# Understanding shelley reward formula (and k, a0 parameters)

**URL:** https://forum.cardano.org/t/understanding-shelley-reward-formula-and-k-a0-parameters/33391
**Category:** Operate a Stake Pool
**Created:** [25 May 2020 13:05 UTC](https://forum.cardano.org/t/understanding-shelley-reward-formula-and-k-a0-parameters/33391 "2020-05-25T13:05:10Z")
**Posts on this page:** 1
**Showing post:** 16

<div class="post-metadata">

### Author: ![ergophobia](https://avatars.discourse-cdn.com/v4/letter/e/eb9ed0/32.png) [@ergophobia](https://forum.cardano.org/u/ergophobia)
#### Post date: [26 May 2020 11:02 UTC](https://forum.cardano.org/t/understanding-shelley-reward-formula-and-k-a0-parameters/33391/16 "2020-05-26T11:02:49Z")

</div>

No let’s take an example with 2 pools with 100% pledge ( s’=σ’ to simplify things), and let’s take a0=5

**One big pool which is saturated (s’=σ’=z0) :**  
s^2/z^2=1  
so its reward formula : f= R/6\*( σ’+5 \* σ’) = R/6\*( 6\*σ’) = **R \* σ’**

**One small pool saturated at 1% (s’/z0=0.01):**  
s^2/z^2= (0.01)^2 = 0.00001  
so its reward formula : f= R/6\*( 1.00005 \* σ’) ~= **R/6 \* σ’**

One get a RoS 6 times higher than the other. If you call that fair, we don’t have the same notion of fairness! 😉

---

_[View the full topic](https://forum.cardano.org/t/understanding-shelley-reward-formula-and-k-a0-parameters/33391)._