# Appendix B

The reward mechanism in Core isn’t terribly complicated, but it does have a lot of moving parts. This section presents a simple example to elucidate its inner workings.

Let’s assume there are two validators, both of which have been elected:

- Validator A, which has two units of delegated hash power and one unit of stake.
- Validator B, which has one unit of hash power and four units of stake.

Let’s assume that there are 10 total units of Bitcoin hash power on the Core network. This would mean validator A has 20% of the hash power (2/10) and validator B has 10% of the hash power (1/10).

Let’s further assume there are 20 total units of CORE staked on the network. This would mean validator A has 5% of the CORE staked (1/20) and validator B has 20% of the CORE staked (4/20).

For this example, m is set to 2/3.

To simplify the calculations, the number of earned rewards distributed is set to one for both validators. And to make things easier, the equations for the hybrid score and rewards are reproduced here:

Hybrid Score:

$\mathrm{S} = \frac{\mathrm{rHp}}{\mathrm{tHp}} * \mathrm{m} + \frac{\mathrm{rSp}}{\mathrm{tSp}} * (1 - \mathrm{m})$

Rewards:

$\mathrm{rH} = \frac{\mathrm{rHp}}{\mathrm{tHp}} * \frac{\mathrm{m}}{\mathrm{S}} * \mathrm{R}$

$\mathrm{rS} = \frac{\mathrm{rSp}}{\mathrm{tSp}} * \frac{\mathrm{(1 - m)}}{\mathrm{S}} * \mathrm{R}$

The rewards per unit:

$\mathrm{rHu} = \frac{\mathrm{rH}}{\mathrm{rHp}}$

$\mathrm{rSu} = \frac{\mathrm{rS}}{\mathrm{rSp}}$

Here are the hybrid scores for validator A (designated as “SA”) and validator B (designated as “SB”):

$\mathrm{SA} = 2/10 * 2/3 + 1/20 * 1/3 = 9/60$

$\mathrm{SB} = 1/10 * 2/3 + 2/10 * 1/3 = 8/60$

Here are the respective hash power rewards and staking rewards for the two validators:

$\mathrm{rHA} = (2/10 * 2/3)/\mathrm{SA} = 8/9 \\ \mathrm{rSA} = (1/20 * 1/3)/\mathrm{SA} = 1/9 \\ \mathrm{rHB} = (1/10 * 2/3)/\mathrm{SB} = 1/2 \\ \mathrm{rSB} = (2/10 * 1/3)/\mathrm{SB} = 1/2$

And here are the rewards per unit for the two validators:

$\mathrm{rHuA} = \mathrm{rHA}/2 = 4/9 \\ \mathrm{rSuA} = \mathrm{rSA}/1 = 1/9 \\ \mathrm{rHuB} = \mathrm{rHB}/1 = 1/2 \\ \mathrm{rSuB} = \mathrm{rSB}/4 = 1/8$

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