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TLDR; Rewards are sized as bips of the current balance, but multiplied by a scale s ∈ (0, 1] chosen to target a fixed expected reward per mint.

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Building Blocks

The basic mechanisms that make up the reward scaling system: Base expected drain fraction (if s = 1):
  • f = BIG_BASE_BIPS/(10_000 × BIG_ODDS) + SMALL_BASE_BIPS/(10_000 × SMALL_ODDS) with defaults f = 0.69/15 + 0.069/4 ≈ 0.06325 (≈ 6.325% of balance per mint in EV when s = 1).
Target EV per mint:
  • τ × avgPriceEMA, where τ = TAU_BIPS/10_000 = 0.70.
Scale factor (computed on a chosen balance B):
  • s = min(1, (τ × avgPriceEMA) / (B × f) ).
Scaled bips used for calculating rewards:
  • bigBips = s × BIG_BASE_BIPS
  • smallBips = s × SMALL_BASE_BIPS.

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Why this works

Here’s how it all comes together to keep rewards pegged to demand, based on recent mint activity:
  • EV matching. Given balance B, the expected reward next mint is EV_payout = B × s × f = min( τ × avgPriceEMA, B × f ). In the usual case where B > (τ × avgPriceEMA)/f, the controller achieves EV_payout ≈ τ × avgPriceEMA independent of B.
  • Contract balance growth in expectation. A minter pays price P. Long-run expected drain caused by that mint is ≈ τ × avgPriceEMA. So the balance drifts upward by ΔB_expected ≈ P − τ × avgPriceEMA. When prices are steady so that P ≈ avgPriceEMA, we get ΔB_expected ≈ (1 − τ) × avgPriceEMA = 0.30 × avgPriceEMA. That is: ~30% of the typical mint price accumulates in the contract on each mint in expectation, despite regular randomized rewards.
  • Auto-stabilization under low demand. If demand softens and price declines, avgPriceEMA follows it down (EMA 1/8). The target EV shrinks proportionally, so the controller reduces rewards, allowing the contract balance to keep growing (or decay much more slowly) until demand returns.
  • Liquidity safety. When the balance is very low, s caps at 1, and EV becomes B × f — the most the system will expect to pay out. Claims themselves also scale off the current pre-claim balance, so the contract never promises what it can’t afford.

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Threshold intuition

The boundary between the capped and matched regimes is at B_threshold = (τ × avgPriceEMA) / f. With defaults and avgPriceEMA = 0.001 ETH, B_threshold ≈ 0.0007 / 0.06325 ≈ 0.0111 ETH. Above ~0.011 ETH in the contract balance, the controller is in EV-matching mode.

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How Rewards are calculated (hit cases)

Let B be the balance used for calculation.
  • Preview during an auction (hypothetical):
    • Uses balanceAfterMint = address(this).balance + getCurrentPrice().
    • Computes (bigTotal, smallTotal) = balanceAfterMint × (scaled bips)/10_000.
    • Splits each win into (minter, randomHolder, owner) shares of 50/10/10 over 70 parts:
      • Minter: 50/70 ≈ 71.43%
      • Random holder: 10/70 ≈ 14.29%
      • Owner: 10/70 ≈ 14.29%
  • At claim time (actual):
    • Uses the current balance B = address(this).balance at the moment of claim.
    • Recomputes s and bips; payout = B × (scaled bips)/10_000.
    • Pays the three parties and emits RewardSent.
Implication. If other mints/claims happened between mint and claim, the claimant’s absolute amounts float up/down with B and s — but the EV at the time of mint was already accounted for by the controller logic.

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Worked Numeric Example (Based on Dev Defaults)

Assume just before claim: B = 0.020 ETH, avgPriceEMA = 0.001 ETH, τ = 0.70, f ≈ 0.06325.
  1. Scale: s = (0.0007) / (0.020 × 0.06325) ≈ 0.553.
  2. Scaled bips: bigBips ≈ 6900 × 0.553 ≈ 3815, smallBips ≈ 690 × 0.553 ≈ 381.
  3. If Big hit: reward ≈ 0.020 × 3815 / 10_000 = 0.00763 ETH.
    • Split: minter ≈ 0.00545, random ≈ 0.00109, owner ≈ 0.00109.
  4. If Small hit: reward ≈ 0.020 × 381 / 10_000 = 0.000762 ETH.
  5. EV check: 0.00763/15 + 0.000762/4 ≈ 0.000699 ETH ≈ τ × avgPriceEMA = 0.0007 ETH.

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Economic Goals & Properties

  • Bounded expected drain: EV_payout ≤ τ × avgPriceEMA, with strict < when s is capped at 1.
  • Pot growth: When prices are roughly steady, expected growth per mint is about (1 − τ) × avgPriceEMA (30% with defaults).
  • Never-overpay: Actual rewards are fractions of current balance; if B = 0, claims revert via payout > 0 requirement.
  • Demand adaptive: Lower demand → lower avgPriceEMA → lower target EV → slower drain.
  • Distribution fairness: Independent draws for Big and Small (Small only evaluated if Big misses); random holder drawn from the historical supply snapshot at mint.