Will staking rewards be maximised in a bigger pool or in a smaller one?

I am aware that this may have been tackled elsewhere in a thread, but still it seems that there is a confusion so I wanted to start a thread about it.

Theoretically speaking, if Bob had N ADAs:

  1. Is the probability for him to get elected slot-leader affected by the fact that he belongs to a bigger pool or a smaller one? or maybe it doesn’t matter?

  2. What is the best optimisation for him to get higher rewards? In a bigger pool or in a smaller one? Or maybe it doesn’t matter?

In short, is staking a random selection between all stakeholders from all pools, or just from the pool you’re staking with? I think it is from all pools but I am not entirely sure, so if someone could confirm?

Thank you all in advance for your thoughts

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This is my understanding which may not be accurate so hopefully other will expand on this. The choice of slot leader is determined by the protocol choosing a lovelace (all lovelaces have a number according to the protocol). The owner of that lovelace is the chosen slot leader. If you are in a pool that does not change your chances of being chosen slot leader, you still own the same amount of lovelaces, but it does change the chance that someone in your pool will be chosen, in which you will get a slice of that reward pie. The bigger the pool the more often someone in that pool will be chosen. So over time there should be relatively little difference in your total reward received regardless of self staking or size of pool. What will change is the frequency of payout. The larger the pool the more frequent payouts you would receive, perhaps daily, where as a small pool or self staking less frequent, perhaps weeks or months.


Are you feeling lucky?

Correct, it doesn’t matter, Bob’s probability is a constant, he directs Xn of Ada.

The pool size comes into play on payout schedule and value size of said payouts:

  • Larger pool increased frequency of payouts but smaller value proportionally
  • Smaller pool lower frequency of payouts but larger value proportionally

Take away, the longer your staking horizon is the less it matters, big pool or little pool your payouts will average out over time. The inverse is also true, the shorter your staking horizon is the more impact your pool size will have, statically speaking.

Proof is in of the law of large numbers:

More info:
Jakob Bernoulli On the Law of Large Numbers - pdf
Chebyshev’s inequality - Britannica.



I’m so so lucky haha. Thanks a lot for the usual quality of your answers, that makes sense now

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It’s been mentioned in another thread, but not in this one yet, that it’s worth more to get 10 ADA at the end of each month than 120 at the end of the year, at least if you do anything with it (including staking it).

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Correct, factoring in the capitalized payouts frequency is impactful.

Think of it like this, you want to be selected, or be in a pool that will be selected a certain number of times over a given period.


  • Total Lovelace’s staked throughout all pools
  • Your total Ada or the pools total you’re considering + your Ada
  • Your payout capitalized horizon payouts frequency

Given (change this number, 20, if block signing frequency changes):

  • 20 seconds per signing
  • 3 minute
  • 180 hour
  • 4,320 day
  • 30,240 week
  • 131,040 month
  • 1,572,480 year

Estimating 15,000,000,000 Ada will be staked, your capitalized payouts frequency becomes the only variable, so you look at pool size for your given time horizon:

(15,000,000,000 Ada) / (3 minute) = 5,000,000,000 Ada pool
(15,000,000,000 Ada) / (180 hour) = 83,333,333 Ada pool
(15,000,000,000 Ada) / (4,320 day) = 3,472,222 Ada pool
(15,000,000,000 Ada) / (30,240 week) = 49,6031 Ada pool
(15,000,000,000 Ada) / (131,040 month) = 114,468 Ada pool
(15,000,000,000 Ada) / (1,572,480 year) = 9,539 Ada pool

The formula, [ (#Ada staked)/(time) ], gives you the number of Ada required to be selected over the time variable.

Capitalized payouts frequency, you want to be selected or be in a pool that is selected to:

Sign 1 block a minute must direct 5,000,000,000 Ada.
Sign 1 block an hour must direct 83,333,333 Ada.
Sign 1 block a day must direct 3,472,222 Ada.
Sign 1 block a week must direct 30,240 Ada.
Sign 1 block a month must direct 131,040 Ada.
Sign 1 block a year must direct 9,539 Ada.

So what is the capitalized payouts frequency of Cardano?

Will they credit you even minute, or every hour, or every day, or every week, or every month, or at the end of the year?

The capitalized payouts frequency matters, by adjusting the time horizon Cardano will influence the profitability and thus the number of node/pool operators who support our distributed ledger.


This means it will, generally, be smarter to stake in a pool, right? Even though you might get super, duper lucky with self-staking.


In the example above for every 49,6031 Ada, you will be selected once a week.