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Lotto 6/45 Draw 217: Winning Numbers and Probability Explained
Winning numbers and bonus number
- 16
- 20
- 27
- 33
- 35
- 39
- 38
The six winning numbers on 2007-01-27 were 16, 20, 27, 33, 35, 39 and the bonus number was 38. The bonus number only decides second prize, so it is left out of the number-feature calculations below.
First and second prize and the amount after tax
7 players won first prize, KRW 1,611,246,172 each (about KRW 1.61 billion). Applying the current tax rules, the amount after tax is about KRW 1,112,534,936 per winner. Second prize went to 29 players, KRW 64,820,249 each, about KRW 50,559,796 after tax.
| Prize | Winners | Per winner | After tax (reference) |
|---|---|---|---|
| 1st | 7 | KRW 1,611,246,172 | KRW 1,112,534,936 |
| 2nd | 29 | KRW 64,820,249 | KRW 50,559,796 |
| 3rd | 1,206 | KRW 1,558,696 | — |
| 4th | 64,156 | KRW 58,601 | — |
| 5th | 1,066,490 | KRW 5,000 | — |
The after-tax figures apply the current rules (income tax withheld at 20%, 30% on the part above KRW 300 million, local income tax of 10% of that, nothing withheld at KRW 2 million or less) to this draw's prize with no purchase cost deducted. The rules in force at the time may have differed. The method is the same as in the prize tax calculator.
Sales in this draw were KRW 48,260,644,000. The five prize levels together paid KRW 24,130,353,557, which is 50.0% of sales. The share varies by draw, for example when a jackpot with no winner is carried to a later draw.
Was the number of first-prize winners ordinary?
48,260,644 games were sold in this draw. If every game were chosen independently at random, the expected number of first-prize winners would be 5.93 (games sold ÷ 8,145,060). The actual number was 7.
| Expected | Actual | P(X = 7) | P(X ≥ 7) |
|---|---|---|---|
| 5.93 | 7 | 13.6% | 38.2% |
7 winners is an ordinary result, close to what the model expects. A count of 7 or more has a probability of 38.2%, about once every 2.6 rounds.
The Poisson distribution is an approximation. In practice many people choose similar numbers, such as birthdays, so the real count varies more than the model says. The model probability is a yardstick only and says nothing about which numbers come up. See How many Lotto 6/45 jackpot winners should each round have? for the full explanation.
Cumulative comparison
Rounds 88 to 217 (130 rounds): the distribution of first-prize winner counts (bars) against the Poisson expectation for the same rounds (line).
The variance of the deviations measured in model standard deviations is 1.23, close to the Poisson value of 1.
Features of the six numbers and their exact probabilities
The probabilities below come from counting all 8,145,060 ways to draw six distinct numbers exactly (no approximation). "Probability of this outcome" is the share of all combinations that have the same feature as this draw.
| Feature | This draw | Probability of this outcome |
|---|---|---|
| Odd and even | 4 odd, 2 even | 25.1% |
| Low and high | 2 low (1–22), 4 high (23–45) | 25.1% |
| Neighbouring numbers | no neighbouring pair | 47.1% |
| Sum of the six | 170 | sum ≤ 170: 85.7% sum ≥ 170: 15.1% |
| All six at most 31 | no (includes 32 or higher) | 91.0% |
- The odd-even split is a common one: 4 odd and 2 even has a probability of 25.1%.
- The low-high split is also a common one (25.1%).
- This draw had no neighbouring numbers. Such combinations are 47.1%, fewer than those with a neighbouring pair (52.9%). See the counting.
- The sum is 170; 85.7% of all possible combinations have a sum of 170 or less, by the exact distribution of sums (mean 138, standard deviation about 29.9). It is near the middle.
- The draw includes numbers above 31. All six being 31 or lower has a probability of only 9.04%, and every combination has the same chance of winning first prize (1 in 8,145,060). The difference is only that it overlaps less with birthday-only picks. The birthday numbers trap
Every individual combination has the same 1 in 8,145,060 chance of being drawn. The shares above only show which shapes of combination are more numerous.
Context: how often each number was drawn
Appearances of each number from 1 to 45 among the six winning numbers (bonus excluded) over draws 1 to 217 (217 draws). If the draws are fully random, each number is expected 28.9 times with a standard deviation of about 5.0. The shaded band is the expectation plus or minus two standard deviations.
Chi-square goodness-of-fit test: χ² = 30.5, 44 degrees of freedom, p-value = 0.939. The p-value is at least 0.05, so the differences between numbers are within random variation.
Why this result tells you nothing about the next draw
Each draw starts from scratch as an independent trial. The drawing machine does not remember earlier rounds, so the numbers, the odd-even split, the sum and the winner count of this draw have no influence on the next one, and this result tells you nothing about it. Every combination has the same 1 in 8,145,060 chance in every draw. The figures on this page explain a draw that has already happened.
Source and collection time
- Donghaeng Lottery: Lotto 6/45 results by draw — draw 217 collected on
- Source data (JSON) for draw 217 — official response with collection time and SHA-256
- Probabilities and tax were calculated by LottoFlick (calculation code, verification method).
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