Two functions, printed in full
Most casinos describe their odds. We can do something better, because both of these games are short enough to quote entirely. Here is every line of maths that decides a Limbo round:
And here is Crash, which is not the same function:
Two different shapes. Write u = h / 2⁵² so both are in the same terms, and the difference is plain: Limbo produces 0.99 / (1 − u), Crash produces (100 − u) / (100(1 − u)). The 0.99 in Limbo is the house edge, sitting in the numerator as a flat discount. Crash has no such constant — its edge is hiding in the shape.
What each one costs
Turn each function into the only two numbers a player needs: how often a target is reached, and what a bet on that target returns on average.
For Limbo, the chance of reaching a multiplier x is 0.99 / x, so a bet paying x returns x × 0.99/x — exactly 0.99, whatever x you chose. For Crash the chance is 99 / (100x − 1), and the return is 99x / (100x − 1), which depends on x.
| TARGET | LIMBO — CHANCE | LIMBO — RETURN | CRASH — CHANCE | CRASH — RETURN |
|---|---|---|---|---|
| ×1.01 | 98.02% | 99.00% | 99.00% | 99.99% |
| ×1.50 | 66.00% | 99.00% | 66.44% | 99.66% |
| ×2 | 49.50% | 99.00% | 49.75% | 99.50% |
| ×5 | 19.80% | 99.00% | 19.84% | 99.20% |
| ×10 | 9.90% | 99.00% | 9.91% | 99.10% |
| ×100 | 0.99% | 99.00% | 0.99% | 99.01% |
| ×1,000 | 0.099% | 99.00% | 0.099% | 99.00% |
| ×10,000 | 0.010% | 99.00% | 0.010% | 99.00% |
Limbo’s return column is flat by construction. Crash’s starts higher and converges downward — it never drops below 99%, and never reaches 100%.
So the honest summary is: Limbo charges one price everywhere. Crash charges slightly less for a short ride and settles into the same price for a long one. The gap is small — at ×2 it is half a percentage point — but it is real, and it is the opposite of what the games’ appearances suggest. Crash feels like the riskier product and is, if anything, marginally the cheaper one.
Why two shapes at all
The answer is not that one is better designed. It is that they are commitments to different things.
Limbo settles per player, per bet. Your seed pair and your nonce produce your number, so the natural construction is “take a fair curve and multiply it by 0.99” — an edge you can point at. That flat 0.99 is why the return is identical at every target, which in turn is why Limbo can honestly say the choice of target is a pure variance decision and nothing else.
Crash settles one number for a whole room. Everybody in the round rides the same curve to the same bust, so the draw cannot depend on any individual’s seed. It comes instead from a hash chain — each round’s link hashes to the previous one, with a public salt — so the entire sequence of future rounds was fixed before the first bet was ever placed, and can be checked backwards forever.
The (100 − u)/(100(1 − u)) shape is the standard construction for a chain-derived bust point, and its edge emerges from the arithmetic rather than from a constant someone chose. That is why its return varies with the target while Limbo’s does not — and why comparing the two required deriving both rather than reading a number off a page.
The cap, and what it costs you
Both functions clamp at the same ceiling: 1,000,000 in hundredths, or ×10,000. Limbo’s uncapped curve would keep going; the clamp cuts the tail off both.
What does the cap actually take? For Limbo, the chance of the curve wanting to exceed ×10,000 is 0.99/10,000 — about 1 in 10,101 rounds. In those rounds you are paid ×10,000 instead of whatever the curve produced. The expected cost of the clamp is therefore small but not zero, and it is the one place where Limbo’s otherwise perfectly flat 99% is not quite the whole story.
We point that out rather than round it away, because “exactly 99% at every target” is the kind of clean claim that deserves its own footnote. It is exactly 99% at every target you can actually select; the ceiling is where the model stops.
One function, ×1 to ×10,000Limbo: name a multiplier, and check the draw afterwards against the curve aboveLimbo →
What is the house edge on Limbo?
1%. The engine’s curve is 0.99/(1−u), and the 0.99 makes the return exactly 99% at every cash-out target you pick — ×1.5 and ×1,000 cost the same.
What is the house edge on Crash?
It depends slightly on where you cash out. The return is 99x/(100x−1) — about 99.99% at ×1.01, 99.50% at ×2, and converging to 99% for high targets. It never falls below 99%.
Are Limbo and Crash the same game underneath?
No. They run different functions for a structural reason: Limbo draws per player from your own seed pair, while Crash draws one number for every player in the round from a pre-committed hash chain.
Does picking a higher multiplier change the house edge?
In Limbo, no — the return is flat at 99% across every target, so the choice is purely about variance. In Crash it changes very slightly, with longer rides converging toward 99%.
What is the maximum win?
×10,000 in both games — the clamp at 1,000,000 hundredths in the engine. In Limbo the curve wants to exceed it roughly once in 10,101 rounds, and those rounds pay the cap.
- Betkyo engine source: curve100 and bust100 in _shared/rng.ts, quoted in full; limbo settlement in _shared/demoLocal.ts and both verification paths in _shared/fairness.tsx
- Chances and returns are derived from those two functions — P(m ≥ x) = 0.99/x for Limbo and 99/(100x − 1) for Crash — not read from a published RTP table
