## Optimizing the Pizza Selection When Ordering for Groups

Apparently, people like to eat.

Moderators: SecondTalon, Moderators General, Prelates

MFHodge
Posts: 4246
Joined: Thu Apr 19, 2007 6:27 pm UTC
Location: :noitacoL Raleigh, NC
Contact:

### Optimizing the Pizza Selection When Ordering for Groups

The department ordered pizza for lunch today ( ). The order was two pepperoni and two supreme ( ). I think was the first on to walk up and I started looking around for the cheese-only pizza. I was stuck with pepperoni. The next guy looks around for anything vegetarian. He ends up with only salad.

This seems to happen all the damn time. Cheese is almost always the first one gone. The leftovers are almost always the one with tons of stuff on it. I suspect that anyone would eat a slice that has a subset of the toppings they like. For example, if your first choice is mushrooms and olives, you would probably be almost as happy with a pizza with only mushrooms or only olives. This leads to the conclusion that in the general case, pizzas with fewer toppings will have the greatest utility. Toppings should only be selected when there is a high degree of probability that sufficient people will prefer that combination as their first choice to account for the whole pizza.

I think with the collective intellegence of the xkcd fora, we can come up with an optimum strategy for ordering pizza for a group.

Here is my initial take, based on casual observation over my life:

• 1/3 Plain Cheese
• 1/3 Pepperoni
• 1/6 Other single topping (Veggie before meat)
• 1/6 Other multi-topping (Meat before veggie)

These are my suggested cases, based on total count.

3 -> 1 Cheese, 1 Pepperoni, 1 Single Veggie
4 -> 1 Cheese, 1 Pepperoni, 1 Supreme, 1 Single Veggie
5 -> 2 Cheese, 1 Pepperoni, 1 Supreme, 1 Single Veggie
6 -> 2 Cheese, 2 Pepperoni, 1 Supreme, 1 Single Veggie
7 -> 2 Cheese, 2 Pepperoni, 1 Supreme, 1 Single Veggie, 1 Sausage
8 -> 2 Cheese, 2 Pepperoni, 1 Supreme, 1 Single Veggie, 1 Sausage, 1 Veggie Supreme
9 -> 3 Cheese, 3 Pepperoni, 2 Supreme, 1 Single Veggie, 1 Sausage, 1 Veggie Supreme
etc.

Thoughts? Improvements? I'm working on an Excel function for it . . .

Bakemaster
pretty nice future dick
Posts: 8933
Joined: Fri Jul 06, 2007 2:33 pm UTC
Location: One of those hot places

### Re: Optimizing the Pizza Selection When Ordering for Groups

I would weight cheese more heavily, myself, for a better margin of error. There aren't a huge number of people who like pizza only with toppings and won't eat plain cheese. Plus, the more slices one person is going to eat, the more likely they are not to care if one of those slices (the last one, I'd assume) is "leftover" or "other". Beacuse they are hungry and they want pizza.

c0 = 2.13085531 × 1014 smoots per fortnight
"Apparently you can't summon an alternate timeline clone of your inner demon, guys! Remember that." —Noc

TigerX
its the squiggles dude!
Posts: 564
Joined: Wed May 30, 2007 5:16 am UTC
Location: Clemson, SC
Contact:

### Re: Optimizing the Pizza Selection When Ordering for Groups

I think you have to account for the specialty pizza as well (i.e.: Pineapple and Ham).

MFHodge
Posts: 4246
Joined: Thu Apr 19, 2007 6:27 pm UTC
Location: :noitacoL Raleigh, NC
Contact:

### Re: Optimizing the Pizza Selection When Ordering for Groups

TigerX wrote:I think you have to account for the specialty pizza as well (i.e.: Pineapple and Ham).

I thought about that and came to the conclusion that they had no place in the Group Order System. That's why they are "specialty". If you have a huge number, then I guess they could take the place of a meat-based multi-topping.

