Is there a positive expected value on the Lotto this week?

[Duke of Marmalade]

I thought I'd bump this thread because of this...

THE REGULATOR OF the National Lottery was alerted after one lottery player bought tens of thousands of tickets for Ireland’s biggest ever Lotto draw last year, and won money on 45,000 of the tickets.
It is not known how many tickets in total the individual bought. The cost of the 45,000 winning tickets alone would have been €180,000.
The player bought the tickets for the ‘Must be Won’ lotto jackpot in January 2022 which reached €19.6 million after many consecutive rollovers...
In total, the prizes amounted to €425,813.

One Irish Lotto player had 45,000 winning tickets in last year's highest ever 'Must be Won' draw

The company that operates the lottery investigated the prize claims because of the sheer volume before paying the player.

www.thejournal.ie

Something really, really weird here. Sure, as I pointed out, there was an expectation of a positive outcome which, if you could do it, justified multiple entries. But how on earth did an individual manage 10s of thousands of entries? Remember they all have to be different - QuickPick doesn't work. The thread points out shop limits of €20 per individual. Clearly this level of entry needed some computerised algorithm. How was that achievable without the co-operation of the Lotto people?
But here's the bit that really doesn't make sense. The chances of a single line wining ANY prize is 3.5%. So 45,000 winning entries suggests around 1.3m entries in total. So park any envy you might have for the "winning" owner.

 

[Leo]

How was that achievable without the co-operation of the Lotto peiople?

Years ago wasn't there a story about a shop closing to the public in the run up to one of the big draws to allow a syndicate dedicated access to their lotto machine?

These days though it's far more likely someone just looked at the web form that is submitted when you select your numbers online, and just wrote a little code to replicated that.

 

[Duke of Marmalade]

There is something extremely fishy about that story. I show the results of that draw below.
The total amount won excluding the jackpot was €27,984,721 - €19,060,800 = €8,923,921
This was shared amongst 357,388 willing lines, that is €24.97 on average for each winning line.
Presuming our hero had only one winning line per winning ticket she should have expected, on average, to collect 45,000 x €24.97 = €1,123,650.
But she only collected €425,813. That seems statistically very, very unlikely.*
One way or the other this person lost big time on their "investment" as 68% of the pot went to the single jackpot winner
* For example, in the very, very unlikely event that she won none of the Match 5 + bonus but scored averagely in the lower wins she would still have won €435,535 or more than she purportedly did win.

 

[Duke of Marmalade]

The only way this makes sense is if the person delayed cashing in all the small prizes. If the 45,000 were made up only of small prizes the amount paid is statistically very close to what would be expected.
So it looks like Match 5 +Bonus prizes were cashed earlier, there would only be double figures of them. If they got their "fair" share of these prizes they may just about break even.
The key was wining at least a share of the €19m jackpot prize or more realistically it not being won and therefore shared amongst the smaller prizes - they were a tad unlucky that it was won and of course that they weren't the winner.

 

[cremeegg]

Ah yes positive expected value on lottery tickets, many bankrupt statisticians.