5February
M'learned friend Jiggers points out that there's another Euro Squillions mass draw this week. An additional €100 million must be given away, cascading to lower prize pools if the jackpot is unwon. Is it worth your while entering in the UK, and is it worth entering in Europe?
First, let's look at the ground rules. There is no roll-over from last week, the jackpot was won. This makes the mathematics a bit easier. Therefore, unless ticket sales run at about two per person across the whole of western Europe, the jackpot fund will be worth precisely €100,000,000. We also note that the game rules (section H) state that exactly 22% of the 42% prize pool goes to the jackpot. Therefore, 78% of the prize pool does not go to the jackpot. That's enough to re-work Jiggers's original work, and model the situation as follows:
Let us assume that t tickets are sold this week. The total entry fee taken in is E, where E = €2 * t .
42% of the entry fees taken, plus any top-up funds, will be paid out as prize money in that draw. The total prize fund paid this time is P, where P = (0.42 * 0.78 * €2 * t) + €100,000,000 .
For the total prize paid to exceed the total entry fees taken we need P > E or
(0.42 * 0.78 * €2 * t) + €100,000,000 > €2 * t
which, subtracting (0.42 * 0.78 * €2 * t) from each side, means that
€100,000,000 > €2 * t - (0.42 * 0.78 * €2 * t)
which, rearranging, means that
€100,000,000 > 0.6724 * €2 * t
and so, dividing both sides by 0.6724 * €2, means that
€100,000,000 / (0.6724 * €2) > t or
€100,000,000 / (€1.3448) > t
and as t must be a whole number, t is no higher than 74,360,499.
A further transformation concerns players in the UK, based on the exchange rate between the euro and the pound. We won't know the final figure until Friday, but this morning, €2 was worth £1.319, so the UK pool grows by approximately 18p per ticket. We may assume tUK ≈ t*(1+(18/150)). This results in a revised figure, tUK ≈ 83,283,759. A similar exercise takes place in Switzerland, resulting in tCH ≈ 76,000,000.
Now, the sale for last week's moderately regular draw was 41,699,374. The 74.4 million sale was almost exactly the one achieved on 27 October, three weeks before the roll-down; the following week's draw secured 83.1 million, The closest approach to a 100 million euro rollover during last autumn's sequence was on ... 27 October! It is absolutely remarkable how this lottery converges almost exactly to the sales level that makes the expected value zero if and only if the jackpot is won that week.
Is it worth one's while buying a ticket? Again, if you're in the UK, you will very probably have a small but positive expected value from a single ticket; as a guide, the expected value of a ticket in last November's roll-down turned out to be about 6 new pence. If you're in Europe, the sign of your expected value is indeterminate at this time; the magnitude is likely to be small; again, the guide figure from last November is roughly minus 1 cent.