22/7
I'm pretty sure I have "The Slavery In My Asshole" on DVD.
Posts: 6475
Joined: Fri Jul 06, 2007 3:30 pm UTC
Location: 127.0.0.1

### Re: Optimizing the Pizza Selection When Ordering for Groups

Yeah, as much as I love me some Hawaiian Pizza, they have no place in the "general case." I think your original pattern looks good, but with introduction of the vegetarian supreme, sausage, etc. you are creating a pain in the ass for the Excel spread sheet (unless there's a "round down" function in Excel I'm not aware of).

Of course, I'm one of the people who you'd love to have at the party, because unless taco or Hawaiian pizzas are present, I pretty much eat whatever there is the most of after the first round. However, if taco or Hawaiian are present, I generally eat as much of that stuff as quickly as possible, occasionally resulting in an ingested hand or shoe. Luckily, none of them have been mine to this point.
Totally not a hypothetical...

Steroid wrote:
bigglesworth wrote:If your economic reality is a choice, then why are you not as rich as Bill Gates?
Don't want to be.
I want to be!

MFHodge
Posts: 4246
Joined: Thu Apr 19, 2007 6:27 pm UTC
Location: :noitacoL Raleigh, NC
Contact:

### Re: Optimizing the Pizza Selection When Ordering for Groups

Here is my revised theory with some good math behind it.

For "n" Pizzas:

Cheese = CEILING(n/3)
Pepperoni = ROUND((n-Cheese)/2)
SingleTop = CEILING(n-(Cheese+Pepperoni)) [Odd Singles are Veg, Even Singles are Meat]
MultiTop = FLOOR(n-(Cheese+Pepperoni)) [Odd Multis include Meat, Even Multis are Veg Only]

Gives:

Code: Select all

` n   C   P   S   M----------------- 3   1   1   1   0 4   2   1   1   0 5   2   2   1   0 6   2   2   1   1 7   3   2   1   1 8   3   3   1   1 9   3   3   2   110  4   3   2   111  4   4   2   112  4   4   2   213  5   4   2   214  5   5   2   215  5   5   3   2`

Robin S
Posts: 3579
Joined: Wed Jun 27, 2007 7:02 pm UTC
Location: London, UK
Contact:

### Re: Optimizing the Pizza Selection When Ordering for Groups

Are you looking to maximize expected utility, or minimum utility? If the latter, just go for all cheese, every time (unless you happen to know exactly what toppings everyone likes).
This is a placeholder until I think of something more creative to put here.

22/7
I'm pretty sure I have "The Slavery In My Asshole" on DVD.
Posts: 6475
Joined: Fri Jul 06, 2007 3:30 pm UTC
Location: 127.0.0.1

### Re: Optimizing the Pizza Selection When Ordering for Groups

Dammit, now I want pizza. Looks good. I'm not familiar with the "ceiling, round, and floor" functions though.
Totally not a hypothetical...

Steroid wrote:
bigglesworth wrote:If your economic reality is a choice, then why are you not as rich as Bill Gates?
Don't want to be.
I want to be!

MFHodge
Posts: 4246
Joined: Thu Apr 19, 2007 6:27 pm UTC
Location: :noitacoL Raleigh, NC
Contact:

### Re: Optimizing the Pizza Selection When Ordering for Groups

Robin S wrote:Are you looking to maximize expected utility, or minimum utility? If the latter, just go for all cheese, every time (unless you happen to know exactly what toppings everyone likes).

Looking to maximize general human happiness. With all cheese, everyone gets fed, but if you have more than a handful of people, you have a fairly good expectation that there is enough interest in a pepperoni pizza that it will be utilized and therefore give a higher return than a plain cheese.

CEILING = Round Up always
FLOOR = Round Down always
ROUND = Round Like Your Momma Taught You

Sprocket
Seymour
Posts: 5951
Joined: Mon Mar 26, 2007 6:04 pm UTC
Location: impaled on Beck's boney hips.
Contact:

### Re: Optimizing the Pizza Selection When Ordering for Groups

Bakemaster wrote:I would weight cheese more heavily, myself, for a better margin of error. There aren't a huge number of people who like pizza only with toppings and won't eat plain cheese. Plus, the more slices one person is going to eat, the more likely they are not to care if one of those slices (the last one, I'd assume) is "leftover" or "other". Beacuse they are hungry and they want pizza.

