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$100M Oz Lotto: What were your chances?… A Statistical Analysis


Earlier this month we witnessed the largest ever lotto draw in Australia, with a Jackpot of $100 Million and a total prize pool of over $178 Million ($178,529,037.79 to be exact)!

I’ve never bought a lotto ticket myself… and I knew any chance of winning would be extremely slim.  But with the lure of the $100 Million I thought, why not try this time just for fun.

Well the bad news (for me) is that I didn’t win the big prize.  Four lucky people DID share the jackpot, winning themselves a cool $29 Million each!

Now it wasn’t all bad news for me, as my Quickpick of 12 games had one line of numbers with some matches… this qualified me for the Division 7 prize!  I couldn’t believe my luck at learning this and when I went to the newsagent to pick up my winnings I found out I’d won… $13.70.  Not bad in my first lotto game.  Perhaps the cost of the ticket of $14.20 made this less impressive.

Upon reflection, the statistician in me wanted to know what my actual chances of winning were.  So I did the calculations and came up with the following results.

The below table shows a summary of the winners in each division of the draw:

Division (numbers) Total Prize Pool Number of Winners Prize money per person
Division1(7 main numbers) $111,972,151.04



Division 2(6 main, 1 supplementary) $1,885,113.60



Division 3(6 main numbers) $3,881,137.00



Division 4(5 main, 1 supplementary) $1,995,918.75



Division 5(5 main numbers) $2,327,714.40



Division 6(4 main numbers) $26,627,841.30



Division 7(3 main, 1 supplementary) $29,839,161.70



I contacted Tattlotto who told me they estimate around 8.5 Million tickets sold, with an average of 12 ‘games’ (one game is a line of numbers) per ticket.  This means that a total of around 102 Million games were purchased in total.  The simple conclusion to draw from this would be that to win the big prize there was a chance of 4 in 102 Million, or 0.000004%, or odds of 25,500,000:1.  However, this is actually the chance that each of the 4 winners had, now that we know that they were winners.  What we can say from these initial numbers is that out of the 102 Million games sold 3,504,877 games won money, which is 3.4362% of the games sold.  Put another way, this is odds of 29:1.

In reality, the chance of winning any of the prizes is independent of how many people buy tickets (of course how much is won is determined by how many people buy tickets).  The REAL ODDS are based on the number of balls and the probability of each ball being drawn matching your number.

When the probability is calculated, the true odds can be determined as shown in the table below.

Division What you need in one game to win Odds based
on 1 Game
Odds based
on 12 Games
Division 1 7 winning numbers



Division 2 6 winning numbers+ 1 or 2 supplementary numbers



Division 3 6 winning numbers



Division 4 5 winning numbers+ 1 or 2 supplementary numbers



Division 5 5 winning numbers



Division 6 4 winning numbers



Division 7 3 winning numbers+ 1 or 2 supplementary numbers



And once a draw has been drawn and the winnings determined, with the knowledge of the above probabilities we can calculate the ‘expected value’ of how much each game was likely to win.  This of course may not match what was ACTUALLY WON!

Therefore, the EXPECTED VALUE of the winnings of 1 game in the $100 Million draw was $0.9621.

Now the average ticket purchaser with 12 games had an expected value of winning $11.5452.  So if you won more than that you’ve done well!

Interestingly, most people that win one or two million dollars in Tattslotto end up blowing the whole lot in a few years and end up in the same (or worse) position.  So, if you ever do win, good planning is the key to making it count.

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