Limbus Company clash calculator
The number in-game is a single-roll estimate. This solves the whole clash, every branch, exactly.
Why this differs from the in-game number
The win rate the game shows you is essentially the first exchange only. But a clash is not decided in one roll — the loser drops a coin and both sides keep clashing with what remains, until one side runs out.
So the true win rate depends on the whole probability tree, not the opening comparison. A side with more coins can lose the first exchange and still come out ahead, simply because it can afford to lose.
The only comparable tool available says so itself: "the in-game win rate is deceiving as it is a naive calculation that does not account for clashes after losing a coin." This solves exactly that part.
Method and verification
The clash is solved exactly with dynamic programming over the state f(your coins, enemy coins):
f(a, b) = P(win)·f(a, b−1) + P(lose)·f(a−1, b) + P(tie)·f(a−1, b−1)
The per-exchange win/tie/lose probabilities come from convolving the binomial coin distributions of both sides.
Verification: checked against a 400,000-run Monte Carlo simulation across five scenarios — mirror matches, lopsided matchups and negative coins. Maximum deviation: 0.0008.
Sanity matters more than people think
Heads chance = 50% + SP. Going from 0 to +45 SP moves it from 50% to 95%.
The real leverage is that multiple coins compound. Three coins all landing heads is 12.5% at 0 SP but 85.7% at +45 SP — nearly a sevenfold difference.
Offense level gives a separate clash bonus
For every full 3 levels of offense level advantage, you gain +1 power to all rolls during the clash only. It does not affect the damage calculation. Add it into base power manually above.
About ties
Community sources disagree on tie handling. The default here is "both sides lose a coin"; you can switch to "re-roll" to compare. The difference shows up most clearly in mirror matches.