A Kaspa solo-mining calculator answers two distinct questions. First, how many blocks should a given hashrate expect to find over a chosen period? Second, given that expectation, what is the probability of finding zero blocks during that same period? The two questions are related but not interchangeable, and conflating them is the most common error in reading a solo-mining estimate. An expected result of one block does not guarantee a block within that period — it means the long-run average, if the same conditions repeated many times, would converge toward one block per period. Any single period remains governed by chance.

This article sets out the probability model behind a Kaspa solo-mining calculator, shows how to compute zero-block probability as an estimate of zero block-reward risk under stated assumptions, and explains how to distinguish an expected result from a guaranteed outcome. The supporting question "how to improve KAS mining luck" is addressed directly: luck, in this context, is not a skill or a setting. It is the outcome of a probability distribution, and at a fixed network target, no timing strategy improves the probability that an individual hash meets that target.

Use current network parameters

A solo-mining calculator for Kaspa needs four inputs: the miner's hashrate (h), the network's estimated hashrate (H), the protocol's target block rate (B), and the length of the period under evaluation (T, in seconds). Convert h and H to the same units before dividing; for example, 1 PH/s equals 1,000 TH/s. Assuming a stable hashrate share, continuous operation, and network conditions consistent with the target block rate, the expected number of blocks over that period is:

μ = (h / H) × B × T

Since Kaspa's Crescendo upgrade, the protocol's target block rate is 10 blocks per second (a 100 millisecond target interval per block), a tenfold increase from the earlier 1-block-per-second design. This change is specified in Kaspa Improvement Proposal 14 (KIP-14). Holding h, H, and T constant, using 1 BPS instead of 10 BPS in this formula understates expected blocks by a factor of ten. It also overstates zero-block probability, but that probability does not change by the same factor.

Network hashrate (H) is not a fixed constant. It is a rolling estimate derived from recent block timing and the network's difficulty adjustment, and it changes continuously as miners join, leave, or adjust output. A calculator's hashrate input should be treated as a recent snapshot rather than a stable long-term figure, and the resulting expected-block and probability outputs are only as reliable as that snapshot's freshness.

Expected time vs probability

Expected time to find a block, derived from the same inputs, is:

Expected time = H / (h × B)

This is a long-run average interval, not a deadline. A miner whose expected interval is seven days will not reliably find a block every seven days; some weeks will produce multiple blocks, and others will produce none. The gap between an average and a single realized outcome is exactly what probability theory — specifically the Poisson distribution — is built to describe. The same probabilistic framing underlies the original Bitcoin design, where block discovery across a network of competing miners is modeled as a Poisson process with a known average rate (Nakamoto, 2008).

The model estimates block discoveries. Under the simplifying assumption that each discovered block qualifies for a reward, zero-block probability also approximates the risk of earning no block reward from mining during that period. It does not measure the probability of a financial loss or of receiving no transfer to a wallet. Actual rewards remain subject to consensus and reward-eligibility rules.

Under a Poisson model, if μ is the expected number of blocks in a period, the probability of finding exactly zero blocks is:

P(0) = e^(-μ)

and the probability of finding at least one block is:

P(≥1) = 1 − e^(-μ)

Worked example. Use hypothetical inputs of h = 0.1 TH/s and H = 1,000 PH/s; these are illustrative values, not a current network snapshot. Converting H gives 1,000,000 TH/s, so h/H = 0.0000001, or 0.00001% of network hashrate. For a seven-day period (T = 604,800 seconds) at the 10 blocks-per-second target rate:

μ = 0.0000001 × 10 × 604,800 = 0.6048

P(0) = e^(−0.6048) ≈ 54.6%

P(≥1) = 1 − 0.546 ≈ 45.4%

Even though the seven-day expectation is about 0.60 blocks, the miner has roughly a 54.6% chance of finding zero blocks during that week. Under the reward assumption above, this also estimates the risk of earning no block reward from that week’s mining. This is the central fact a solo-mining calculator needs to communicate clearly: expected value and realized outcome are not the same thing.

The table below applies the same formula across a range of expected-block values, so readers can locate their own calculator output without recomputing the exponential each time.

An expected-block value of roughly 4.61 is simply the point at which the zero-block probability falls to about 1% for that specific period; it is a mathematical threshold, not an industry benchmark or a recommended operating target.

On the supporting question of improving mining luck: at a fixed network target, each independent hash attempt has the same probability of meeting that target. Increasing hashrate increases the number of attempts per second, not the success probability of each attempt. Kaspa’s PoW implementation checks whether the resulting hash is less than or equal to the target.

Within this model, μ depends on hashrate share, block rate, and effective mining time. Increasing effective hashrate or reducing downtime can increase expected discoveries during a calendar period; evaluating a longer period also increases the chance of finding at least one block. Operational improvements can help work reach the network and qualify for rewards, but they do not make an individual hash luckier at a fixed target.

Account for changing conditions

Two Kaspa-specific details affect how a calculator's output should be read over time.

First, network hashrate and difficulty are linked through Kaspa's difficulty adjustment algorithm, which samples recent blocks to retarget difficulty toward the protocol's intended block rate. Crescendo introduced sparse sampling while preserving the intended DAA window duration, as described in KIP-14. A displayed network-hashrate estimate reflects recent conditions rather than a permanent network state. A calculator result computed today can diverge materially from reality if network hashrate rises or falls, so update the inputs when conditions change and treat longer-range outputs as scenarios rather than fixed forecasts.

