The shape of the game
Pagoda is a climb: nine floors, each holding a row of tiles, exactly one of which is a trap. Pick a safe tile, the multiplier grows and the next floor unlocks; pick the trap, the stake is gone; cash out any time. Difficulty sets the row width — 4 tiles on EASY, 3 on MEDIUM, 2 on HARD — so HARD is a nine-round coin flip with a tower attached.
Ladder games are a genre, and most of them hide a design sin we wanted to name and avoid: pricing the climb worse than the first step, so that the ambitious player pays a higher edge per decision than the cautious one — usually without either of them knowing.
One haircut, not nine
The fair multiplier for surviving one floor is t/(t−1) — on HARD, ×2 for a 1-in-2 survival. A fair nine-floor HARD tower would pay 2⁹ = ×512. Ours pays ×506.88, which is exactly 512 × 0.99: the entire tower carries a single 1% haircut, applied once at the base of the ladder.
The alternative — shaving each floor by 1% — looks identical on floor one and compounds viciously by floor nine: 0.99⁹ ≈ 0.914, a 8.6% effective edge reserved specifically for the bravest players. We considered it for roughly one meeting minute. A house that advertises a 1% game and charges 8.6% to anyone who dares to climb is running the near-miss trick in slow motion.
| FLOOR | MULTIPLIER | SURVIVAL ODDS TO HERE | EXPECTED RETURN |
|---|---|---|---|
| 1 | ×1.98 | 1/2 | 99% |
| 3 | ×7.92 | 1/8 | 99% |
| 5 | ×31.68 | 1/32 | 99% |
| 7 | ×126.72 | 1/128 | 99% |
| 9 | ×506.88 | 1/512 | 99% |
Same law on every difficulty: EASY tops at 0.99 × (4/3)⁹ ≈ ×13.18, MEDIUM at 0.99 × 1.5⁹ ≈ ×38.05.
The tower is decided before you touch it
One more decision worth writing down: the entire tower derives from a single committed draw. Every floor’s trap position comes from one HMAC stream — floor k reads its own cursor of the same (server seed, client seed, nonce) triple that was committed before your stake left your balance.
- The house cannot move a trap mid-climb — floors you never reached were already fixed, and a seed rotation lets you recompute all nine, including the ones above your cash-out.
- Your choices cannot be punished — which tile you pick changes which cell you reveal, never where the trap sits.
- The reveal is the derivation — when the trap shows, you are seeing the committed value, not an animation deciding your fate after the fact.
Strategy-free is itself a design stance. In video poker skill moves the return and we say so; in Pagoda we wanted the opposite promise — a pure nerve game where the only decision that matters is the honest one: how much variance do you enjoy? That is a question about you, priced at a flat 1% whatever you answer, and it pairs with the essay on what a house owes its players.
Climb the tower — free demoNine floors, one committed seed, 99% at every exit. See how high nerve alone takes you.Pagoda →
Is it smarter to cash out early or climb in Pagoda?
Neither, by expected value — every exit returns exactly 99% of stake in the long run. Climbing buys a smaller chance of a larger payout at the same price; the right floor is a preference about variance, not a strategy.
Could the trap move after I start picking?
No. All nine trap positions derive from the seed pair committed before the round, each floor from its own cursor. Rotate your seed and you can recompute the full tower — including floors above where you stopped.
Why does HARD pay ×506.88 and not ×512?
×512 is the fair value of nine doubled floors (2⁹); 506.88 is 512 × 0.99 — the house edge applied once to the whole ladder. That single application is what keeps the expected return identical at every cash-out point.
- Betkyo engine source: pagoda derivation and pagodaMult100 — the article derives every figure from these constants
