Hello everyone,

I want to share my finding, perhaps it might uncover a bug that needs attention. Or perhaps I don’t know how leaders are selected exactly with randomness.

I am running a staking pool (ASKP) since February, epoch 245. At first I had a very small delegation (<200K). I would mint a block every month or so, get a 1000% luck for example. Since I found a delegator with 1.3M ADA my luck is always under 100. Here are the numbers:

Epochs 245-280: Average Luck 139%

Epochs 281-308: Average Luck 86% (27 epochs now!)

Total Average Luck 115%

Is that normal? Does ouroboros count in my previous luck or does it select pure randomly?

I never lost a block, I have 100% uptime and my ROA is 1.5% for the last 30 days and 2.8% total. With 1.5M it should be around 3.8%, right?

Please shed some light on this topic, I appreciate the help from this great community!!

Hey @christop,

I think you can actually expect your ROA to decrease a little bit more. It certainly is hard out there for small pools, and I am much smaller than you.

Hi @Benagain that says for 1M ROA should be around 2.62%. For 2M it should be about 3.9%, so I would expect for 1.45M to be about halfway, 3.2%. But my concern is how is it possible to have **86% luck on the past 27 epochs**? A real random system should normalize to 100% eventually, and 27 epochs is a pretty good sample, right? So my question is, is Ouroboros really random, or does it take into consideration our past state? Like if you had too much luck first, it tries to give you less later, so that it averages to 100% in total?

Just the law of averages at work.

Slot leader selection is based on a verifiable random function (VRF) that takes the pool identity, the vrf.skey and the pool’s active stake as input. There is no notion of previous events. It is more like rolling a dice with 23b sides once every second - you have so many winning sides as ADA delegated to your pool.

Mathematically, the process follows the Bernoulli distribution. With 1.45m active stake you can expect to win about 95 blocks in a year (i.e. 73 epochs). If you roll a dice six times, there is no “guarantee” that your winning side comes up exactly one time. Instead, you have the event that you loose on all six rolls in one round and win more than ones in another round.

With your stake, the Bernoulli 0 blocks event is about 30% wich you can see here. You can therefore expect with a probability of 30% that you will not win a block in any given epoch. In the other 70% you will win one or more blocks.

To the delegator, it does not make a difference how your blocks cluster around the epochs in any given year. A mathematically inclined delegator would care about “cost per block” or more precisely “effective cost per block”.

A good reward calculator that shows the Bernoulli distribution for large numbers is here.