There's been a lot of discussion on the forums on the best method of opening "Bonus Level Up" donut boxes. Should you use a pattern? Should you always pick the first? The last?I decided to apply a little high school statistics to this problem, since I hadn't seen anyone do that here yet. There could be multiple ways to go about this, but I chose to test this question: Is always choosing the third donut box going to average out to two donuts?Short answer: Yes. I leveled up 3,000 times in the last few weeks, always choosing only the third box. If I got one or two donuts, I just collected them - I didn't pay to open a box after that one. The results:1 Donut: 981 (32.7%)2 Donuts: 1,007 (33.6%)3 Donuts: 1,012 (33.7%)Average donuts: 2.010So it looks like maybe choosing the third box every time gave me a slight advantage, right? Well, no, not really. Not according to statistics. Here's why.In any large random sample, you expect some variation due to chance. So if you flip a fair coin 100 times, you don't expect to always get 50 heads. A fair coin will sometimes give only 48 or 49 heads. Or more rarely, maybe even 40 heads.How can you know if it's "close enough"? You conduct a Chi-Square Goodness of Fit Test. Basically, you compare the number of each donut box you got against how many you expected, then check out how likely that variation is due to random chance.If you really want to relive your high school days, you can check out http://stattrek.com/chi-square-test/goodness-of-fit.aspx for details on how to do this.Our null hypothesis is that the third donut box has a 1/3 chance of being 1, 2, or 3 donuts. Our alternate hypothesis is that they're not 1/3 chances.In my case, the above numbers give me a Chi-Square value 0.55. Is that good or bad? Well, you can check it out on a table such as https://www.medcalc.org/manual/chi-square-table.phpTo use that table, we have two degrees of freedom, so look in the row for DF = 2. Then notice that our Chi-Square statistic falls somewhere between the 0.975 and 0.20 columns. You don't get suspicious in stat until you reach all the way into 0.05 territory, which in our case WOULD be a Chi-Square value of 5.99.Since our statistic of 0.55 is WAY less than 5.99, we accept the null hypothesis that your chances are 1 in 3 for 1, 2, or 3 donuts in the third box.Any questions? Would anyone like to suggest a different method for choosing donut boxes that we could apply statistics to?

Id ask a question but Im still not sure what you just said. Seriously nice work. You definitely put quite an effort into this. But Im sure the conspiracy theories will continue. Along with the jokers who claim to get 3 donuts 95% of the time or whatever.

6000 donuts in a week? Jealous!

Now level up another 3000 times and always choose only the first box. And then level up another 3000 times and always choose only the second box.

"stinkbugger;c-1823725" wrote:Now level up another 3000 times and always choose only the first box. And then level up another 3000 times and always choose only the second box.We'll see him in 2 weeks. Just in time for the next event.

Nicely done, of course this really only answers half the question. This shows that the donuts are evenly distributed, but not that they are randomly distributed. What needs to be shown, in other words, is that there is no recurring pattern or tendency. This is much more difficult to prove. You need to show that where you find the donuts one time has no bearing on where they will be in the future. You could, for example, test for correlations between where the donuts are in one round and where they are the next round. If, say, you find them in box 1, the first time, there should still be a 33% chance of finding them in any given box the next round. You could then check for longer correlation lengths by making sure that the third round is still random after the first (or first and second) round. You could easily get carried away with this, but I don't think anyone really has THAT much spare time! :)

Donut Boxes: Using Stat to Uncover the Truth

hackamacka1
8 years ago
"wiedmannaj;c-1824537" wrote:
"bqlehmann;c-1824336" wrote:
"HappyGamer73;c-1823795" wrote:
Nicely done, of course this really only answers half the question. This shows that the donuts are evenly distributed, but not that they are randomly distributed. What needs to be shown, in other words, is that there is no recurring pattern or tendency. This is much more difficult to prove. You need to show that where you find the donuts one time has no bearing on where they will be in the future. You could, for example, test for correlations between where the donuts are in one round and where they are the next round. If, say, you find them in box 1, the first time, there should still be a 33% chance of finding them in any given box the next round. You could then check for longer correlation lengths by making sure that the third round is still random after the first (or first and second) round.

