CARPET-BOMB DEFENSE

We Monte-Carlo'd this.

140 attack configurations from the original analysis grid. 2,000 random targets per cell. Deterministic (seed=42). Structural conclusions apply to the Minnow 100-slot field.

Numbers below were derived from the original analysis grid (extrapolated whale-strategy outcomes across slot counts). Minnow uses 100 slots from 0.001 → 0.1 Ξ. The structural conclusions hold: random-bomb always loses; expensive-bomb always loses; cheap-bomb requires irrational honest play to profit. Dollar figures scale linearly with slot range.

The attack we worried about

A whale claims K slots strategically to extract value from honest players. We tested four strategies:

  • Random slot picks
  • Uniform spread (evenly across the bracket)
  • Cluster LOW (cheap slots 0-K)
  • Cluster HIGH (expensive slots N-K to N)

Each tested across a range of honest-player counts. Whale-as-late-arrival (the actual extraction case · whale captures zero seed dividend).

Result · 115 of 140 configs lose for the whale

StrategyOutcomeEV range
RandomALWAYS loses-3% to -15%
High (expensive)ALWAYS loses (catastrophic)-39% to -96%
Uniform spreadMostly loses; some marginal gain at small K-10% to +11%
Low (cheap)Profits when H ≥ K+5% to +68%

The only winning whale strategy is LOW (cheap-slot carpet-bomb). And it only works under specific conditions.

What the cheap-low attack requires

  • Real ETH committed · to fill the cheap half of the field a whale must spend the sum of those slot values across every bracket they target. Real money, not gas-cheap.
  • Multiple sybil wallets · per-address cap is 50 slots per round. Filling a meaningful portion of the field requires funding gas across each wallet.
  • Irrational honest participation· the whale needs dozens of honest players continuing to pile into expensive slots despite the whale's presence being obvious in the heatmap.
  • Variance tolerance · single-round outcomes have wide spread; the whale can lose their entire committed stake outright on bad target draws.
  • Late arrival (no seed bonus) · if honest seeds first, whale captures 0% seed dividend.

What we DON'T claim

❌ "Whales can never profit." Wrong. Cheap-low against many irrational honest can profit.

❌ "Symmetric play always loses." Wrong. Uniform spread vs comparable H can win ~10% in some configs.

What we DO claim (empirically validated)

✅ Random-strategy carpet-bombing always loses 10-15%.

✅ Expensive-slot carpet-bombing always loses 60-96%.

✅ Cheap-slot carpet-bombing requires honest H ≥ K AND irrational opponents AND multi-wallet sybil setup AND late-arrival (no seed bonus).

✅ Per-address cap (50 slots) bounds single-wallet damage.

✅ Whichever side wins, 5% of every pot flows to $BURN buyback. The protocol always wins.