Using a random number generator, generate 100,000 sets
of
four numbers. Email these to 100,000 different people,
accompanied by the message "These are four of the five
numbers which will be drawn in next week's lottery."
Keep
track of which recipients were
sent which numbers.

Assuming that at least one of those sets of four numbers
happens to be correct, email that same person (or those
same persons)
the next week, again with four randomly-chosen
numbers;
and offer to send them the 5th number for a fee.

Halfbakery: Become Astoundingly RichBecome Astoundingly Rich See [imaginality]'s comment about millions of email recipients and stock-market predictions [zen_tom, Apr 04 2016]

Actually, thinking about it, what's needed is a
website which displays a set of random numbers that
is different for each IP address viewing the page (but
consistent between views, for any one IP address).

I think I've heard about this being done with football scores.
Send out a bunch of predictions and keep track of who
received the right ones then charge them for next week's
scores. If you're sending out enough, you can even send out
a second week of scores so a very small number of people
think you're right every week.

It is similar to a common stock market scam run by stockbroker salesmen. Tell 64 people where any volatile stock is headed. "Just watch it. Ya don't gotta buy nuttin. "

32 up 32 down

then 16 up and 16 down

then 8 up and 8 down

and finally 4 up and 4 down.

Then call the ones you've guessed right on 4 times in a row. They think you really know and put in big money and their friends money into whatever cockamamie stock you are flogging.

If you knew 4 of the winning numbers, couldn't you just buy a ticket for each of the remaining options?

Also, you would have to be really stupid to fall for this scam. If someone knew the winning numbers to a lottery, why would they possibly need a stranger to buy the winning ticket? If the numbers where arrived through clairvoyance, the person could get buy the ticket themselves; if the numbers where arrived at by nefarious means (and didn't want to be directly associated with the win), the person would find a trustworthy friend.

There's prior annotation discussion - I've linked an idea I think rather neatly dovetails with this one in an upside-down sort of way - [imaginality] mentions therin something along similar lines, but regards stock market predictions (rather than lottery numbers)

The effect is more pronounced when you can show repeated success over a period of time - but that's tricky with lottery numbers as the field of possibility thins rather rapidly due to the number of starting conditions you'd have to cover.

Just predict two of the required numbers. Then you don't even need to randomly generate them, just work in multiples of every combination. There are 10 successfully predictions per combination cycle. Also, this makes it more likely that the mark will pay to get the remaining numbers rather than buying the four you provide plus a random fifth ball, for a smaller win.

Or just predict a single ball. Then the odds are big enough that you could iterate on the fraction of successful predictions.

// Also, you would have to be really stupid to fall for this
scam. //

The Nigerian email scam deliberately uses poor spelling and
grammar so that smart people will realize it's a scam and
self-select out, leaving only the stupid recipients for the
scammers to work with.