I don't like pizza without toppings. ::shrug: I'm unusual. As a kid I didn't like peperoni because it was too spicy, later I really liked peperoni, and today I only generally like veggie of some kind, but plain cheese pizza sorta makes me go "blech"
"She’s a free spirit, a wind-rider, she’s at one with nature, and walks with the kodama eidolons”

Zohar wrote: Down with the hipster binary! It's a SPECTRUM!

Robin S
Posts: 3579
Joined: Wed Jun 27, 2007 7:02 pm UTC
Location: London, UK
Contact:

### Re: Optimizing the Pizza Selection When Ordering for Groups

Personally, when it comes to pizza I will eat more or less any topping I am likely to encounter. However, I still have preferences and so if there is competition for slices I will still follow the basic rule that Bakemaster outlined.
This is a placeholder until I think of something more creative to put here.

Bakemaster
pretty nice future dick
Posts: 8933
Joined: Fri Jul 06, 2007 2:33 pm UTC
Location: One of those hot places

### Re: Optimizing the Pizza Selection When Ordering for Groups

That may be in part due to a surfeit of really good pizza places in this area. There's pizza I like, and there are specific specialty pizzas I adore, like the Urban Cowboy—bacon, red onion, grilled chicken, sliced tomato with a blue cheese-based white sauce—but I have yet to find a really stunning traditional cheese pizza. The Sicilian pizza at Pinnochio's is pretty good, and Upper Crust makes a good effort. I haven't explored the North End, which I probably should if I ever want to be authoritative on Boston area pizza.

c0 = 2.13085531 × 1014 smoots per fortnight
"Apparently you can't summon an alternate timeline clone of your inner demon, guys! Remember that." —Noc

22/7
I'm pretty sure I have "The Slavery In My Asshole" on DVD.
Posts: 6475
Joined: Fri Jul 06, 2007 3:30 pm UTC
Location: 127.0.0.1

### Re: Optimizing the Pizza Selection When Ordering for Groups

Who makes this urban cowboy? It sounds delicious.
Totally not a hypothetical...

Steroid wrote:
bigglesworth wrote:If your economic reality is a choice, then why are you not as rich as Bill Gates?
Don't want to be.
I want to be!

PictureSarah
Secretary of Penile Nomenclature
Posts: 4576
Joined: Fri Jul 06, 2007 8:37 pm UTC
Location: Sacramento, CA
Contact:

### Re: Optimizing the Pizza Selection When Ordering for Groups

I think the pizza of last week was pretty damn good. A tad puffy, but tasty. Not applicable to discussion of mass pizza ordering I suppose, though.
"A ship is safe in harbor, but that's not what ships are for."

Azrael
CATS. CATS ARE NICE.
Posts: 6491
Joined: Thu Apr 26, 2007 1:16 am UTC
Location: Boston

### Re: Optimizing the Pizza Selection When Ordering for Groups

Hodge, I like the numbers laid out above, but suggest a couple of non mathematical bounds:

I wish to suggest that you remove Supreme entirely - I feel that people who want supreme will be satisfied with other options with a 90% happiness ratio.

Besides a Veggie Supreme, no pizza should have more than 3 toppings total. All multi-category pizzas (category = meat, veggie) should have three toppings in a 2:1 ratio of one type category to the other, probably favoring a 2 veggie to 1 meat.

On a side note, we've had this exact discussion before 'round the lunch table. One time we had a 200 person pizza lunch. One of the chosen pizzas was ... garlic. And I think they got a half dozen of them (out of maybe 70 total). Re. Tard. Ed.

Bakemaster
pretty nice future dick
Posts: 8933
Joined: Fri Jul 06, 2007 2:33 pm UTC
Location: One of those hot places

### Re: Optimizing the Pizza Selection When Ordering for Groups

22/7 wrote:Who makes this urban cowboy? It sounds delicious.

