MASTERING-BITCOIN

Why Bitcoin Mining Isn't Really About Mining

IKey Formulas Reference

Formula	Name	Description
$S_n = 50 \cdot \left(\tfrac{1}{2}\right)^n$	Block subsidy after $n$ halvings	Starts at 50 BTC, halves every 210,000 blocks
$\text{Total} = 210{,}000 \cdot \displaystyle\sum_{n=0}^{\infty} 50 \cdot \left(\tfrac{1}{2}\right)^n$	Geometric series cap	Sums to just under 21,000,000 BTC
$\text{Fee} = \sum \text{inputs} - \sum \text{outputs}$	Transaction fee	Difference kept by the miner
$\text{Revenue} = \text{Subsidy} + \text{Fees}$	Miner revenue per block	Two-part paycheck

IIVisualization 1: The Halving Staircase

Bitcoin's block subsidy is cut in half every 210,000 blocks (roughly every 4 years). Use the slider to step through halvings and see how the per-block reward decays exponentially.

Conceptual question: How quickly does the subsidy approach zero, and when does it become economically negligible?

⚙ interactive visualization — coming to this page format soon

Notice: On a log scale, halving is a straight line down. After 32 halvings the subsidy rounds to zero — that is the year 2140 cutoff. The schedule is hard-coded; no committee can change it.

IIIVisualization 2: Why the Cap Lands Near 21 Million

The total supply is the sum of all subsidies ever paid: $\text{Total BTC} = 210{,}000 \times \left(50 + 25 + 12.5 + 6.25 + \dots\right)$

This is a geometric series. Slide the cutoff to see the partial sum approach (but never exceed) the 21 million ceiling.

⚙ interactive visualization — coming to this page format soon

Reflect: The first era alone (50 BTC × 210,000 blocks) issues 10.5 million BTC — exactly half the total. Each subsequent era adds half of what remains. The series converges to $210{,}000 \times 100 = 21{,}000{,}000$ BTC. Rounding losses make the actual final supply slightly less.

IVVisualization 3: From Subsidy to Fees

Today most miner revenue comes from new coins. As halvings continue, fees must take over. Adjust the year and the assumed total fee revenue per block to see where the crossover happens.

⚙ interactive visualization — coming to this page format soon

Notice: Even modest fees overtake the subsidy within a few halvings. The open question is whether fee markets will stay valuable enough — for centuries — to keep paying for network security after 2140.

VQuiz Questions

Question 1

The 2024 halving reduced the block subsidy to 3.125 BTC. What will the subsidy be immediately after the next halving (around 2028)?

✅ Correct! Half of 3.125 is 1.5625 BTC.

❌ Not quite. A halving cuts the current subsidy in half. Compute 3.125 / 2.

Show solution

Solution:

A halving divides the current subsidy by 2: $3.125 \div 2 = 1.5625 \text{ BTC per block}$

The full halving sequence is $50 \to 25 \to 12.5 \to 6.25 \to 3.125 \to 1.5625 \to \dots$

Each halving is triggered automatically when the block height reaches the next multiple of 210,000. No vote required.

Question 2

True or False: When the block subsidy reaches zero around the year 2140, Bitcoin miners will have no source of income and the network will immediately shut down.

✅ Correct! Transaction fees continue to pay miners after the subsidy ends.

❌ Not quite. Recall that miners earn two things per block — only one of them runs out.

Show solution

Solution:

False. Miners earn two types of revenue:

Block subsidy — newly created BTC (decays to zero by 2140)
Transaction fees — paid by users to prioritize their transactions: $\text{fee} = \sum \text{inputs} - \sum \text{outputs}$

After 2140 the subsidy is gone, but transaction fees remain. Whether fees alone provide enough security is an open design question — but the network does not automatically stop. Today fees are a small fraction of revenue; over the next century that ratio is expected to invert.

Question 3

Bitcoin's total supply approaches a cap given by the geometric series: $210{,}000 \times \left(50 + 25 + 12.5 + 6.25 + \dots\right)$

Using the formula for an infinite geometric series $\sum_{n=0}^{\infty} a r^n = \dfrac{a}{1-r}$ , what is the theoretical maximum supply?

✅ Correct! The series converges to 100 BTC per block-equivalent, times 210,000 blocks per era = 21M.

❌ Close, but that's only era 0. The first era issues 10.5M, but all subsequent eras add another 10.5M. Sum the full series.

❌ Not quite. A geometric series with $|r| < 1$ converges. Here $r = 1/2$ , so the sum is finite.

❌ Not quite. Apply $a / (1-r)$ with $a = 50$ and $r = 1/2$ , then multiply by 210,000.

Show solution

Solution:

With first term $a = 50$ and ratio $r = 1/2$ : $\sum_{n=0}^{\infty} 50 \cdot \left(\tfrac{1}{2}\right)^n = \frac{50}{1 - 1/2} = \frac{50}{1/2} = 100$

Multiplying by the number of blocks per era: $210{,}000 \times 100 = 21{,}000{,}000 \text{ BTC}$

A common pitfall: 10,500,000 is just the first era's issuance (era 0 alone). The remaining eras together also sum to 10,500,000, giving a total of 21,000,000.

The actual final supply is slightly under 21M due to integer rounding of satoshis and a few miners who voluntarily underclaimed their reward.

Question 4

Why does proof-of-work — burning electricity to solve a cryptographic puzzle — make the Bitcoin ledger secure?

✅ Correct! Security comes from the real-world energy cost of overwriting history.

❌ Not quite. Think about what makes an attack expensive, not about authority, secrecy, or the supply cap.

Show solution

Solution:

The correct answer is: Rewriting history would require redoing all the energy-intensive work, making attacks prohibitively expensive.

Why the other options are wrong:

❌ "Trusted authority" — proof-of-work is permissionless. Anyone can mine; no whitelist exists. Trust comes from cost, not credentials.
❌ "Encrypts transactions" — Bitcoin transactions are public, not encrypted. The blockchain is a transparent ledger. Proof-of-work secures the ordering of transactions, not their secrecy.
❌ "Prevents exceeding 21M" — the supply cap is enforced by the halving rules and the coinbase transaction limit, not by proof-of-work. PoW determines who writes the next block, not how much they can pay themselves.

The key idea: every block contains a hash linking it to the previous block. To rewrite block $k$ , an attacker must redo the work for block $k$ and every block after it, faster than the honest network produces new blocks. The energy cost grows without bound. As the script puts it: "burn energy to earn the right to write."

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