My friend Farida posted a quiz question yesterday, and I responded that the graphic she used looked like a lottery ticket. I suggested that it would be a good question. What are the odds of winning the lottery?
I’m gonna pre-empt that question, by answering it myself, today.
In the UK, you need to match 6 numbers, from a possible 59. That 6:59 format seems quite a common combination globally.
On the night of the draw:
- before you start, there are 59 balls in the pot, and you have six possible numbers on your ticket, so the chance of getting a hit is 6/59.
- Let’s assume you got a hit.
- Second number. One ball has been removed from the bag, but one ball, too, has been crossed off your ticket, so the odds are 5/58.
The odds of getting both the first and second numbers are those two numbers, multiplied, i.e. (6/59) * (5/58). Which is 30/3,422, or 1/115. That’s for getting the first two numbers.
- Now, third ball out. You know the drill.
There’s one less ball in the bag – 57.
There’s also one less number on your ticket – 4.
So, to get just the third ball, you’re 4/57.
And to get all all of the first three balls, you’re
(6/59) * (5/58) * (4/57)
I won’t work that out, because we’re not through yet.
- Fourth ball. Again, one less ball in the bag, one less number on the ticket.
Balls in bag – 56
Numbers on ticket – 3
And, the odds to get all four of the balls so far,
(6/59) * (5/58) * (4/57) * (3/56)
- Fifth ball.
55 balls to choose from
2 numbers left on your ticket.
Odds of getting all five numbers:
(6/59) * (5/58) * (4/57) * (3/56) * (2/55)
- And lastly, the sixth ball.
54 balls to choose from
1 number left on your ticket.
Odds of getting all six numbers:
(6/59) * (5/58) * (4/57) * (3/56) * (2/55) * (1/54)
Phew! So, where are we at? Well, if you got to the very end there, congratulations! You just won the lottery! But let’s finally work out that sum.
(6/59) * (5/58) * (4/57) * (3/56) * (2/55) * (1/54) = about 1/22,500,000.
But it’s not impossible. People do win the lottery, here maybe every month or so.
But more often, nobody wins. On their site at the moment, they say the next draw is a triple rollover – so that is the last two draws, where nobody has won. In fact, winners are sufficiently rare that the lottery company has a rule of no more than five rollovers in a row. After that, they share the prize money out between the people who came closest.
But, would you back a horse at those odds?
My answer, by the way, is “no”. I don’t buy a ticket, which I figure is the most profitable move of all!
Mister Bump 
Like you, I win all the time at the lottery. Because I don’t play.
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I once wrote a prodram which gave me six random numbers. Then as an experiment, I played them for a year. Never even won a tenner! They probably came up the week after I stopped.
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I used to tell my students my dream w to win the lottery. Then I told them I don’t play the lottery. It always confused the. But, I agree. I win by not playing.
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i dont waste money on long odds.
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I don’t buy lottery tickets either. Here in the Netherlands, there’s this postal code lottery where everyone in the winning postcode shares in the prize. The postal codes aare four digits and two letters grouped by neighborhood. They always say that the lottery is coming nearer, but of course if my postcode is 1234AB, only those in the 1234 area win anything and those in the 1234AB area win the most. Then if the lottery fell on 1233AB, that could be nearby, but I wouldn’t win anything.
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Whereabouts in NL are you Astrid? I have many happy memories of North Holland, in particular. Alkmaar region.
We have a postcode lottery too but it is a private company (well, none of them are government-backed any more), Ironically the name started out referring to a bad thing – that the standard of e.g. health services varied depending on where you lived. This has been a factor in COVID too.
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Oh I’m so glad you have fond memories of Alkmaar. I live in Raalte, which is in the province of Overijssel in the east of the Netherlands.
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Ah, I see you. We spent some time once halfway between Nijmegen and Venlo, I forget the name of the town but we visited both cities. It was autumn and there were lots of leaves 🙂. I was pleasantly surprised to find lots of WW2 history around there, but of course it is right on the border. A lovely part of the world, you are so civilised!
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I just read your about me post. Good luck with that arm! I often think if I went back to therapy maybe I could walk again, but it’s foolish when my legs simply don’t work. It’s a pita (pain in the a—) but otherwise I function as normally as any other old lady!🤪. More power to you!👍🏻🥰
Sent from my iPad
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It took me ages in hospital to walk again, but I walked for a mile last summer (took me about 40 mins). I’m still quite doddery though and can lose my balance. Every now ang again, that is a pita too (literally!) 😆
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I never played but Pierre does every week. Love needs to conquer all!
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Yeah, my wife plays it too, but she never wins much except a free go. It’s her money…
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The probabilities are against us lol (says the stats lecturer aka Me lol).
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yes it is amazing that people bother, I think.
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