mine 24 blocks daily, representing 100% luck. In this context, the implications are:

- 100% luck means no deviation from the expected rewards;
- 99% is slightly unlucky (rewards below expectation); and
- 101% means slightly lucky (rewards above expectation).

In summary, anything less than 24 blocks would mean the pool was unlucky, and anything more than 24 blocks would imply good luck for the miners.

**Luck with Payout Methodology**

A pool that uses Pay-Per-Last-N-Shares (PPLNS) methodology will distribute the actual rewards the pool mined according to a miner’s contributions to the pool’s computing power. In this case, the miners participating will also experience the variability of luck at the pool level. For example, miners will report higher revenue than expected if the pool excavates more blocks than expected in a day and vice versa.

On the other hand, a pool that uses Full-Pay-Per-Share (FPPS) will distribute the rewards according to the statistically expected revenue a miner would receive (including transaction fees) given their percentage of the network. This methodology ensures the miner gets paid whether the pool finds a block or not, and removes the variability of luck.

Many don’t fully appreciate the volatility and risk that an FPPS mining pool absorbs on behalf of miners. With payouts, FPPS acts as insurance for the miners by absorbing cash flow variability and allowing them to plan with greater certainty. The graphic below helps to illustrate the odds of various monthly luck results by pool size as a percentage of the network:

If luck is above 100%, more blocks were found than expected, and if below 100%, fewer blocks were found. For instance, if the pool is expected to extract 10 blocks but instead finds 9, its luck is reported as 90%. Over one month, a pool that is 30% of the network has a 34.1% chance of having 99% luck, and a 1.5% chance of having 95% luck. In comparison, a pool that is 15% of the network has a 39.3% chance of having 99% luck, and 8.4% chance of having 95% luck.

Let’s look at what different luck outputs mean at various prices. In this case, we will assume a pool encompasses 25% of the network.

At a $50K BTC price, 99% luck equates to a monthly cash shortfall conditional mean of $9,331,662, and 95% luck corresponds with a dollar shortfall conditional mean of $20,424,037. In other words, at a $50K BTC price, a pool with 25% market share has a ~3% chance of losing an average $20M in one month. A prudent pool operator must hold enough capital reserve to withstand the volatility of these swings, which can be tens of millions of dollars. Since the cost of capital to run an FPPS pool is enormous, on top of the cost of the technology infrastructure, miners must consider the pool operator’s ability to withstand volatility, as well as its solvency in the context of potential large downswings in luck.

**Factors Impacting Luck Variance**

We can gain insight into the dynamics of luck by looking at the distribution curves of the two primary factors that impact the variance of luck — pool size and time. Let’s look at luck distribution for pools with 10% and 25% of the global network over a fixed period of one month.

If we focus on the area between 95–105% luck, we can see that the smaller 10% pool has ~72% of the distribution compared to ~94% for the larger 25% pool. With BTC at $28k, the smaller pool has a ~14% chance of a very negative outcome (less than 95% luck) which would result in ~$5.5M average monthly loss, while the larger pool only has a ~2.8% chance of a poor outcome in percentage terms. However, in dollar terms, it’s more than double the exposure of the smaller pool at ~$11.4M. Although we see a reduction in variance in percentage terms for the larger pool, the monetary exposure is growing.

We can perform a similar analysis, keeping the pool size static while changing the time frame. Let’s look at the distribution of outcomes for a pool representing 25% of the network over one quarter and one year.

Here we see ~49% of the distribution lies between 99–100% luck for one quarter compared to ~81% when looking at the same-sized pool over one year. Similar to the previous analysis, although we see a reduction in luck as a percentage, the exposure is more significant for the longer time frame. With BTC at $28k, a ~26% chance of negative outcome (luck of 99% or less) over one quarter represents a quarterly loss of $10.8M. On an annual basis, there is only a ~9% chance of a substantially negative outcome (luck of 99% or less), though this represents a yearly loss of ~$30.9M.

Both distribution patterns show a reduction in pool luck variance in percentage terms but an increase in monetary terms as the period expands or the pool grows relative to the network.

**Conclusion**

In conclusion, luck plays a crucial role in the success of a Bitcoin mining pool. While many factors contribute to a pool’s performance, luck is the one element that cannot be controlled or predicted. It’s important for miners to understand that luck can swing both ways — and even if a pool has been lucky in the past, it doesn’t mean it will continue to be in the future. Miners looking to minimize cash flow volatility should allocate their hashrate to a pool that utilizes FPPS payouts and has a solid financial position able to withstand potential large cash outflows due to luck.

**Disclaimer**

*The contents of this post have been provided by Foundry Digital LLC (“Foundry” or “we”) for informational purposes only, and should not be construed as giving legal, financial or any other kind of advice. Although we strive to provide quality information, we do not guarantee or warrant any particular results from the use of this information or any opinions provided. Foundry accepts no liability whatsoever for any damages, costs or any other consequences resulting from any actions taken on the basis of the information or opinions provided. Furthermore, Foundry has no control over information provided in any third-party sites linked herein, and Foundry accepts no liability whatsoever over any consequences resulting from any actions taken on the basis of that information. Foundry reserves the right to make changes to this information at any time without prior notice and makes no commitment to update the information contained in this post.*