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Merge pull request #2197 from derekpierre/hypothetical-schmypothetical 

Modify WorkLock properties/values to be more closely related to actual limits
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David Núñez 2020-08-27 18:20:44 +02:00 committed by GitHub
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docs/source/architecture/worklock.rst
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@ -47,10 +47,10 @@ Hypothetical WorkLock Scenarios
For each scenario, assume the following **hypothetical WorkLock properties**:
#. WorkLock holds 280,000,000 NU and the minimum escrow is 15 ETH.
#. The minimum amount of NU required to stake is 15,000 NU and the maximum stake size is 4,000,000 NU.
#. WorkLock holds 225,000,000 NU and the minimum escrow is 8 ETH.
#. The minimum amount of NU required to stake is 15,000 NU and the maximum stake size is 30,000,000 NU.
#. The total number of participants is 1000 (including you) with a total of 50,000 ETH escrowed (including your escrow).
#. For our purposes, a `whale` escrow is an escrow that causes the calculated stake size to be larger than the maximum stake size (4,000,000 NU).
#. For our purposes, a `whale` escrow is an escrow that causes the calculated stake size to be larger than the maximum stake size (30,000,000 NU).
.. note::
@ -61,7 +61,7 @@ For each scenario, assume the following **hypothetical WorkLock properties**:
Scenario 1: Resulting stake size does not exceed maximum stake size (no whale escrows)
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
**You submit an escrow of 22 ETH i.e. 15 ETH minimum + 7 bonus ETH.**
**You submit an escrow of 29 ETH i.e. 8 ETH minimum + 21 bonus ETH.**
*How many NU would be allocated to your network node?*
@ -70,33 +70,33 @@ Scenario 1: Resulting stake size does not exceed maximum stake size (no whale es
.. math::
280,000,000 NU - (15,000 NU \times 1000 \,participants) = 265,000,000 NU
225,000,000 NU - (15,000 NU \times 1000 \,participants) = 210,000,000 NU
- Bonus ETH supply (i.e. total ETH not including minimum escrows) is
.. math::
50,000 ETH - (15 ETH \times 1000 \,participants) = 35,000 ETH
50,000 ETH - (8 ETH \times 1000 \,participants) = 42,000 ETH
- Your bonus portion of the bonus ETH supply is
.. math::
\frac{7 ETH}{35,000 ETH} = 0.02\%
\frac{21 ETH}{42,000 ETH} = 0.05\%
- Your allocation of the remaining NU is
.. math::
0.02\% \times 265,000,000 NU= 53,000 NU
0.05\% \times 210,000,000 NU = 105,000 NU
**Total NU received = 15,000 NU + 53,000 NU = 68,000 NU**
**Total NU received = 15,000 NU + 105,000 NU = 120,000 NU**
Scenario 2: Resulting stake size exceeds maximum stake size (1 whale escrow)
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
**You submit an escrow of 715 ETH i.e. 15 ETH minimum + 700 bonus ETH.**
**You submit an escrow of 6,308 ETH i.e. 8 ETH minimum + 6,300 bonus ETH.**
*How many NU would be allocated to your network node?*
@ -105,29 +105,29 @@ Scenario 2: Resulting stake size exceeds maximum stake size (1 whale escrow)
.. math::
280,000,000 NU - (15,000 NU \times 1000 \,participants) = 265,000,000 NU
225,000,000 NU - (15,000 NU \times 1000 \,participants) = 210,000,000 NU
- Bonus ETH supply (i.e. total ETH not including minimum escrows) is
.. math::
50,000 ETH - (15 ETH \times 1000 \,participants) = 35,000 ETH
50,000 ETH - (8 ETH \times 1000 \,participants) = 42,000 ETH
- Your bonus allocation of the bonus ETH supply is
.. math::
\frac{700 ETH}{35,000 ETH} = 2\%
\frac{6,300 ETH}{42,000 ETH} = 15\%
- Your allocation of the remaining NU is
.. math::
2\% \times 265,000,000 NU= 5,300,000 NU
15\% \times 210,000,000 NU = 31,500,000 NU
However, the total amount of NU to be allocated is 15,000 NU + 5,300,000 NU = 5,315,000 NU which is greater than
the maximum stake amount (4,000,000 NU). Therefore, the amount of NU allocated to you needs to be reduced,
However, the total amount of NU to be allocated is 15,000 NU + 31,500,000 NU = 31,515,000 NU which is greater than
the maximum stake amount (30,000,000 NU). Therefore, the amount of NU allocated to you needs to be reduced,
and some of your bonus ETH refunded.
