Koshin StudioLottery win chance calculator
How many entries until you win?
If you enter several lotteries, what is the chance that you win at least one? Enter the odds (for example “1 in 5”) or the win chance (%). If each lottery has different odds, list them in “Win chance per entry” separated by commas and the calculator combines them. Trading-card stores in Japan often sell hot items by lottery, which is why this exists; it works for any lottery.
If you enter odds, they take priority over the win chance field (chance = 100 ÷ odds). If you fill in “Win chance per entry”, the odds, chance and entries fields are ignored.
Example: five lotteries at 1 in 5
- Each entry has a 20% chance (1 ÷ 5). The chance that all five lose is 0.8 to the 5th power, 32.8%. So the chance of at least one win is 67.2%.
- The average number of wins is 5 × 20% = 1.0. But exactly 1 win happens only 41.0% of the time; 2 or more is 26.3% and 3 or more is 5.8%.
- “I entered five 1-in-5 lotteries, so I should win one” is not true. About one person in three loses all five.
Quick table: chance of at least one win
Same odds on every entry, each result independent of the others.
| Odds (win chance) | 1 entry | 3 | 5 | 10 | 20 |
|---|---|---|---|---|---|
| 1 in 2 (50%) | 50.0% | 87.5% | 96.9% | 99.9% | 99.99%+ |
| 1 in 3 (33.3%) | 33.3% | 70.4% | 86.8% | 98.3% | 99.97% |
| 1 in 5 (20%) | 20.0% | 48.8% | 67.2% | 89.3% | 98.8% |
| 1 in 10 (10%) | 10.0% | 27.1% | 41.0% | 65.1% | 87.8% |
| 1 in 20 (5%) | 5.0% | 14.3% | 22.6% | 40.1% | 64.2% |
| 1 in 50 (2%) | 2.0% | 5.9% | 9.6% | 18.3% | 33.2% |
Ten entries at 1 in 10 give 65.1% for at least one win, so about one person in three (34.9%) wins nothing. Doubling the entries does not double the chance (1 in 10: 41.0% with 5 entries, 65.1% with 10).
Quick table: entries needed
| Odds (win chance) | Half win | 90% win | 99% win |
|---|---|---|---|
| 1 in 2 (50%) | 1 entry | 4 entries | 7 entries |
| 1 in 3 (33.3%) | 2 entries | 6 entries | 12 entries |
| 1 in 5 (20%) | 4 entries | 11 entries | 21 entries |
| 1 in 10 (10%) | 7 entries | 22 entries | 44 entries |
| 1 in 20 (5%) | 14 entries | 45 entries | 90 entries |
| 1 in 50 (2%) | 35 entries | 114 entries | 228 entries |
The entries needed for 90% grow roughly in proportion to the odds (22 at 1 in 10, 45 at 1 in 20).
How it works
- No win at all: multiply the chance of losing (1 − win chance) for every entry. At least one win is 1 minus that. With equal chances it is 1 − (1 − p)n.
- Distribution of wins: entries are added one at a time, updating “exactly j wins” (a Poisson binomial distribution). It works when chances differ per entry.
- Entries needed: the smallest n with n ≥ ln(1 − q) ÷ ln(1 − p).
I checked the maths a second way. For equal chances (20% five times, 8% ten times) and for different chances (10%, 30%, 5%, 50%), I simulated 200,000 runs each and compared “exactly j wins” with this calculator. Every value was within 0.2 percentage points, which is the noise of 200,000 trials.
When this does not apply
- You supply the win chance. Stores rarely publish the number of applicants, so “odds” are an estimate. The calculator cannot tell if your number is right.
- Each entry is independent. If a lottery bans duplicate entries, or favours members or past buyers, the real chance differs from these numbers.
- You meet the entry rules. One entry per person, ID checks, purchase limits and pickup locations are set by each store. Entering under multiple names or accounts is often against the rules.
- This is probability, not a promise. Do not buy things you do not want just to raise your number of entries.
For gacha, see the gacha rate and pity calculator and the complete-the-set calculator.