Avoid any such systematic choices! Too many other players may think along your lines, and some may copy your selection. Be aware of the two players who split the jackpot in the Irish Lottery, both having picked their numbers using the dates of birth, ordination and death of the same priest! One idea is to choose your numbers completely at random, perhaps by use of an ordinary deck of cards (discard three of them, shuffle well the other 49), or the official Lucky Dip facility. But do not fall into the trap of believing that spreading your choices *evenly* across the card is the same as choosing *randomly*: far from it!

If the combinations listed above, with 133 and 57 winners are marked on the Lottery ticket as set out at the time (nine rows of five numbers, a bottom row with four numbers), you will see thatIt is as though players had run their pencils down the middle of the ticket, dodging a little from side to side, *thinking* they were choosing at random. They were not – as their disappointing jackpot prize proved https://www.irishresults.net/

One further factor: many players choose numbers based on family birth dates, and so the numbers 1 to 31 are be selected more often. To help avoid their choices, bias your random choice towards the higher numbers. How? Plainly, the mean value of a single number is and so the mean total over six numbers chosen at random is . The calculation for the variance is more complicated – successive choices are not independent – but Riedwyl’s advice is to select your numbers at random, but then reject them en bloc unless

We have concentrated on the prospects of winning a jackpot share, as that is the main motivation for most Lottery players. But working out the chances of the other prizes is not difficult. Call the six winning numbers the Good numbers, the other 43 the Bad numbers. So to match exactly five of the winning numbers, your selection combines five of the six Good numbers (with 6 ways to select them) along with one of the 43 Bad numbers (43 choices), making possible winning tickets. The Bonus number is just one of the Bad numbers, so six of these choices win a share of the Bonus prize, the other 252 qualify for a Match 5 prize.

Similarly, to win a Match 4 prize, you select 4 of the 6 Good numbers (in ways), along with 2 of the 43 Bad numbers (in ways), giving combinations that match exactly four winning numbers. And there are choices that give the fixed Match 3 prize of . This gives a grand total of 260,624 out of the different choices that win some prize, meaning that each ticket has chance , or about one in 54, of winning something. Buy one ticket a week, and expect about one win a year. With average luck, you will spend about before you win your first prize of more than .

The Table shows what prize (round figures) you might expect. The winning chance, at any prize level, is just the corresponding Frequency, divided by *N*.