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Loot box odds, calculated: expected tries, pity counters and "1% times 100"
Games and apps often let you open a box or spin a draw to obtain an item; these are commonly called loot boxes or probability-based items. When the page says "chance of the item you want: 1%", many people read it as "do it 100 times and one will come". Calculating shows that the chance of at least one in 100 tries is 63.4%. In more than a third of cases you still do not get it after 100 tries. This page presents the basic tools for the odds of such items: expected tries, the chance of "at least one", how a guarantee (a pity counter) changes the expected number, and how many tries it takes to collect everything. It also reports, from the original text, what Korean law actually says about disclosing probabilities. It does not rate or promote any game or company.
First, the calculator
Enter the chance per try and the number of tries to see the chance of at least one, the expected number of tries, and the tries needed for 50%, 90% and 99%. Fill in "Guaranteed on this try" to see the values when there is a pity counter.
Basic 1: expected tries is the reciprocal of the probability
If the chance per try is p, the average (expected) number of tries until the first success is 1/p. At 1% that is 100 tries, at 0.1% it is 1,000, at 0.6% about 167. The important word is "average". An average of 100 does not mean the success comes on the 100th try. It could come on the first, or not appear in over 500.
Basic 2: "1% times 100"
The probability of no success is (1 − p)n, so the probability of at least one success is 1 − (1 − p)n.
| Tries | Chance of at least one |
|---|---|
| 10 | 9.6% |
| 50 | 39.5% |
| 100 | 63.4% |
| 200 | 86.6% |
| 300 | 95.1% |
Even at 100 tries, equal to the expected number, only 63.4% succeed, and 36.6% still have nothing. The intuitive "almost certain" at 100 shrinks to 63%. That is the misunderstanding in "1% times 100 will do it". Getting close to certainty needs many more tries.
| Chance per try | 50% | 90% | 99% |
|---|---|---|---|
| 1% | 69 | 230 | 459 |
| 0.6% | 116 | 383 | 766 |
| 0.1% | 693 | 2,302 | 4,603 |
At 1% the expected number is 100 tries but 90% confidence needs 230, more than twice the expectation. This asymmetry warns that planning by the average alone is risky.
Basic 3: how a guarantee changes the expectation
Some loot boxes have a rule "fill a count and you get it for sure", commonly called a pity counter. It puts a ceiling on the number of tries. With chance p per try and a guarantee on try N, the expected number of tries until the first success is (1 − (1 − p)N) ÷ p.
| Chance per try | Guarantee | Expected tries | Without guarantee | Share who reach the guarantee |
|---|---|---|---|---|
| 1% | on try 100 | about 63.4 | 100 | about 37.0% |
| 1% | on try 50 | about 39.5 | 100 | about 61.1% |
| 0.6% | on try 90 | about 69.7 | about 166.7 | about 58.5% |
A guarantee rules out the worst cases, though the average can fall by more or less than one expects. At 1% with a guarantee on try 100, the expected number is 63.4, so the guarantee cuts the average by about 37%. Meanwhile 63% obtain the item before the guarantee, and 37% reach it and receive it by guarantee. Some designs have a very large share reaching the guarantee (58.5% at 0.6% and try 90). The probabilities and guarantee counts in this table are assumptions for explanation and are not figures from any real service.
One more point. Even where the guarantee count is the same, the chance per try may not be fixed but may rise with the number of tries; then the formula above does not apply. How a probability changes is, as seen below, something the law requires to be displayed.
Basic 4: collecting every kind
What if you want not one kind but all n kinds? With equal probability for every kind, the expected tries to collect all n is n × (1 + 1/2 + 1/3 + … + 1/n), a calculation known as the coupon collector's problem.
| Kinds n | Expected tries |
|---|---|
| 5 | about 11.4 |
| 6 | about 14.7 |
| 10 | about 29.3 |
| 20 | about 72.0 |
The last kind takes the longest to get: for 10 kinds, the last one alone needs 10 tries on average. This assumes every kind has the same probability. Where some kinds are rarer, the expected number rises a lot, and the table must not be used.
What the law says about disclosing probabilities
Korea requires probability information for such items to be displayed. What follows is a summary of the original text read at the National Law Information Center.
- Act on the Promotion of the Game Industry, article 33(2) (added 21 March 2023): a person who produces, distributes or provides a game must display, on the game, its website and each advertisement, the kinds of probability-based items used in the game, the supply probability for each kind, and other matters set by presidential decree. The version we read is Act no. 20485 (in force 22 October 2024).
- Enforcement Decree, annex 3-2 (added 9 January 2024): what to display depends on how the item works. For example, for items obtained by drawing, the supply probability of every item by kind, grade and performance; for combining, the probability of every combination result; where the total supply or period is limited, that total or period; where probabilities change with game progress, what changes. Also, an item obtained with certainty after a number of purchases, openings, upgrades or combinations (a pity counter) requires the condition to be displayed.
- How to display: supply probability is shown as a percentage, with rounding allowed at a decimal place at least four places below the first non-zero digit. In the game it must be shown directly on the purchase, viewing or use screen; on the website it must be shown in a form searchable as text or numbers. When changing displayed information, the change and its timing must be announced in advance.
The meaning links directly with the calculations here. If a probability is displayed, enter it in the tool above for the expected tries and "chance of getting it by this point"; if there is a pity counter, the displayed condition becomes N in the formula. How the displayed probabilities are produced and verified, and what the penalty is for failing to display, we did not verify. Also, news reports say the Act was later amended with effect planned from 1 August 2025, but we could not confirm the amendment from the original. Please check the current text at the National Law Information Center.
A few principles for reading probabilities
- Look at the 90% number of tries, not the expected number. The average is only a midpoint and unlucky runs can be far longer.
- Check that tries are independent. If the chance is the same each time, earlier failures do not bring the next success closer (the gambler's fallacy). Only with a pity counter does an accumulated count mean something.
- Set the budget as money, not tries. Multiply the 90% number of tries in the table by the price per try to see the scale of money required.
- Count the target. The cost of getting one kind and of collecting everything differ greatly.
Limits
- The probabilities and guarantee counts here are assumptions for explanation, not figures from any service.
- The calculations assume independent tries and a fixed probability.
- The law is summarised from the version we read. We could not confirm the reported later amendment, so we do not guarantee it matches the current text.
- This is not an article to encourage or discourage purchases. If overspending worries you, see Responsible play.
Sources and verification
- Act on the Promotion of the Game Industry, article 33 (display duty); paragraph 2 added 2023-03-21; version read: Act no. 20485, in force 2024-10-22 — verified · later amendments reported in the press (promulgated 2025-01-31) were not checked
- Enforcement Decree, annex 3-2 (added 2024-01-09): what and how to display probability information (read from the official PDF) — verified · whether this annex is still in force unchanged was not checked
- LottoFlick calculator code (values pinned by tests) — computed by LottoFlick