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
| Strategy | Outcome | EV range |
|---|---|---|
| Random | ALWAYS loses | -3% to -15% |
| High (expensive) | ALWAYS loses (catastrophic) | -39% to -96% |
| Uniform spread | Mostly 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.