Omikuji Tools Life & Calc

Probability Calculator

Permutations, combinations, gacha and lottery odds, deck draw odds and expected value with distribution tables.

✨ Features

  • nPr, nCr, permutations with repetition and circular permutations, exact even for large numbers (big integers)
  • Binomial odds for gacha, lotteries and coins: exactly k, at least k, at least once, with a distribution table
  • Hypergeometric odds for decks and bags (without replacement), with a distribution table
  • Expected value, variance and standard deviation from a value/probability table; recalculates as you type; share a URL

🪄 Use cases

Gacha pity math

A 1% rate over 100 pulls gives 63%; over 300 pulls 95%.

TCG deck building

Compare opening-hand odds for 3 vs 4 copies of a card.

Homework

Check permutations, combinations and binomial probabilities.

Designing a raffle

Estimate prize cost from expected value.

🔒 Privacy

Input is processed in your browser and never sent to a server. Only when you shorten a share URL is that URL (including the input) sent to the shortening service.

❓ FAQ

Permutation vs combination?

Permutations (nPr) count ordered arrangements; combinations (nCr) count selections regardless of order. Choosing 3 of 5 people in a row gives 60; just choosing them gives 10.

How is "at least once" calculated?

1 − (probability of never) = 1 − (1−p)^n. At 1% over 100 trials: 1 − 0.99^100 ≈ 63.4%.

Deck odds vs repeated trials?

Drawing from a deck changes what remains (no replacement) – hypergeometric. Gacha has the same probability every time (with replacement) – binomial.

What is expected value?

The sum of value × probability: the average outcome over many repetitions. Standard deviation measures the spread.

🔗 Related tools

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Permutations & combinations

Repeated trials (gacha, lottery, coins)

%

Independent trials with the same probability (binomial distribution): "3% gacha, 100 pulls, at least one" or "7+ heads in 10 flips".

k 0…
kExactly kAt least k

Drawing from a deck or bag (no replacement)

Drawing without replacement (hypergeometric distribution): "4 copies in a 40-card deck, chance of at least one in a 5-card opening hand".

k 0…
kExactly kAt least k

Expected value

Value (prize, score…)Probability (%)

Example: 1st prize 10,000 (1%), 2nd 1,000 (10%), nothing 0 (89%) → expected value 200.