House edge, proven

The claim

Boarding returns 0.960 per $1 staked; each ride from a cleared gate returns 0.970 per $1 carried. The edge is 4.0% at gate 1 and compounds by 3% a gate (6.9% at gate 2, 15.0% at gate 5). Every lane opens fresh wires at the live mid, so on a driftless martingale no cash-out strategy beats these per-decision returns. The real mid was not quite a martingale (section 04); the fix was verified on 15 days × 2 markets of real ticks.

The physics

A lane is a Papertrade 1000x position that is never opened. The hairline is its hard-bust trigger, d = 1/leverage − bustBuffer, from the live instrument tuple; the gate sits u = k·d the other way. Both wires are set from the Hyperliquid BBO mid at the fill print, and the first one touched settles the lane. On a driftless martingale P(gate first) = d / (u + d) at any volatility. Each ride opens a new lane at the current mid, so earlier lanes say nothing about the next.

Why not mirror Papertrade

Run STRIDE as a real Papertrade position ($1 margin at 1000x, take profit at +d, bust at −d) and settleClose() pays ×1.32 on a win where a fair coin pays ×2.00: a 0.2 bp deadband, the asymmetric-impact haircut and a 2% win fee. That is a 34% edge. HOPLINE pays ×1.92 on the same wires, so lanes cannot be routed through Papertrade. The game borrows its geometry; the house bankroll settles.

Momentum and the cooldown

The martingale argument failed its first backtest. BTC (train 1–10 Oct 2026, test 11–15 Oct 2026, Binance USDT-M perp aggTrades), STRIDE lanes chained at ±5.24 bp with no pause: after gate 1 the next lane survived 57.4% of the time out of sample, and martingale pricing returned 1.099 per $1 at gate 2 and 1.93 at gate 6. The cause is short-horizon momentum: a lane ends on a move, and moves persist for seconds. Overshoot was negligible. A 15 s cooldown before the next fill lets it decay; conditional survival returns to 0.5 within sampling error.

Calibration

Survival is measured per gear and market with the cooldown in place, then priced at pooled + max(1 pt, 1 daily sd); STRIDE is pinned at 0.5. Gate 1 pays rtp / pricing P in cents. On BTC, TAP survives 3.5 pts below theory and LEAP 1.0 pts above, so prices use measurement, not theory. HAUL (u = 4d) is not shipped: its BTC daily estimates span 0.136 to 0.267.

Out of sample

Shipped pricing, 15 s cooldown, BTC STRIDE, scored on 11–15 Oct 2026. Every gate returned under $1 per $1. Test survival ran slightly above 0.5, so returns sit above design; the compound margin absorbed it. Lanes overlap, so the sample that counts is effective independent chains, and past gate 2 the standard error exceeds the edge. Gates 5+ are not validated, hence the compounding margin and the win cap.

Risk controls

A head start δ moves P(gate first) to (d + δ) / (u + d). On STRIDE's 10.48 bp corridor, predicting the post-lock move by 0.22 bp on average erases the whole 4% edge (0.19–0.24 bp across gears). The informed-flow budget is that small; every control below exists to keep it out.

PAPER and the mirror book

Every mirrored lane is a real Papertrade position. For each player stake the house opens a fraction of it as margin, same market and side, at 1000x, so the lane's hairline is the position's own bust trigger, up to the fill difference. When the player busts, the position is liquidated and Papertrade mints PAPER to the house wallet at 12.07 PAPER per $1 lost (the live rate read 2026-10-17). When the player reaches the pad, the house closes it and settleClose() pays less than fair (section 03), so mirroring loses $0.28–$0.36 per $1 mirrored: the house buys PAPER for USDC at $0.047–$0.065 each. Player PAPER in the game stays sim (section 07); this is the house wallet. On devnet the book is a dry run: intents are signed, never submitted, and P&L and PAPER are estimated with Papertrade's own math.

PAPER is non-transferable at launch; its value is the staker share of Papertrade fees (lifetime fees per PAPER so far ≈ $0.006 after 11 days).

What is not proven

• Deep gates. Under 60 effective chains from gate 5. The margin and cap mitigate; they are not evidence.
• Regime shifts. 15 days of October 2026 is one regime. A trending news day can lift conditional survival above the priced level, and the cooldown was fitted on this sample.
• Oracle basis. Calibration used Binance perp trades; lanes settle on the Hyperliquid BBO mid, which has not been calibrated on its own.
• BBO manipulation. Wires sit 5.2 bp from one venue's top of book, with no TWAP or cross-venue check. Caps bound the payoff of moving it; nothing here proves that unprofitable.

The running audit is the realised RTP in the game footer: paid ÷ staked over every settled round, voids excluded, from the live engine. No strategy expects more than 0.960, so over a large sample it should sit at or below that. If it drifts above, this page is wrong.