# Coquito Tezem, Ergo Sum — Expected Rewards from Solo Baking Tezos

As mentioned in the previous article on Understanding Inflation in the Tezos Protocol, the implications of inflation to token holders who choose to *hodle *their coins becomes more tangible if we look at the expected earnings from making XTZ productive, by baking or delegating. This article will cover the expected earnings **from solo baking**.

This article is structured as follows: It starts with the global variables, the calculation process until I reach the expected reward values, and cover three cases: holders of 10K, 100K and 1,000K XTZ. The last section provides an overview of other benefits, to often overlooked, that derives from baking experience, which go beyond economic incentives.

*Note*: Before reading this article, I strongly recommend taking a look at the previous ones in our economics series:

**Understanding Overdelegation and Self-bond Requirements**: https://medium.com/cryptium/is-your-favourite-baker-overdelegated-understanding-self-bond-requirements-in-tezos-bb005a05c609**Introduction to Tezos Proof-of-Stake and Understanding Rewards**: https://medium.com/cryptium/hello-admin-when-payout-tez-19fc5e460cce**Understanding Inflation in the Tezos Protocol**: https://medium.com/cryptium/did-they-pull-the-5-51-out-of-their-oven-understanding-inflation-in-the-tezos-protocol-13493829a533

### Expected Rewards of a Solo Baker

A* solo baker* is a token holder that is operating his/her own Tezos bakery. The solo baker possesses at least 10,000 XTZ, which is the minimum required to participate.

In this section, I will calculate how much a solo baker, with different initial balances of XTZ, can expect to generate at the end of Cycle 34 — **in the most optimistic scenario**. One can extrapolate to the following Cycles, assuming that the Rolls Distribution percentages do not vary significantly.

In the tables below, you can find the calculations for three different token holders: *Thurar*, *Leenkath*, and *Anry*, who hold respectively 1, 10, and 100K XTZ. They all want to become a solo baker and **will not take public delegation***.

**Technically, a baker** cannot deny delegations**. Delegators might generate the originations and appoint any baker to it. The only measurement that a baker, who does not want to provide the service, can take is simply refuse to pay out the corresponding rewards to the delegators.*

#### The Global Parameters

The global parameters I took are from **Cycle 34**, you can find the values if you check TzScan:

- Global supply of XTZ is the total XTZ in circulation,
**764,317,931 XTZ**during Cycle 34 - Global rolls is
**41,074**, which equals to**410,740,000 XTZ staked** - The ratio of staked / total supply is
**53.7394%** - Which gives a Global Self-Bond Requirement of
**8.1557%**(you can check for other values in this gist): - I will assume that transaction fees (gas prices) are 0 in every block

For simplicity, I will assume the most optimistic case, **where endorsement rewards are always 2 XTZ** .

#### Thurar’s Solo Baking

Now that I have the global parameters, let’s walk through the calculations using Thurar’s case.

Thurar has an initial balance of 10,000 XTZ, just enough to become a baker. 10,000 XTZ earns Thurar 1 Roll, which in Cycle 34 represents 0.0024% of the Global Rolls Distribution:

Thurar's Roll Distribution =Thurar's Rolls / Global Rolls

Thurar's Roll Distribution =1 / 41074 = 0.0024%

Because the Tezos Protocol assigns baking and endorsement slots pseudo-randomly, a way of reading Thurar’s Roll Distribution is *the likelihood of Thurar getting the next baking and or endorsement slot*.

In the longer term, Thurar should receive 0.0024% of the total inflation (assuming that the rolls distributions do not change overtime). However, in the shorter term Thurar’s slots will depend on luck (in some cycles he might get more or less than 0.0024%).

For the purpose of this example, I will assume the most optimistic scenario, where Thurar gets exactly 0.0024% of all bakings and endorsements of an entire cycle. Considering that a cycle has 4096 blocks and that the maximum time between blocks is 1 minute, then:

Likely Received Baking Slots =0.0024% * 4096 = 0.0997 Units

Likely Received Endorsement Slots =0.0024% * 131072 = 3.1911 Units

# the 131072 comesfrom 32 (max endorsements per block) * 4096

Following this, the rewards that Thurar would earn at the end of this cycle would be:

Total Baking Rewards =0.0997 * 16 = 1.5956 XTZ

Total Endorsement Rewards =3.1911 * 2 = 6.3822 XTZ

Of course, these values are not possible: Either you get a slot or not, but you can’t get half a slot. Similarly, if you bake a block, you will receive 16 XTZ, if you make an endorsement you will receive 2 XTZ.

But a way one can read these numbers is that for a baker with the same conditions as Thurar, it might take more than a cycle to receive a baking slot, **baking an average of 0.0997 blocks/cycle, and endorse on average 3.1911 endorsement slots/cycle over cycles**.

### Thurar, Leenkath, and Anry

In the previous section, we walked through the calculation process. The following table shows all the numbers broken down, together with the three different cases:

### So, Should I Solo Bake or Not?

Whoever asks me if he/she should bake,** my answer is always yes**. The reasons go beyond economic gains:

- Baking, even if you’re just trying it out,
**is the most efficient way of learning about the Tezos Protocol**. In the times where there will be more and more PoS blockchains going alive, it’s unique and valuable experience that anyone can acquire. - Besides the learning experience,
**it is a fun game that can turn into handsome rewards**. Even if you have only 10,000 XTZ, if you’re lucky, you might wake up with lots of baked blocks and endorsements. It feels even better when you earn your first rewards after working hard to setup a baker. **It increases decentralisation of the Tezos network**. It starts by increasing the number of distinct bakers. But it does not stop there: by for example operating physical infrastructure in your own location, you can contribute to a more geographically decentralised validating set and placing less weight to major cloud providers.**You will be participating directly in on-chain governance**and steer the wheel of future Tezos Protocol upgrades.