Second, meeting the network’s PoW target does not by itself guarantee that the miner receives a reward. Kaspa’s BlockDAG consensus and reward-eligibility rules also apply. Blue blocks are not limited to the selected chain: the reward implementation processes eligible blue blocks in the mergeset. The calculator’s zero-block probability should therefore be read as an approximation of zero block-reward risk under the simplifying assumption stated above, rather than an exact model of final rewards.

Model downtime

The formulas above assume the miner's hashrate is applied continuously across the full period T. Any downtime — hardware faults, connectivity loss, maintenance, or curtailment — reduces the actual mining time within that period and should be reflected by substituting the effective online time for T, rather than the full calendar period. For example, a miner evaluating a 30-day period but experiencing a cumulative two days of downtime would use 28 days as the effective T when computing μ, rather than 30.

Because μ scales linearly with T, downtime has a proportional effect on expected blocks and a direct effect on zero-block probability: reducing effective time increases P(0). Readers using a solo calculator for planning purposes may find it useful to run the calculation twice — once assuming full uptime and once using a realistic downtime assumption based on their own equipment history — to see the range of plausible outcomes rather than relying on a single best-case figure. This is a practical modeling adjustment, not a fixed industry requirement, and the appropriate downtime assumption will vary by equipment, network connection, and operating environment.

Compare with pooled settlement

True solo mining means a miner's equipment obtains work directly from a Kaspa node and submits a solved block to that node; reward depends entirely on whether the miner's own hashrate produces a qualifying network block within the period evaluated (Kaspa Mining Guide). Pool mining works differently: the pool distributes work at an easier share target so it can measure each participant's contribution, and it pays participants according to its own settlement rules once that work is credited. A submitted share only becomes a network-valid block when it also meets the much harder network target; the pool's share target and the network's block target are not the same threshold, and describing them interchangeably would misstate how pool accounting works.

This distinction matters directly for zero-reward risk. In true solo mining, the scenario modeled above — a real chance of completing an entire period with no reward — is the defining characteristic of the approach. In pool mining, payout exposure to pool-level block-finding variance depends on the payment method. ViaBTC currently lists PPS+ and PPLNS as its KAS payment methods (ViaBTC KAS pool information); as of May 20, 2026, SOLO was discontinued as a payment method across ViaBTC's coin pools, including KAS (ViaBTC announcement on SOLO discontinuation). Under PPS+, the subsidy component of a miner's reward is settled based on submitted work rather than on whether the pool itself finds a block during a given period, while the transaction-fee component follows PPLNS-style distribution; under PPLNS, settlement remains more directly tied to blocks the pool actually finds. A fuller explanation of how each method handles variance is available in ViaBTC's PPS+ and PPLNS explainer.

The practical implication for a reader running a solo-mining calculator: if the zero-block probability for a realistic hashrate share and period is high, that result describes the variance inherent to true solo mining specifically, and does not describe the settlement behavior of a pool account using PPS+ or PPLNS.

FAQ

What does an expected-block value of 1 actually mean?

It means that if the same conditions were repeated many times, the average outcome across those repetitions would converge to one block per period. It does not guarantee a block in a single period. When μ = 1, the probabilities are approximately 36.79% for zero blocks, 36.79% for exactly one block, and 63.21% for at least one block. “Exactly one” and “at least one” describe different outcomes.

Can I improve my probability of finding a block on any given hash attempt?

At a fixed network target, timing or configuration cannot make an individual hash more likely to meet that target. More effective hashrate provides more attempts per second, while more online time provides more attempts over the evaluation period. A change in the network target changes per-hash success probability; a change in your hashrate alone does not.

Why does Kaspa's 10 blocks-per-second rate matter for this calculation?

The block rate (B) is a direct multiplier in the expected-blocks formula. Holding the other inputs constant, using 1 BPS instead of 10 BPS understates expected blocks by a factor of ten and overstates zero-block probability nonlinearly. In the worked example, the incorrect zero-block probability would be about 94.13%, compared with 54.62% using 10 BPS.

Does a higher block rate reduce mining variance?

For the same hashrate share and evaluation period, a higher block rate increases expected block discoveries, lowers zero-block probability, and reduces relative fluctuations in the block count. This does not mean the absolute variance of the count falls: under the Poisson model, that variance equals μ. At any given μ, zero-block probability still follows the same formula.

More blocks also do not mean a proportional increase in KAS output. Crescendo adjusts the per-block subsidy for the higher BPS to preserve the emission schedule, as explained in KIP-14.

Is solo mining riskier than pool mining for the same hashrate?

True solo mining exposes the miner to the zero-block probability calculated above, which approximates zero block-reward risk under the stated assumptions. Pool mining distributes risk differently depending on the payment method; PPS+ settles the subsidy portion independently of whether the pool itself finds a block, while PPLNS remains more directly dependent on the pool's own block-finding outcomes.

References

• Kaspa Improvement Proposal 14 (Crescendo), kaspanet/kips, GitHub
• Satoshi Nakamoto, "Bitcoin: A Peer-to-Peer Electronic Cash System"
• Kaspa PoW implementation, kaspanet/rusty-kaspa
• Kaspa reward implementation, kaspanet/rusty-kaspa
• Kaspa Mining Guide
• ViaBTC, Mining Pools Information
• ViaBTC, Announcement on the Discontinuation of SOLO Payment Method for All Coins
• ViaBTC, PPS+ and PPLNS Explained