- Typically the calculation for the NU allocated from the bonus portion is
@ -144,52 +144,52 @@ and some of your bonus ETH refunded.
\text{stake size} = \frac{\text{(your bonus ETH - x)}}{\text{(bonus ETH supply - x)}} \times \text{remaining NU}
- Since you will be allocated a 15,000 NU minimum, and the maximum stake size is 4,000,000 NU, the most you can be allocated from the remaining NU is
- Since you will be allocated a 15,000 NU minimum, and the maximum stake size is 30,000,000 NU, the most you can be allocated from the remaining NU is
.. math::
4,000,000 NU - 15,000 NU = 3,985,000 NU
30,000,000 NU - 15,000 NU = 29,985,000 NU
- Therefore using values in the equation above yields
.. math::
3,985,000 NU = \frac{700 ETH - x ETH}{35,000 ETH - x ETH} \times 265,000,000 NU
29,985,000 NU = \frac{6,300 ETH - x ETH}{42,000 ETH - x ETH} \times 210,000,000 NU
- Reorganizing the equation
.. math::
x &= \frac{700 ETH \times 265,000,000 NU - 35,000 ETH \times 3,985,000 NU}{265,000,000 NU - 3,985,000 NU} \\
&\approx 176.33 ETH
x &= \frac{6,300 ETH \times 210,000,000 NU - 42,000 ETH \times 29,985,000 NU}{210,000,000 NU - 29,985,000 NU} \\
&\approx 353.47 ETH
- Therefore, your final bonus escrow is
.. math::
700 ETH - 176.33 ETH \approx 523.67 ETH
6,300 ETH - 353.47 ETH \approx 5,946.53 ETH
- Your portion of the bonus ETH supply is
.. math::
\frac{523.67}{(35,000 ETH - 176.33 ETH)} \approx 1.504\%
\frac{5,946.53}{(42,000 ETH - 353.47 ETH)} \approx 14.279\%
- Your allocation of the remaining NU is
.. math::
1.504\% \times 265,000,000 NU \approx 3,985,006.46 NU
14.279\% \times 210,000,000 NU \approx 29,985,900 NU
**Total NU allocated ~ 15,000 NU + 3,985,006.46 NU (rounding) ~ 4,000,000 NU, and refunded ETH ~ 176.33 ETH**
**Total NU allocated ~ 15,000 NU + 29,985,900 NU (rounding) ~ 30,000,000 NU, and refunded ETH ~ 353.47 ETH**
Scenario 3: Resulting stake size exceeds maximum stake size (2 whale escrows)
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
**Someone else submitted an escrow of 715 ETH (15 ETH + 700 bonus ETH); we'll call them `whale_1`.**
**Someone else submitted an escrow of 6,108 ETH i.e. 8 ETH + 6,100 bonus ETH; we'll call them "whale_1".**
**You submit an escrow of 785 ETH i.e. 15 ETH minimum + 770 bonus ETH; you are `whale_2`.**
**You submit an escrow of 6,308 ETH i.e. 8 ETH minimum + 6,300 bonus ETH; you are "whale_2".**
*How many NU would be allocated to your network node?*
@ -198,28 +198,28 @@ Scenario 3: Resulting stake size exceeds maximum stake size (2 whale escrows)
.. math::
280,000,000 NU - (15,000 NU \times 1000 \,participants) = 265,000,000 NU
225,000,000 NU - (15,000 NU \times 1000 \,participants) = 210,000,000 NU
- Bonus ETH supply (i.e. total ETH not including minimum escrows) is
.. math::
50,000 ETH - (15 ETH \times 1000 \,participants) = 35,000 ETH
50,000 ETH - (8 ETH \times 1000 \,participants) = 42,000 ETH
- Your portion of the bonus ETH supply is
.. math::
\frac{770 ETH}{35,000 ETH} = 2.2\%
\frac{6,300 ETH}{42,000 ETH} = 15\%
- Your allocation of the remaining NU is
.. math::
2.2\% \times 265,000,000 NU= 5,830,000 NU
15\% \times 210,000,000 NU= 31,500,000 NU
However, the total amount of NU to be allocated to receive is 15,000 NU + 5,830,000 NU = 5,845,000 NU which is greater than
the maximum stake amount (4,000,000 NU).
However, the total amount of NU to be allocated to receive is 15,000 NU + 31,500,000 NU = 31,515,000 NU which is greater than
the maximum stake amount (30,000,000 NU).
- From the previous scenario, the equation for the bonus part of the calculation is as follows, where `x` is the refunded ETH
@ -230,28 +230,28 @@ the maximum stake amount (4,000,000 NU).
