The national lottery is currently running an ad campaign (It could be you), trying to persuade us to buy a lottery ticket.

It got me wondering if the odds were 'significantly' different, if I don't buy a ticket?

It's math above my pay grade, so feel free to work out the number's for me. 🙂

The math is not very complicated; it involves factorals, depending on the quantity of numbers to choose, and the quantity ti choose from.

I do play the lottery, but I've heard it best described as a tax on the poor.

If you don't buy a ticket, you have a zero chance of losing. If you do buy a ticket, you have, ball park, 45 million - 1 chances of losing.

Edited Sunday at 01:52 PM3 days by StringJunky

3 minutes ago, StringJunky said:

If you do buy a ticket, you have, ball park, 45 million - 1 chances of losing.

Not really.

"The players who match all six main numbers win equal shares of the Lotto jackpot. The chance of doing so is 1 in 45,057,474, but the odds of winning any prize on the game are a much more manageable 9.3 to 1. "

So the rate of return on this “investment” is 9.3 to 1 (free another ticket according to ChatGPT).

Edited Sunday at 02:06 PM3 days by Sensei

10 minutes ago, Sensei said:

Not really.

"The players who match all six main numbers win equal shares of the Lotto jackpot. The chance of doing so is 1 in 45,057,474, but the odds of winning any prize on the game are a much more manageable 9.3 to 1. "

So the rate of return on this “investment” is 9.3 to 1 (free another ticket according to ChatGPT).

I was just thinking of the main prize.

1 minute ago, StringJunky said:

I was just thinking of the main prize.

I know. But you lose if you have less than £2 after playing.

Actually ...
The chance of winning or losing is 1/2 ; you either win, or you lose.
The probability of winning by choosing the correct 6 numbers out of 49 choices is

6! / ( 49 - 6 )! which is approximately 1 in 14 Million.

( x-posted with String junky and Sensei )

Edited Sunday at 02:15 PM3 days by MigL

9 minutes ago, MigL said:

6! / ( 49 - 6 )! which is approximately 1 in 14 Million.

It is:

but it is a different game than NL in UK.

"Pick 6 numbers from 1–59 or go with a Lucky Dip® for randomly selected numbers." (from NL website)

ps. I have an interesting conversation with ChatGPT about how this free Lucky Dip gives you a better chance of winning than hand-picked numbers: because people choose their own, their family's birthdays etc., and these are numbers from 1 to 12 and 1 to 31. This limits the number of combinations it can handle, as they must be numbers from 1 to 51 (or from 1 to 49, in a different version).

Edited Sunday at 02:28 PM3 days by Sensei

Ooops ...
Forgot the 6 factoral when editing my last post.

I guess we have it a little better with only 49 numbers to choose from, but the average prize is only 5 Million Canadian ( not real dollars ) in 'Lotto 6/49' lottery.

3 minutes ago, MigL said:

I guess we have it a little better with only 49 numbers to choose from, but the average prize is only 5 Million Canadian ( not real dollars ) in 'Lotto 6/49' lottery.

I like that if you get a 2, you also "win" and have another chance.. so now we need to complicate our mathematical formula to take this into account. Because it changes a lot..

For a deeper dive into how the probability of a state depends on the number of allowed microstates, see the first part of this video.
The rest of it goes on to describe how the 'arrow of time' emerges, from an estimation of the early universe's entropy, compared to the possible maximal entropy.

1 hour ago, MigL said:

For a deeper dive into how the probability of a state depends on the number of allowed microstates, see the first part of this video.
The rest of it goes on to describe how the 'arrow of time' emerges, from an estimation of the early universe's entropy, compared to the possible maximal entropy.

Nicely laid out for this neophyte. Cheers.

@MigL

"What Are the Odds the Universe Exists?"

What you are analyzing are only photons from different directions, with different frequencies, with different polarization.

I can show you an image of the sky generated by my app, which will be indistinguishable from the real sky. "AI", these days, can generate even better ones.

So what are the odds that you're looking at something that's real?

Besides, such mathematics treats all particles as if they were identical and doesn't distinguish them by their positions on the map. It treats hydrogen on Earth and hydrogen on the Sun, or on the other side of the universe, as the same thing. And they're not the same. It's like counting people in statistics and forgetting that they are different people. Which is done all the time. We teleport MigL to the UK, and someone from the UK to Canada. It's not the same state as when you were in Canada and they were in the UK. Isn't?

Give those coins from the movie indexes and positions in the series, and start all the calculations again..

Edited Sunday at 09:23 PM3 days by Sensei

Thanks guy's for all the answer's (nice link @MigL)...

But the question, assuming one winner, is the difference between buying a ticket or not.

I see it as 1 degree of separation (50:50), as in not buying a ticket doesn't mean you won't subsequently, be in possession of one.

So given the probability of winning is very large, one toss of the coin at such an early stage of the equation, wouldn't be all that significant in my choice "to pay a voluntary tax on my optimism"...

You do not have zero chance of winning if you don't buy a lottery ticket, so I maintain there is little difference. I have never bought a lottery ticket in my life but am ahead of the Pennsylvania lottery. One day I found a lottery ticket for 2 free lottery tickets, so I got the free tickets and one of them was a $2 winner, the exact amount I am now ahead. The cashier couldn't believe I took the $2 until I explained that I had never bought a lottery ticket.