The Neopian Lottery – to Play Or Not to Play...

Being curious about the whole thing I set out to try and establish as many facts as possible and the first few are indisputable:

- The Neopian Lottery awards a trophy. The exact color of your trophy depends on how much you win with over 1 million neopoints being a gold, 500,000 to 999,999 being silver and less than that a bronze.

- The prize fund is determined by how many people enter that day.

- There are 30 possible numbers (amazingly 1 to 30!) and from those 6 are randomly selected.

- You can buy a maximum of 20 tickets a day for 100 neopoints each.

- You win if you matched the most numbers that day. If nobody matches all 6, then we move to who matched 5. If none matched 5, then to who matched 4 and so on.

- You win an equal share of the prize fund with everyone else who matched that many numbers plus a bonus 5000 neopoints.

Now, armed with some data, we can make some observations, including those all important odds, but it's not going to answer all of our questions. In particular, I am putting in a disclaimer:

The odds are statistics and averages. For example, just because the odds are 50% of winning a coin flip, it does not mean if you toss a coin twice, you will win once (ever played Double or Nothing?). What it does mean is that if you play a lot, then on average the win percentage should even out to those odds. That said, some people are lucky, some unlucky. Don’t blame me if the odds in this article don’t work out for you; they are a guide only. Any protest should be directed to the neopets lawyerbot, not my inbox. Thanks!

On with the facts:

Nobody can win a gold trophy unless the prize fund is at least 1 million neopoints. At 100 neopoints a ticket, this means 10,000 tickets must be sold in the day. This rarely happens these days, so gold trophies are as rare as a super attack pea (ok, not that rare, but you catch my drift). The only way anyone is going to win gold is for more people to play – hopefully at the end of this you may well help to that end!

The more people buy tickets, the bigger the prize fund (yay!), but the less chance of you being the only winner (boo!). Also, the more people that play, the more chance someone will match 5 or maybe 6 numbers, meaning your chances of winning having matched only 4 have decreased.

OK, basic odds here. If you buy one ticket, your odds of matching numbers is as follows:

Matching 6 numbers – 593,775:1 or 0.0002%

Matching 5 numbers – 4,123:1 or 0.024%

Matching 4 numbers – 143:1 or 0.7%

Not too encouraging, I think you would agree. However, we can buy 20 tickets, giving us the opportunity to improve those odds somewhat, but it's important what numbers you pick. As an extreme example, if we buy 20 tickets with exactly the same numbers, then we don’t improve our chance of winning (but if those numbers came up, we would win 20 times!). We need a good spread to maximize the probability of getting winning numbers.

I work on the basis that I don’t want to buy any tickets where if I get 4 numbers on one, I would get 4 or more on any of the others. It’s very rare you win matching less than 4 numbers so I want 20 tickets which give me the maximum chance of matching 4 numbers. Makes sense? Maybe not, so here is an example:

The following would be bad:

Ticket 1 5 8 10 15 25 29

Ticket 2 6 8 10 15 26 29

If 8, 10, 15 and 29 are picked in the winning numbers, we would match 4 numbers with both tickets. However, if on ticket 2 we had picked 30 instead of 29:

The following is good:

Ticket 1 5 8 10 15 25 29

Ticket 2 6 8 10 15 26 30

If 8, 10, 15 and 29 come up, then we match 4 numbers with ticket 1 but if 8, 10, 15, and 30 come up, we match 4 numbers with ticket 2. We are maximizing our chances of hitting a winning combination. On ticket 3, pick numbers that make sure if you match 4 numbers on tickets 1 and 2, you don’t match 4 on ticket 3 and so on.

Now, this gets complicated by the time you get to the last tickets and it will take time to get 20 tickets which meet this criteria. No way would I want to sit down and try and do that every day, so work out your set of 20 tickets and then use the same numbers every day to save time. As it’s all random, there is no problem with using the same numbers; the odds don’t change.

So we have 20 tickets with different number ranges maximizing our chance of matching the winning numbers; what are the odds now? Well, the daily odds look a lot better:

Matching 6 numbers – 29,689:1 or 0.003%

Matching 5 numbers – 206:1 or 0.49%

Matching 4 numbers – 7:1 or 13.9%

Odds of matching 6 numbers still stink, but if you play every week, then on average you should match 4 numbers once. The trouble is that the day you match 4 numbers might be a day when someone else matches 5 and you don’t win (which is extremely annoying but unfortunately part of the rich fabric of Neopian life).

Surely you can calculate the odds of that happening, you cry! Well, no. It depends on how many people buy tickets and what numbers they pick. I could probably go through the academic exercise of saying, well, if everyone buys tickets with an even range and the number of people buying tickets was X, then the odds are dah de dah de dah. But what’s the point? People don’t always buy 20 tickets and many don’t spread their bets and the number of people buying tickets varies daily.

So I’m going to take a sneaky shortcut based on the last 20 results as at the day of writing this. In the last 20 days, 10 times people won with 4 numbers and 10 times with 5 numbers so 50% of the time matching 4 numbers wins you a prize. We said our odds of matching 4 numbers are 7:1 when we buy 20 tickets so on average (please go back and read disclaimer – that’s on average, folks), we should match 4 numbers once a week and every other week that should win us a share of the jackpot, giving odds of 14:1 that we will win the jackpot with 4 numbers. The odds of matching 5 numbers are 206:1 and as we are saying 5 numbers will always win you the jackpot; the odds are unchanged. I’m ignoring 6 numbers – it’s just so unlikely.

Now if you are trophy hunting, I think that’s pretty good odds. Even if you are unlucky, a trophy should be yours within a month if you play daily. However, does it make financial sense?

This all depends how many other people picked the winning numbers and how many people played. As I write this, yesterday there were 83 winners sharing a jackpot of 740,800 neopoints having matched 4 numbers. That’s 8,925 each as a share of the pot. Considering it costs 100 NP per ticket, which is 2,000 NP per day, you are losing money at odds of 14:1 (14x2000=28,000 neopoints to play). The biggest win with 4 tickets was 56,300 neopoints each, so now it looks more attractive. Broadly it looks like you will roughly break even on the 4 ticket wins based on the above if you play over a long period of time.

5 numbers won in the range of 69,000 neopoints (but that looks exceptionally low) to over 700,000 neopoints (where there was only one winner). At odds of 206:1 you are going to have to invest 412,000 neopoints to win once with 5 numbers on average (lawyerbot is hovering....)

Does it make sense financially? No, it’s gambling; of course it doesn’t make financial sense. Don’t gamble neopoints you are unprepared to lose. Chances of winning big are slim. However, the chances of winning a trophy are pretty good; it was enough to get me to play. The other thing is the more people play, the more chance that elusive gold lottery trophy will again begin to be awarded and to those lucky few who do win big, it will mean more neopoints.

Good luck if you decide to play and choose that range of numbers carefully. Don’t share your numbers with friends; if one of you wins, surely you want to win big, not share it between you and guarantee a trophy downgrade? Have fun!