[Math] Probabilities Pick 3 Lottery

probability

In a Pick 3 lottery three numbers are drawn from three separate sets of numbers, between 0 and 9.
Matching 2 winning numbers, one of them duplicated, can be done in 3 ways, according to all lotteries websites.
But I found 18 ways to do it.
As an example:
If the winning numbers are 1 2 3, then there are 18 possible ways to win:

112-113-121-122-131-133-211-212-221-223-232-233-311-313-322-323-331-332

Since the probability is equal to the number of favourable outcomes divided by the number of possible outcomes, it will be 18 divided by 1,000. The odds would be 1 in 55.55

Please let me know if I am making a mistake in my calculations.

Thanks and regards,

Best Answer

When you fill in a Pick-3 lottery card, you:

  • choose three digits between $000$ and $999$, and then
  • choose "Straight" or "Box" (or some other option)

"Straight" means that you only win if your digits come up in the exact order.

"Box" means that you win if they come up in any order—but they must be the same digits in the same quantities.

If you choose $123\text{ Box}$ then there are six ways you can win; if you choose $122\text{ Box}$ then there are only three ways you can win, and that is reflected in a doubled payout.

Pick-3 lotteries generally do not offer a payout for the partial matches you describe.

Options like "Straight/Box" and "Combo" are considered equivalent to filling in a multiple bet.

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