§ WHY IT'S HARD, AND WHY THE ODDS ARE HONEST
Real chaos, limited hands, an empirical engine
Each team pushes with its own chaos stream — a deterministic logistic map, not a random-number call. Team + shoves the token right, team − shoves it left, and because the two streams have identical statistics the push is symmetric: with no input, the token is captured by + and − equally often — a true 1:1. That symmetry is the honest floor the whole game stands on (verified: no-input reach ≈ 5%, captures ≈ 48% / 47%).
What makes it adversarial is momentum plus limited hands. The token drifts with inertia, and your nudges are rate-limited — you can't clamp it to the centre, only time impulses against a random walk that grows more violent every floor (d10 buffets far harder than d1). Reaching the engine on luck alone is a ~1-in-20 event; skill bends that upward, but the top floors can still tear you to a wall.
The odds start at 1:1 and stay honest — the engine reports the frequencies you actually produce, not a number I picked. Beating the chaos is the only thing that moves them.
The probability engine at the top is just that: an empirical tally. Every attempt drops into it — reached, captured by +, captured by − — and it shows the running frequencies. It is the tenant the void room earned: a machine that turns your fight against the chaos tower into a measured probability.
HONESTY LEDGER · THE PROBABILITY ENGINE
REALThe noise is deterministic chaos — two logistic streams (r ramps 3.85→4.0 with height), not Math.random. The baseline is genuinely symmetric: Node Monte-Carlo (6000 runs, no input) gives reach ≈ 5%, + captures ≈ 48%, − captures ≈ 47% — a true 1:1. The odds and P(reach) shown are empirical frequencies of your actual attempts, computed live, not assigned.
CHOSENDifficulty knobs are game design, not physics: chaos base strength, the per-floor ramp (d10 hardest), nudge power, the cooldown, momentum/damping, and climb speed. Tuned so no-input ≈ 5% reach, reactive play ≈ 70–80%, near-perfect anticipation approaches 100% — a real skill band. The 10 floors echo the tower's d1–d10; here they are noise sources, not the tower's exact attractors.
NOTEThis is the void room's tenant, at last: the door 0,0,0,0,5,0,0,0 that read ∅ now leads up through the chaos to a probability engine. Nothing here is faked — the chaos is real chaos, the odds are your own frequencies, and 1:1 is where everyone starts. Want it truly two-player (a + human vs a − human), or the floors driven by the tower's actual attractors instead of logistic streams? Say so.