Bitcoin Solo Mining Probability: Why 1 in 6.5 Million and 1 in 18,000 Years are Both Correct

By Dominik Lederer, Founder and Solo-Mining Expert at Polarblocks. July 18, 2026, estimated reading time 7 minutes.

On July 13, the Bitcoin Foundation portal published a puzzling headline: "Odds Were 1 in 6.5 Million". In the body text of the same article, a few paragraphs later, a completely different number appears: "roughly one in 16,000 to 18,000 years". Both sentences describe the same event: a Bitaxe finding block number 957,382 on July 10 via the Public Pool, earning 3.1382 BTC, equivalent to approximately 200,000 US dollars. For readers without a calculator, this looks like a contradiction. But it isn't.

What is the probability of finding a Bitcoin block with a Bitaxe?

The formula behind it is unspectacular. The chance that your device will solve the next block corresponds to the share of your hashrate in the total network hashrate. A Bitaxe Gamma 601 delivers approximately 1.3 terahashes per second in continuous operation. The Bitcoin network overall was at about 908 exahashes per second on July 11, 2026, equivalent to 908,000,000 terahashes (Source: Hashrate Index/CoinWarz). Divide 1.3 by 908,000,000 and you get the probability per single solved block: about 1.43 in a billion. A number that no one can make sense of. That's why statisticians multiply it by a time period, and that's exactly where the confusion begins.

Why are "1 in 6.5 million" and "1 in 18,000 years" both true at the same time?

A block is found on average every ten minutes, which makes 144 per day. If you multiply the per-block probability by 144, you get the daily chance. For a 1 TH/s device, as was running on July 10, self-calculation with a network hashrate of approximately 936 exahashes per second yields exactly 1 in 6.5 million per day. This assumption fits the headline, but is not explicitly stated in the source itself, so it is transparently recalculated here rather than simply adopted. If you instead multiply the same per-block probability by 52,560 blocks per year (6 times 24 times 365) and take the reciprocal, you get a completely different kind of number: the average waiting time between two finds in years. For the same device, it is between 16,000 and 18,000 years, depending on which hashrate snapshot is used.

"A miner using a Bitaxe Gamma device mined bitcoin block #957,382 through the Public Pool. At that power, the statistical probability of finding a block is roughly one in 16,000 to 18,000 years." Bitcoin Foundation, July 13, 2026

Both numbers describe exactly the same probability, just expressed in different units: once per day, once as the expected waiting time in years. The proof is simple: 13,285 years multiplied by 365.25 days results in 4,852,000 days, almost exactly the 4.85 million that comes out further down for the Bitaxe Gamma 601. Two editorial teams, two perspectives, one and the same mathematics.

How do you calculate your own solo mining probability?

Four steps, no software needed, a calculator is enough.

First: Read your own hashrate. In the Bitaxe's AxeOS dashboard, it is displayed in real-time; at factory clock speed, the Gamma 601 can reach up to 1.4 terahashes per second, realistically around 1.3 in continuous operation.

Second: Look up the current network hashrate, for example at CoinWarz or Hashrate Index, usually given in exahashes. Multiply by 1,000,000 to get terahashes.

Third: Divide your own hashrate by the network hashrate. The result is the probability per single solved block.

Fourth: Multiply by 144 for the daily chance. For the annual chance, multiply by 52,560 and take the reciprocal; this gives the expected waiting time in years.

What does this mean for the Bitaxe Gamma 601 at the current network hashrate?

The Bitaxe Home Solo Miner in the Arctic Night Edition, the entry-level device from Polarblocks for 149 euros, delivers up to 1.4 terahashes at factory clock speed, realistically around 1.3 terahashes per second in continuous operation at approximately 17 watts and a recommended ambient temperature of 0 to 40 degrees. With a network hashrate of 908 exahashes (as of July 11, 2026), the above calculation yields: statistically one find every 13,285 years, or converted to a chance of 1 in 4.85 million on any given day the device is running. The block value itself is 3.125 BTC base premium plus fees. At the current exchange rate of 55,623.54 Euros (BTC-ECHO, as of July 18, 2026), that's approximately 173,824 Euros from the base premium alone, with fees usually added on top.

Does Bitcoin difficulty change this chance?

On July 11, the difficulty decreased by 5 percent to 127.17 trillion, the fourteenth adjustment of 2026. Difficulty and network hashrate are directly related: if one decreases, the other reference value in the formula above also decreases in the short term, and one's own chance improves minimally. The effect of a single adjustment is small, usually in the low single-digit percentage range. The next adjustment is expected on July 27.

Criterion	Bitaxe Gamma 601	Traditional Lottery	3,500-watt Industrial Antminer
Winning chances per year	52,560 chances a year, a new ticket entered every ten minutes around the clock, without you having to do anything	Two draws per week, making 104 chances a year, with significantly worse basic probability per ticket	Same 52,560 chances a year as the Bitaxe, but with approx. 2,700 times the hashrate, thus a statistically higher hit rate
Running costs in a home office	Around 4.34 euros in electricity per month, runs unnoticed next to the monitor	From 2.50 euros per number field and draw, with no refund for not winning	Over 10,700 euros in electricity costs per year at German household electricity prices, plus soundproofing measures required
Drawer danger (boredom factor)	Low: Live dashboard, LED, and quiet fan noise remind you daily of the ongoing chance	High: the ticket usually ends up in the trash before the draw or is forgotten	Very high for living room use: size, noise level, and heat emission banish the device to the basement or industrial hall
Learning effect and tangible blockchain fascination	High: open firmware (AxeOS), block height, difficulty, and hashrate viewable live in the browser, mining you can touch	None: a random number generator behind closed doors, no insight into the mechanism	Technically available, but practically often outsourced to data centers, no living room experience

"Two numbers for the same find are not a contradiction. They are an invitation to do your own calculations instead of believing headlines."

Is recalculating worthwhile, or does only gut feeling count?

Both belong together. Those who only rely on gut feeling quickly fall for marketing promises, whether from a lottery provider or the next hyped trading signal. Those who only calculate lose sight of the actual appeal: the dashboard that runs live around the clock, the quiet hum next to the desk, the difficulty number that one can follow oneself instead of just believing it. The Eurojackpot offers 104 draws a year and no insight into the mechanism behind it. A 3,500-watt industrial Antminer offers better pure odds, but also an electricity bill, noise pollution, and heat emission that banish it from any living room. The Bitaxe sits in between: worse individual odds than the Antminer, better basic probability than any lottery ticket, yet whisper-quiet, transparent, and within arm's reach on your own desk.

Is 1 in 18,000 years the same as a bad chance?

No, it is an expected waiting time in statistical terms, not an expiration date. Some devices find a block after eight hours, as happened on July 10, most never. The expected value remains honestly low, that's part of the truth.

How often does my solo mining probability change?

With every difficulty adjustment, approximately every two weeks, and with every major fluctuation in the network hashrate. If you want current figures, check CoinWarz or Hashrate Index directly before making your own calculations.

Do I have to manually recalculate the probability?

No, the AxeOS dashboard displays your hashrate live, and external calculators do the rest. However, if you understand the number yourself, you'll also understand why two headlines for the same event can sound so different.