The Ally’s Dilemma

The mining payoff game

“Hashrate” is a generic unit: GPUs, nodes, compute, bandwidth, or any additive resource.
The mathematics is identical for all proportional reward systems. Here it is shown as H/s.

Before inviting entities i
0
Average tokens / day without the invited entities.
After inviting entities i
0
Average tokens / day with the invited entities in the network.
Difference i
0
What inviting changes for you, in tokens.

Enter the network’s tokens emitted per day to see your earnings.

Network

Resources you contribute. Example: 100. Everyone else already mining, before you invite anyone. Example: 900.
Entities are allies you invite; their H/s is added to the network.
Whole-network daily reward, shared by hashrate. Example: 1000. Length of the period to simulate. Empty = 1 day.
Whether the daily emission shrinks over time.
How the rest of the network changes during the period. Applied to both before and after.

Network State

Hnet after invite (start) iTotal network size after adding entities, H/s
Hnet effective iAverage over selected days, H/s
Your share beforeAverage % of rewards without entities
Your share afterAverage % of rewards with entities

Break-even i

Inviting entities only pays off if something else makes up for the dilution. Two ways to get back to even:

Token value increase neededHow much more each token must be worth (e.g. because allies make the network more valuable) so that “after” is worth as much as “before”.
Your hashrate needed after invitingOwn H/s you would need, with the entities in, to earn as many tokens as before.

Tokens / day

Average per day, before vs after.

Entity % split

Share of the invited hashrate per entity.

Cumulative tokens over the period

Running total of tokens earned by day, before vs after (first 3650 days max).

Enter “Total network tokens emitted per day” to see token earnings.
  1. Network sizes. Before = you + others. After = before + all invited entities.
  2. Network growth is the same extra H/s in both cases. Linear: day d adds (end − after-start) × (d−1)/(N−1). Average: before uses average − invited.
  3. Daily emission on day d = tokens/day × decayd−1 (decay = 1 when empty or “Zero decay”).
  4. Your tokens on day d = daily emission × your H/s ÷ network H/s that day.
  5. Total = sum of all days. Per day = total ÷ days.
  6. Break-even token value = before ÷ after − 1. Break-even hashrate = the own H/s that makes after-total equal before-total (found numerically).

Linear-growth mode needs an end value; average mode needs an average value. If empty, the network stays at its start size.