Empirical RANDAO Distribution

Empirical distribution of the randomness beacon (=RANDAO) provided by the Beacon chain. The first Proof-of-Stake (PoS) block number is 15537394. Beginning with 15537394, every Beacon node sets the value of the mixHash, i.e. the field with the number 13 (0-indexed) in a block header, to the latest RANDAO mix of the post beacon state of the previous block. The probability of the RANDAO value to fall into the range between 0 and 2**64 is drastically low^*. For more details, I refer to EIP-4399.

^* The probability of RANDAO > 2**64 is $1-\left(\frac{1}{2}\right)^{192}$ = 0.9999999999999999999999999999999999999999999999999999999998406908088867547722971119602232288194408895444807381213926114146613837099.

Visualisation from blockNumber=15537394 to blockNumber=15568555