Mining Calculator

Section 01 — Gaussian Coin Flip Board

Intuition

Each flip is ±1 (heads or tails). Run thousands of independent trials and watch the Central Limit Theorem emerge — the sum of random variables converges to a bell curve regardless of the underlying distribution. This is the foundation of all Monte Carlo reasoning.

Coin bias (p heads) 50%

Flips per trial 50

Number of trials 2,000

Sum distribution across all trials

Theoretical mean

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Observed mean

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Theoretical σ

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Observed σ

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Mean = n×(2p−1) | σ = 2√(np(1−p)) | As n→∞ the histogram converges to N(mean, σ²) regardless of p. This is why miners can model revenue as a Gaussian even though each block find is a Bernoulli trial.

Section 02 — Monte Carlo Estimation

Convergence

The core MC loop: sample uniformly, evaluate a condition, aggregate the fraction. Here we estimate π by checking whether random points land inside a unit circle. Watch the 1/√N convergence rate — doubling samples halves the noise, not halves the error.

Batch size 500

Total samples

π estimate

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Error from π

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Inside circle

π estimate convergence

Section 03 — Profitability Monte Carlo

Applied

GBM price paths, stochastic difficulty growth, and electricity cost uncertainty — propagated through the full mining revenue model across thousands of scenarios.

Uncertainty Inputs

BTC monthly price vol 15%

Geometric Brownian Motion σ/month

QUAI monthly price vol 30%

Higher for emerging asset

BTC diff growth/mo range (%)

→

Uniform distribution

QUAI diff growth/mo range (%)

→

Uniform distribution

Electricity cost range ($/kWh)

→

Fixed per simulation draw

Annual price drift 0%

Applied equally to both prices

Expected Net (period)

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P5 / P95 Net — BTC

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5th to 95th percentile

P5 / P95 Net — QUAI

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5th to 95th percentile

P(BTC profitable)

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P(QUAI profitable)

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P(QUAI beats BTC)

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Cumulative Net Profit — P5 / P50 / P95 Bands

BTC

QUAI

Final Period Net — Distribution

BTC

QUAI

Each simulation independently samples price paths (GBM), difficulty growth (uniform), and electricity cost (uniform). Capex deducted. Results show post-capex net income over the projection period. Past distributions do not predict future outcomes.

Section 04 — Point Estimate Calculator

Deterministic

Single-scenario projection using fixed inputs. Use this after Monte Carlo to dial in your base case, understand the formula mechanics, or generate a specific monthly table.

Hardware

Hashrate (TH/s)

Power Draw (kW)

Unit Cost ($)

Operating

Electricity ($/kWh)

Pool Fee (%)

Projection (Months)

₿ BTC Network

BTC Price ($)

Network Hashrate (EH/s)

Block Reward (BTC)

Monthly Diff Growth (%)

◈ QUAI Network

QUAI Price ($)

Network Hashrate (PH/s)

Daily Emission (QUAI)

Monthly Diff Growth (%)

QUAI Profit Advantage

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Monthly Profit

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Payback Period

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12-Mo Net Income

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Net After Capex

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Why the Difference?

Daily Unit Economics

₿ BTC

Daily Coins—

Revenue—

Power—

Profit—

◈ QUAI

Daily Coins—

Revenue—

Power—

Profit—

Monthly Projection

Mo	BTC Coins	BTC Profit	QUAI Coins	QUAI Profit

Formula: Daily Coins = (Your Hashrate ÷ Network Hashrate) × Daily Emission