The Urban Gourmet restaurant in Somerville, where I used to work. Unfortunately the owners sold the place along with the menu, and then it burned down and the guy who bought it is still rebuilding. They reopened a new place in another part of the city and while they can't legally call it the "urban cowboy" anymore, they still are probably the only ones who know how to make it right so they call it "chicken club" which is a much lesser name. I wouldn't want to eat any pizza that's named after a sandwich involving mayo.

Back on the topic of ordering pizzas, Hodge, your 2.0 is much improved. I think 2 cheese for 8 total pizzas was a dangerous proposition. What about the danger of getting only one of an interesting and uncommon specialty pizza in a large group where more than 8 people want to try a slice? Should we take that into consideration for cases of a certain size?

c0 = 2.13085531 × 1014 smoots per fortnight
"Apparently you can't summon an alternate timeline clone of your inner demon, guys! Remember that." —Noc

MFHodge
Posts: 4246
Joined: Thu Apr 19, 2007 6:27 pm UTC
Location: :noitacoL Raleigh, NC
Contact:

### Re: Optimizing the Pizza Selection When Ordering for Groups

Bakemaster wrote:Back on the topic of ordering pizzas, Hodge, your 2.0 is much improved. I think 2 cheese for 8 total pizzas was a dangerous proposition. What about the danger of getting only one of an interesting and uncommon specialty pizza in a large group where more than 8 people want to try a slice? Should we take that into consideration for cases of a certain size?

Agreed about 2 Cheese / 8 Pizzas . . . that was a bad one.

Local specialties might just have to be a case-by-case. If it is true that most people would want at least on slice of it, then it should probably be handled before any algorithm. I generally think you get one pizza for every 3-4 people (depending on your crowd and party type). If you have twenty people, you probably get two or three specials and then just apply the four or five pizza system for the rest.

Also: I'm now thinking that pepperoni may be over-emphasized here. It is the most popular topping, but should it be 1/3 of overall?

bbctol
Super Deluxe Forum Title of DESTINYâ„¢
Posts: 3137
Joined: Tue Mar 06, 2007 10:27 pm UTC
Location: The Twilight Zone
Contact:

### Re: Optimizing the Pizza Selection When Ordering for Groups

Just eat a damn sandwich.

MFHodge
Posts: 4246
Joined: Thu Apr 19, 2007 6:27 pm UTC
Location: :noitacoL Raleigh, NC
Contact:

### Re: Optimizing the Pizza Selection When Ordering for Groups

bbctol wrote:Just eat a damn sandwich.

Don't even get me started on ordering sanwiches!

Tractor
Posts: 2467
Joined: Mon Jan 08, 2007 6:17 pm UTC
Location: no

### Re: Optimizing the Pizza Selection When Ordering for Groups

Bakemaster wrote:Back on the topic of ordering pizzas, Hodge, your 2.0 is much improved. I think 2 cheese for 8 total pizzas was a dangerous proposition. What about the danger of getting only one of an interesting and uncommon specialty pizza in a large group where more than 8 people want to try a slice? Should we take that into consideration for cases of a certain size?

This leads to other questions on numbers:
What size pizza are we talking about here? 8-slice? 12-slice? Party square-cut style? Other?

I think for groups less than around 10, 8-slice would be optimal. I'm not sure where the cutoff from 12-slice to party style occurs though, may be on a per-case basis, not size-dependant.

How many people merit multiple pizzas?

I think optimal use of the chart doesn't start until you have at least 5 people. 4 or less and you can stick to 2 pizzas, having half-topped pizzas where necessary. From my experience, it tends to be that a person will eat about 4 pieces of pizza. This should probably be the general idea when deciding how many pizzas to order, rounding up of course.
9 x 6 = 42

Note: Randall kicks ass.

