← Back to index

Kakeraloot Calculator

Luck analysis and reward forecasts from your $lk display

Your Loots State

How to use this calculator
1
Run $lk in Discord and copy the reply.
2
Paste the full display text into the box below.
3
Your luck percentile and forecast for the next N loots fill in automatically. Optionally enter a Desired +N per reward to see how many loots it'd take to get there.
Tip: Your submission also helps improve the calculator's predictions over time. Fill in the Submit for data analysis section with your guild ID and survey answers, then click Submit.
Inputs
Submit $lk for data analysis
If you're the owner of a Mudae server that's willing to let me scrape message history for kakeraloots data, please contact colblitz in Discord!
Luck Analysis
Your counts vs similar user state; model estimates if not enough data. Not ranked: RT cooldown (capped) and rolls / kakera / mudapins (no cumulative count).
Reward Current Loots to get target
p5 Median p95 Mean P(≥1) Desired +N Est. loots
Important — accuracy & uncertainty
  • Forecasts are averages, not guarantees. Every loot is an independent random draw — your actual results will vary, sometimes a lot.
  • Mean vs Median: the mean (average) is often higher than the median (typical outcome) because a few lucky streaks pull it up. If mean > median, expect most loots to give less than the mean, with occasional big wins.
  • The p5–p95 range shows where your actual results will land about 90% of the time. About 1 in 10 times you'll fall outside it — usually above p95 on a lucky streak.
  • Forecasts far into the future (millions of loots) rely on a mathematical model and are less precise — the spread of estimates increases accordingly. Short-term forecasts are more reliable.
  • Forecasts beyond 12,000 loots assume you buy loots in batches of 12,000 (Mudae's max per purchase). This matters for stacked rolls: the rate tier is locked in per purchase, so each later batch uses the tier mix at your loot count when that batch starts.
  • Disablelist counts are extra noisy because $lk mixes in $kt contributions, so its spread is wider than other rewards.
  • All counts shown are what you'd actually receive (doubled by quantity), not raw spawn counts. For kakera, make sure to enter your server's $klvalue so the amounts are right.

For more information on the models used by this calculator, refer to the full writeup of the investigation.

How it works
1 Two rate estimators

The calculator estimates your per-loot spawn rate two ways and blends them:

  • Empirical — a cell table keyed on (reward type, kakeraloot-usage bin, cumulative-count bin, quality bin). Each cell stores an observed spawn rate, an effective sample size (N_eff), and a bootstrap confidence interval, built from real $lk snapshots submitted by players.
  • Parametric — a gen-hyperbolic decay fit that captures how spawn rates drop as your kakeraloot usage grows. It smooths and extrapolates sparse or unseen cells.

The two are blended by sample size: trust the empirical table where N_eff is high, fall back to the parametric model where it is low. The blend constant κ is tuned by calibration.

Blended rate rate = w · empirical + (1 − w) · parametric
w = N_eff / (N_eff + κ)

Parametric decay parametric = A · (1 + q/100) · (1 + kl/k)−α
← A, k, α fitted per reward type; q = quality
2 Two-part uncertainty

Every estimate has two independent sources of uncertainty:

  • Aleatoric (outcome randomness) — each loot is an independent draw from a negative-binomial distribution with Var = r · mean, where r is a per-type over-dispersion parameter. This is the natural variance you'd see even with a perfect rate estimate, and it's what makes a single loot's result unpredictable.
  • Epistemic (rate uncertainty) — the empirical cell's bootstrap rate confidence interval, widened toward the parametric point for sparse cells. This models "we don't know the true spawn rate exactly" — the less data behind a cell, the wider this band.

Both combine into the forecast and inverse bands you see in the results.

Aleatoric (per-loot outcome) count ~ NegBin(mean, r)
Var(count) = r · mean
← r fitted per reward type (over-dispersion)

Epistemic (rate CI) [ci_lo, ci_hi] = w · [emp_ci_lo, emp_ci_hi]
                       + (1 − w) · parametric
← widens toward parametric as N_eff falls
3 The three queries

Luck ranks your observed cumulative count against players in a similar state. Peer snapshots near your loot count, at compatible quality and quantity, are projected to your exact loot count and your count is ranked among the projections — so the percentile measures how you compare to typical players at your state, not where you sit inside a bin. When too few peers exist, a negative-binomial model at your state is used instead ("modeled"). This peer-based comparison is what shows as "empirical" in the results. >50% means you're luckier than a typical player at your stage.

Forecast is a Monte Carlo simulation: it draws thousands of negative-binomial outcomes at your blended rate, each scaled by an epistemic rate-CI sample, then takes percentiles for the band.

Inverse works backwards from a target: "how many loots until I get N more of this reward?" It bisects on the decay integral to find the smallest horizon X where the expected count reaches your target. The band comes from the rate CI — optimistic (high rate) needs fewer loots, pessimistic (low rate) needs more.

Forecast (Monte Carlo) for i in 1..N:
  s_i ~ Normal(1, rel_sd) ← epistemic scale
  d_i ~ NegBin(mean · s_i, r) ← aleatoric draw
band = percentiles(d)

Inverse (bisection) find X s.t. E[count over X] ≥ target
X_lo = loots_for(ci_hi) ← optimistic
X_hi = loots_for(ci_lo) ← pessimistic