Euromillions lottery anomaly

[Matty1973]

Since there is a big roll over this week I have bought some tickets. I was looking on the prize information and I saw that getting 3 main numbers correct pays more than 3 main numbers plus a Lucky Star number. Surely getting the Lucky Star number as well makes it more difficult and thus should pay more - am I missing something?

I having formatting problems so I can't reproduce the whole payout information here but the important lines for the Tue 10 May 11 Draw 379 is:

Match 3 + 1 Star 78,180 winners each receive £7.10 total £134,317.80
Match 3 + 0 Star 128,824 winners each receive £7.30 total £242,024.20

from https://www.national-lottery.co.uk/player/euromillions/results/prizeBreakdown.ftl
(page shows most recent draw)

 

[AvalonXQ]

As I understand it, each category pays a percentage of the total prize fund according to the expected likelihood of results in that category.
If it just so happens that there are a disproportionate number of Match 3 winners who also got one lucky star, their prize per person may end up being a bit smaller than expected value would indicate.

 

[Rasmus]

Since there is a big roll over this week I have bought some tickets. I was looking on the prize information and I saw that getting 3 main numbers correct pays more than 3 main numbers plus a Lucky Star number. Surely getting the Lucky Star number as well makes it more difficult and thus should pay more - am I missing something?

I having formatting problems so I can't reproduce the whole payout information here but the important lines for the Tue 10 May 11 Draw 379 is:

Match 3 + 1 Star 78,180 winners each receive £7.10 total £134,317.80
Match 3 + 0 Star 128,824 winners each receive £7.30 total £242,024.20

from https://www.national-lottery.co.uk/player/euromillions/results/prizeBreakdown.ftl
(page shows most recent draw)

Not sure about *this* lottery, but in Germany this can happen:

The prices are determined, basically, as follows:

For each level, a specific percentage of the total price-money (around as much as a staggering 50% of all money paid for tickets, I think, excluding the service fees - but don't quote me on that, please!) is used to build up the price pool for that level.

So, three numbers right might be 2%, three numbers and the extra ball might be 5%, and so on.

The payout is then determined by dividing the pool for a particualr level by the number of people that have won in that level.

If for some reason many more people hit the higher level, they will get less money than those (few) on the lower level.

This might happen, e.g. if the numbers can be used to build any significant combination. (Suppose the numbers drawn are 1,2,3,4,5,27 - since millions of people will play 1,2,3,4,5,6 there will be millions of people here with 5 right numbers. There will only be relatively few people who plaid any of the possible 4-number-combinations. (Still a lot of them, I guess, trying to be clever and breaking the sequence after the 4, etc.)

I am not sure if rollovers are handled per level, or if they would be added to the next higher class if nobody won - but that would not be relevant for the lower levels I guess.

 

[AvalonXQ]

By the way, you could very easily fix this problem by calculating the prize amounts cumulatively.
That is, everyone who got two OR MORE numbers would earn a set amount from the lowest prize pool, and the limited set of people who ALSO got three or more numbers would earn an additional amount above that, etc. The additional amounts could be pretty small, potentially, but at least you'd never end up with a situation where a person would actually prefer to have matched FEWER numbers.

 

[Matty1973]

By the way, you could very easily fix this problem by calculating the prize amounts cumulatively.
That is, everyone who got two OR MORE numbers would earn a set amount from the lowest prize pool, and the limited set of people who ALSO got three or more numbers would earn an additional amount above that, etc. The additional amounts could be pretty small, potentially, but at least you'd never end up with a situation where a person would actually prefer to have matched FEWER numbers.

That sounds like a good solution.