Azrael
CATS. CATS ARE NICE.
Posts: 6491
Joined: Thu Apr 26, 2007 1:16 am UTC
Location: Boston

### Re: Optimizing the Pizza Selection When Ordering for Groups

For the sake of this thread, all pizzas are standard national size -- 16" round with 8 slices

And I've found that 2.5 people per pizza works fairly well.

hendusoone
Mr. Dreambeard butts butts butts butts butts butts butts butts butts butts butts butts butts butts butts butts butts butts butts butts butts butts butts butts butts butts butts butts butts butts butts butts butts butts butts butts butts. Butts.
Posts: 1570
Joined: Fri Jun 29, 2007 5:30 pm UTC
Location: Spaceship
Contact:

### Re: Optimizing the Pizza Selection When Ordering for Groups

Regarding the Pepperoni issue:
Break it into its own group, single-topping meat. Every Odd number pizza in this group is Pepperoni, every Even number is some other meat of choice - ham or sausage, never anchovies, possibly chicken.

Number of pizzas can depend upon the time of day, with culture taken into account. In areas where the large meal is dinner, do 1 pizza for every 3 people at lunch and 1 pizza for every 2 people at dinner. The other way around when the large meal is lunch.
Jack Saladin wrote:Humanities salvation relies on us sending the Earth into a giant black hole.

22/7
I'm pretty sure I have "The Slavery In My Asshole" on DVD.
Posts: 6475
Joined: Fri Jul 06, 2007 3:30 pm UTC
Location: 127.0.0.1

### Re: Optimizing the Pizza Selection When Ordering for Groups

Thanks Bake. If ever I'm in Boston(ish) I'll look you up so you can point me in the right direction.

VTHodge wrote:Also: I'm now thinking that pepperoni may be over-emphasized here. It is the most popular topping, but should it be 1/3 of overall?

Agreed that the pepperoni is over-emphasized, but that's probably just me (I'll eat it, but it's not my favorite, by any stretch). I would tend to slide the second pizza of a new set down to the single topping or multi-topping first, but again, I don't particularly care for pepperoni enough to eat 4 or 5 slices of it. That said, what about *not* separating pepperoni from the other single topping pizzas, and deciding the content of those single topping pizzas based on a group consensus, and when one is not available, maybe make it 1/3 or 1/2 (of the single toppings) pepperoni and then separate the rest among things like sausage, onion, pineapple, goat anus, etc.

Edit: Ninja'd

hendusoone wrote:Regarding the Pepperoni issue:
Break it into its own group, single-topping meat. Every Odd number pizza in this group is Pepperoni, every Even number is some other meat of choice - ham or sausage, never anchovies, possibly chicken.

This doesn't really change the ratio of pepperoni to non-pepperoni single topping pizzas from what it is now, as it's currently at (approximately) 1/2 of all single topping pizzas, if not a little more.

Edit 2.0: Just kidding, I was going off the first one. This would indeed decrease the number of pepperoni pizzas from Hodge v2.0. And I'm ok with it.

Edit 2.1: I just got back from lunch. I had pizza. This thread is to blame.
Totally not a hypothetical...

Steroid wrote:
bigglesworth wrote:If your economic reality is a choice, then why are you not as rich as Bill Gates?
Don't want to be.
I want to be!

Narsil
Posts: 2995
Joined: Thu Oct 26, 2006 6:59 pm UTC
Location: Columbus.

### Re: Optimizing the Pizza Selection When Ordering for Groups

I order all pepperoni.
If someone protests, I sock them and say "eat the god damn pepperoni".

Q.E.D.
Spoiler:
EsotericWombat wrote:MORE JUNK THAN YOUR BODY HAS ROOM FOR

Mother Superior wrote:What's he got that I dont?
*sees Narsil's sig*
Oh... that.

Ptera
Posts: 78
Joined: Fri Aug 17, 2007 10:47 pm UTC
Location: In teh lab, growin cellz

### Re: Optimizing the Pizza Selection When Ordering for Groups

I'm allergic to cheese, but I can get by pretty well by taking apart my pizza, and then reassembling it cheese-free. For my case, it's nice to have something with toppings, otherwise I'm just eating saucy bread. (Sauc-ay!)

wing
the /b/slayer
Posts: 1876
Joined: Tue May 29, 2007 5:56 am UTC

### Re: Optimizing the Pizza Selection When Ordering for Groups

Based upon EXTREME amounts of pizza ordering for nerds on a college campus, I have the following rules:

For groups of 20 or less:
2 people per large pizza.
50% cheese. 50% pepperoni. Add one Meatpocalypse (Every meat on the menu except the ones that swim) for every 10 people.

