Quote from: BlackHatCoiner on January 11, 2025, 08:59:19 PM

Quote from: philipma1957 on January 11, 2025, 06:08:51 PM

It is about 33% vs 100%

That implies there is complete certainty that a block will be mined within the next 10 minutes, which is false. The probability that at least one block is found within the next 10 minutes is not 100%, but 63.2%. Explanation in here.

The probability that k blocks are mined within the next t minutes is: P(X = k) = e^(-λt) * (λt)^k / k!

For k=3, the probability that at least 3 blocks are mined within the next t minutes would be P(X >= 3) = 1 - P(X = 0) - P(X = 1) - P(X = 2).

Applying with λ = 0.1 (blocks per minute), t = 3 minutes, X = 0, 1, 2 blocks, and you have:
- P(X = 0) = 2.718^(-0.3) * (0.3)^0 / 0! = 0.7408
- P(X = 1) = 2.718^(-0.3) * (0.3)^1 / 1! = 0.2222
- P(X = 2) = 2.718^(-0.3) * (0.3)^2 / 2! = 0.0333

=> P(X >= 3) = 1 - 0.7408 - 0.2222 - 0.0333 = 0.0037.

So, the probability that at least 3 blocks are mined within the next 3 minutes is 0.37%. Pretty rare.

It just goes to show the randomness. It's the same sort of with small bitcoin miners. The amount of years it would take with 500Gh/s or 1Th/s for example, it crazy. But, someone did find a block with that amount of hashing power.