You could easily get carried away with this, but I don't think anyone really has THAT much spare time! :)

You're totally right. I'm hoping someone suggests their personal method for getting more donuts that I could apply some statistics. So far no one's suggested "Pick Box 3, then 1, then 1, then 2 until you get 1 donut, then box 3 will definitely have 3 donuts!" or anything like that, but I'm hoping someone still will!

My personal method always gets me 3 donuts.

Keep opening boxes until you get 3 donuts?
jukan00
New Spectator
8 years ago
When the boxes pop up the one with three seems to flicker. This has worked about 66% of the time using my own simple tally. Good enough for me.
Plus I got so much money it doesn't matter at this point.
daved7637397
8 years ago
"1ahackamacka;c-1825028" wrote:
"wiedmannaj;c-1824537" wrote:
"bqlehmann;c-1824336" wrote:
"HappyGamer73;c-1823795" wrote:
Nicely done, of course this really only answers half the question. This shows that the donuts are evenly distributed, but not that they are randomly distributed. What needs to be shown, in other words, is that there is no recurring pattern or tendency. This is much more difficult to prove. You need to show that where you find the donuts one time has no bearing on where they will be in the future. You could, for example, test for correlations between where the donuts are in one round and where they are the next round. If, say, you find them in box 1, the first time, there should still be a 33% chance of finding them in any given box the next round. You could then check for longer correlation lengths by making sure that the third round is still random after the first (or first and second) round.

You could easily get carried away with this, but I don't think anyone really has THAT much spare time! :)

You're totally right. I'm hoping someone suggests their personal method for getting more donuts that I could apply some statistics. So far no one's suggested "Pick Box 3, then 1, then 1, then 2 until you get 1 donut, then box 3 will definitely have 3 donuts!" or anything like that, but I'm hoping someone still will!

My personal method always gets me 3 donuts.

Keep opening boxes until you get 3 donuts?

Thats how I do it ;) absolutely foolproof!
1sflowers330
8 years ago
"heyababy47428;c-1825317" wrote:
"daved7637397;c-1825264" wrote:
"1ahackamacka;c-1825028" wrote:
"wiedmannaj;c-1824537" wrote:
"bqlehmann;c-1824336" wrote:
"HappyGamer73;c-1823795" wrote:
Nicely done, of course this really only answers half the question. This shows that the donuts are evenly distributed, but not that they are randomly distributed. What needs to be shown, in other words, is that there is no recurring pattern or tendency. This is much more difficult to prove. You need to show that where you find the donuts one time has no bearing on where they will be in the future. You could, for example, test for correlations between where the donuts are in one round and where they are the next round. If, say, you find them in box 1, the first time, there should still be a 33% chance of finding them in any given box the next round. You could then check for longer correlation lengths by making sure that the third round is still random after the first (or first and second) round.

You could easily get carried away with this, but I don't think anyone really has THAT much spare time! :)

You're totally right. I'm hoping someone suggests their personal method for getting more donuts that I could apply some statistics. So far no one's suggested "Pick Box 3, then 1, then 1, then 2 until you get 1 donut, then box 3 will definitely have 3 donuts!" or anything like that, but I'm hoping someone still will!

My personal method always gets me 3 donuts.

Keep opening boxes until you get 3 donuts?

Thats how I do it ;) absolutely foolproof!

foolproof, but ultimately wasteful if your multiplier is over 600%

Also ultimately irreverent, when you have billions of dollars, and nothing to spend them on
johncolombo
Hero+
8 years ago
"Coldshot101;c-1826321" wrote:
"frosted1414;c-1825659" wrote:
"Coldshot101;c-1825433" wrote:
From a programmer's POV it would be wasteful to assign a specific number of donuts to each specific box. Since they can't know how many boxes a player will pick ultimately, it's far likelier they just assign you a random string of numbers: 1 2 3, 3 2 1, 2 1 3, etc. That way no matter which box you pick first you'll get the first number on your list, the second the second and so on.