For groups of 21-50:
3 people per large pizza
33% cheese 66% pepperoni. Meatpocalypse rule is strictly optional.

For larger events:
5 people per large pizza
50% cheese. 50% pepperoni. NO meatpocalypse

For paid entrance events:
Take an informal poll at the least - at best, take ORDERS. I've ordered 90 individual-person medium pizzas before.

For recurring events where the same people are expected (i.e. meetings, etc.):
On the first occurance, follow the appropriate rule above, and somewhere on the agenda MUST be "Arrive at pizza consensus" where the group selects the toppings and quantity of pizza required for the future.
I AM A SEXY, SHOELESS GOD OF WAR!
Akula wrote:Our team has turned into this hate-fueled juggernaut of profit. It's goddamn wonderful.

Zohar
COMMANDER PORN
Posts: 8573
Joined: Fri Apr 27, 2007 8:45 pm UTC
Location: Denver

### Re: Optimizing the Pizza Selection When Ordering for Groups

Just a note, as a vegetarian, I wouldn't eat a cheese-only slice from a pizza with meaty areas. Since it usually only gets complicated if you have a group larger than three people and then you order multiple pizzas, why not completely seperate vegetable and meat pizzas?

Also, I was in Spain and I had pineapple and banana toppings on a pizza. It was yummy and weird (my favorite is pineapple + onion).
Mighty Jalapeno: "See, Zohar agrees, and he's nice to people."
SecondTalon: "Still better looking than Jesus."

Not how I say my name

Toeofdoom
The (Male) Skeleton Guitarist
Posts: 3446
Joined: Wed Jan 10, 2007 10:06 am UTC
Location: Melbourne, Australia
Contact:

### Re: Optimizing the Pizza Selection When Ordering for Groups

I'd usually go with ordering half a pizza for each person, asking their preferences then adding a couple of margheritas on the end (thats what "cheese" pizzas are called around here. also this reminds me I need to make another one of those macaroni cheese pizzas, in a couple of weekends when my family is away maybe.) I mean, you cant really get too much pizza anyway.
Hawknc wrote:Gotta love our political choices here - you can pick the unionised socially conservative party, or the free-market even more socially conservative party. Oh who to vote for…I don't know, I think I'll just flip a coin and hope it explodes and kills me.

Website

idont_know12
Posts: 206
Joined: Sat Jul 07, 2007 9:11 am UTC
Location: The East Galaxy

### Re: Optimizing the Pizza Selection When Ordering for Groups

Bakemaster wrote:I have yet to find a really stunning traditional cheese pizza.

That's probably on an individual basis though.

22/7
I'm pretty sure I have "The Slavery In My Asshole" on DVD.
Posts: 6475
Joined: Fri Jul 06, 2007 3:30 pm UTC
Location: 127.0.0.1

### Re: Optimizing the Pizza Selection When Ordering for Groups

So far I've found almost every pizza tastes better (to me) with barbecue sauce rather than the traditional tomato sauce. Of course, this is highly dependent upon the type of barbecue sauce being used.
Totally not a hypothetical...

Steroid wrote:
bigglesworth wrote:If your economic reality is a choice, then why are you not as rich as Bill Gates?
Don't want to be.
I want to be!

Bakemaster
pretty nice future dick
Posts: 8933
Joined: Fri Jul 06, 2007 2:33 pm UTC
Location: One of those hot places

### Re: Optimizing the Pizza Selection When Ordering for Groups

@idont_know12: I was talking specifically about Boston area restaurants. I've had a really incredible homemade pizza and one example of great traditional neapolitan restaurant pizza somewhere I was traveling years ago... I was visiting family, so that narrows it down to Chicago, Richmond, or the general L.A. area. Not much help.

c0 = 2.13085531 × 1014 smoots per fortnight
"Apparently you can't summon an alternate timeline clone of your inner demon, guys! Remember that." —Noc