Limbo odds and multipliers

The one formula

In Limbo you choose a target between 1.01× and 1,000×. A result is generated, and if the result is greater than or equal to your target, your stake is returned multiplied by that target. If not, the stake is lost. There is no cash-out decision and no timing element.

The win chance is fixed by the target:

win chance (%) = 98 / target

That 98 is the whole game. A fair coin-style game would use 100; the missing two points are the 2% house edge, applied identically at every target.

Reading the odds table

Plug a few targets into the formula and the shape of Limbo becomes obvious.

Notice that 2× does not pay even money odds — it wins 49% of the time, not 50%. And the maximum target of 1,000× lands roughly once every 1,020 rounds, not once every 1,000. That small gap, repeated at every target, is the edge.

Why every target costs the same

Expected return per unit staked is win chance multiplied by payout:

EV = (98 / m) / 100 × m = 0.98

The m cancels. Whether you set 1.01× or 1,000×, you get back 98 units for every 100 staked on average, and lose 2. There is no "value" target, no sweet spot, no multiplier that the maths likes better than the others. The only thing your choice changes is variance: how violently the bankroll moves on the way to that same 2%.

Two illustrations of the same price:

• 1.01×: you win 97.03% of rounds, gaining 0.01 units each time, and lose 1 unit the other 2.97% of the time. 0.9703 × 0.01 = 0.0097 gained; 0.0297 lost. Net −0.02.
• 1,000×: you lose 99.902% of rounds and win 999 units the rest. 0.00098 × 999 = 0.979 gained; 0.99902 lost. Net −0.02.

How long you wait

Rounds are independent, so the number of bets until a win follows a geometric distribution. Two useful numbers: the median wait, and the chance of a complete blank over a session.

median bets to first win = ln(0.5) / ln(1 − p)
P(no win in N bets)      = (1 − p)^N

Read the last row carefully before hunting 1,000×. Nine sessions in ten of a hundred bets will end with nothing at all, and the median hunter waits around 700 rounds. The payout is large because the wait is long, not in spite of it.

A worked session

Say you stake 1 USDT per round at a 10× target, 200 rounds.

• Expected wins: 200 × 0.098 = 19.6
• Expected return: 19.6 × 10 = 196 USDT
• Staked: 200 USDT, so expected loss = 4 USDT, exactly 2%

Now the spread. For a single unit staked at 10×, the variance of the return is p × m² − 0.98² = 9.8 − 0.96 = 8.84, so the standard deviation is about 2.97 per round. Over 200 independent rounds the standard deviation of the total return is 2.97 × √200 ≈ 42 USDT.

So the honest description of that session is: expect to be down 4, give or take 42. Being 50 up or 50 down after 200 bets at 10× is completely ordinary. The edge is small per round and the noise is large — which is precisely why short results tell you nothing and long results tell you everything.

Run the same numbers at 1,000× and the per-round standard deviation is about 31, so over 200 rounds the spread is roughly 440 USDT around the same 4 USDT expected loss. Same price, wildly different ride. More on sizing stakes against that noise in bankroll and volatility.

Limbo and Crash are cousins, not twins

Crash uses a very similar tail: the chance a round reaches multiplier m is about 0.97/m, against Limbo's 0.98/m. The differences that matter:

• Crash carries a 3% edge, Limbo 2%, so at the same target Limbo's win chance is slightly higher (9.8% versus about 9.7% at 10×).
• In Crash you can cash out early or late and the round plays out in real time; some rounds end immediately at 1.00×. In Limbo the target is locked before the bet and the result is instant.
• Crash lets you change your mind mid-round, which is also what makes it easier to mis-play. Limbo removes the decision entirely.

If you like the tail-chasing shape but not the reflex test, Limbo gives you the same long-shot shape without the clock, at a 2% edge instead of Crash's 3%. See crash mathematics for the curve in detail.

Provably fair results

Each round's result comes from HMAC-SHA256(server seed, "client seed:nonce"). The hash is converted into a number and scaled so that the probability of the result reaching any multiplier m is 0.98/m — the edge is baked into the distribution, not applied afterwards to your payout.

The SHA-256 hash of the server seed is published before you bet, and the seed itself is revealed when you rotate it, so every past round can be recomputed from the seed pair and nonce. You can also set your own client seed; the nonce increases by one per bet. The public verifier recomputes any round, and how provably fair works walks through the check step by step.

Target switching and staking systems

A common habit is to raise the target after a dry run, or to double the stake after each loss at a 2× target until it lands. Neither changes anything. Rounds are independent: the hash for nonce 41 knows nothing about nonce 40, and a 100× target that has missed 300 times still has a 0.98% chance on the next round.

Doubling after losses converts a frequent small loss into an infrequent large one. At 2× (win chance 49%), eleven losses in a row happens about once every 1,650 sequences — and when it does, the eleventh stake is 1,024 times the first. The expected return per unit staked is still 0.98 no matter how the stakes are arranged, because expected value adds across bets regardless of size.

The house edge wins over the long run by construction. If target switching has started to feel like a way to get money back rather than a way to choose variance, the limits and self-exclusion tools on responsible gambling are the right page, not this one.