- Additionally, there is more than one whale escrow, which would also cause the bonus ETH supply to reduce as well
- Instead the following `whale resolution` algorithm is employed:
#. Select the smallest whale bonus ETH escrow; in this case 700 ETH from `whale_1` < 770 ETH from `whale_2`
#. Equalize the bonus ETH whale escrows for all other whales (in this case, just `whale_2` i.e. just you) to be the smallest whale bonus escrow i.e. 700 ETH in this case
#. Since your bonus ETH escrow is > 700 ETH, you will be refunded
#. Select the smallest whale bonus ETH escrow; in this case 6,100 ETH from `whale_1` < 6,300 ETH from `whale_2`
#. Equalize the bonus ETH whale escrows for all other whales (in this case, just `whale_2` i.e. just you) to be the smallest whale bonus escrow i.e. 6,100 ETH in this case
#. Since your bonus ETH escrow is > 6,100 ETH, you will be refunded
.. math::
770 ETH - 700 ETH = 70 ETH
6,300 ETH - 6,100 ETH = 200 ETH
#. This reduces the resulting bonus ETH supply which will now be
.. math::
35,000 ETH - 70 ETH = 34,930 ETH
42,000 ETH - 200 ETH = 41,800 ETH
#. We now need to calculate the bonus ETH refunds based on the updated bonus ETH supply, and the maximum stake size.
#. Remember that everyone is allocated a 15,000 NU minimum, and the maximum stake size is 4,000,000 NU, so the most that can be allocated to you from the remaining NU is
#. Remember that everyone is allocated a 15,000 NU minimum, and the maximum stake size is 30,000,000 NU, so the most that can be allocated to you from the remaining NU is
.. math::
4,000,000 NU - 15,000 NU = 3,985,000 NU
30,000,000 NU - 15,000 NU = 29,985,000 NU
#. Since we have multiple participants, our equation is the following , where `n` is the number of whale escrows
#. Since we have multiple whales, our equation is the following , where `n` is the number of whale escrows
.. math::
@ -261,42 +261,42 @@ the maximum stake amount (4,000,000 NU).
.. math::
x &= \frac{(700 ETH \times 265,000,000 NU - 34,930 ETH \times 3,985,000 NU)}{(265,000,000 NU - 2 \times 3,985,000 NU)} \\
&\approx 180.15 ETH
x &= \frac{(6,100 ETH \times 210,000,000 NU - 41,800 ETH \times 29,985,000 NU)}{(210,000,000 NU - 2 \times 29,985,000 NU)} \\
&\approx 184.14 ETH
- hence each whale gets refunded ~ 180.15 ETH
- hence each whale gets refunded ~ 184.14 ETH
#. Therefore,
- `whale_1` is refunded ~ 180.15 ETH
- `whale_2` (i.e. you) is refunded ~ 180.15 ETH + 70 ETH (from Step 3) = 250.15 ETH
- `whale_1` is refunded ~ 184.14 ETH
- `whale_2` (i.e. you) is refunded ~ 184.14 ETH + 200 ETH (from Step 3) ~ 384.14 ETH
#. Based on the refunds
- The bonus escrows for the whales will now be equalized:
- `whale_1` bonus = 700 ETH - 180.15 ETH = 519.85 ETH
- `whale_2` bonus = 770 ETH - 250.15 ETH = 519.85 ETH
- `whale_1` bonus ~ 6,100 ETH - 184.14 ETH ~ 5,915.86 ETH
- `whale_2` bonus ~ 6,300 ETH - 384.14 ETH ~ 5,915.86 ETH
- The updated bonus ETH supply will be
.. math::
35,000 ETH - (180.15 ETH + 250.15 ETH) = 34,569.70 ETH
42,000 ETH - (184.14 ETH + 384.14 ETH) \approx 41,431.72 ETH
#. Each whale's portion of the bonus ETH supply is therefore
.. math::
\frac{519.85 ETH}{34,569.70 ETH} \approx 1.504\%
\frac{5,915.86 ETH}{41,431.72 ETH} \approx 14.279\%
#. And each whale's allocation of the remaining NU is
.. math::
1.504\% \times 265,000,000 NU = 3,985,600 NU
14.279\% \times 210,000,000 NU \approx 29,985,900 NU
**Total NU allocated ~ 15,000 NU + 3,985,600 NU (rounding) ~ 4,000,000 NU, and refunded ETH ~ 176.33 ETH**
**Total NU allocated ~ 15,000 NU + 29,985,900 NU (rounding) ~ 30,000,000 NU, and refunded ETH ~ 384.14 ETH**
.. note::