I'm pretty sure this was mentioned before elsewhere in the forum and I'm sorry for not remembering where or by whom.

Do you program?

Used to. But it's been a while.
Coldshot101
8 years ago
"johncolombo;c-1826368" wrote:
"Coldshot101;c-1826321" wrote:
"frosted1414;c-1825659" wrote:
"Coldshot101;c-1825433" wrote:
From a programmer's POV it would be wasteful to assign a specific number of donuts to each specific box. Since they can't know how many boxes a player will pick ultimately, it's far likelier they just assign you a random string of numbers: 1 2 3, 3 2 1, 2 1 3, etc. That way no matter which box you pick first you'll get the first number on your list, the second the second and so on.

I'm pretty sure this was mentioned before elsewhere in the forum and I'm sorry for not remembering where or by whom.

Do you program?

Used to. But it's been a while.

Yeah, we used to punch data holes in cuneiform tablets and feed them into "computer banks" made out of rocks and fireflies. Ah, the good ol' days.
nissa762
7 years ago
"nissa762;c-1825247" wrote:
"jukan00;c-1825063" wrote:
When the boxes pop up the one with three seems to flicker. This has worked about 66% of the time using my own simple tally. Good enough for me.
Plus I got so much money it doesn't matter at this point.

Yes this is what works for me. Not sure if it's timing related or lights pattern. It happens really fast and if I pay attention too much I will miss the window. It seems like the lights flickering is actually one light is on, the next light is off, alternating around the whole square. For me it's a slight delay from the start and I have to hit the first lights flickering pattern. I would also guess I'm hitting it somewhere around the same range as you, 65-75% of the time. Again, I don't track this as it seems quite difficult to do. Thought about taking a video while I tap though. Typically if I miss the window on the first try, I'll get it again on the second, which is why I don't think this is box dependent.

This is what I mean where the * is a light on and - is a light off. And it has to be tapped right at the start of this without delay - seems like the start of this "light state" has some type of flicker you have to hit while it's still flickering for a split second.
*-*-*-*

Sorry to bump an old thread, but just now got some time to test this a little more.

So I've actually paid attention more to test this out... I have proven my theory incorrect. I believe it is now more likely that I've been hitting this by chance.

Tried a bunch of tests and while not perfect tests, it's enough to convince me that this was fluke and there isn't anything here i.e. I think it's random.
bqlehmann
7 years ago
@nissa762 : Thanks so much for your follow-up - I'd been wondering how I could "test" your trick without fully understanding. Sounds like more evidence that picking any box is as good as any other.
darrenholm736
Rising Newcomer
7 years ago
There used to be a pattern back in the day. I remember threads about it. The bonus donuts used to flow from left to right - so if your first three were in the left hand box, the next time they would be in the middle and the next time the right, and then back far left, middle, right etc etc etc.

This was waaaaaayyyyyy back in the day before level 939, KEM farms and bloodmobiles etc so getting a chance at bonus boxes was pretty rare, so you had to try and remember where the last three donuts were.

I used to put a trash can in front of my Simpsons house either to the left of it, in the middle or to the right to remind me where the donuts were in the last bonus box I had.

The devs have obviously changed where the three donuts are and made it totally random as I've had many bonus boxes since hitting 939 and there's never been a pattern to where the three donuts are.
devilhunt1449
7 years ago
It's probably around/over a year ago but I created an excel spreadsheet for opening 1000 donut boxes and can't say that it was virtually even on which box contained 3 donuts, I can't remember the exact percentage ( somewhere around 31.X, 32.X and 33.X percent) but it's near enough to say that it appears equally in each slot and a larger sample would probably be even closer.