Tuesday, April 29, 2014

The Birthday Problem

Maybe it was all the resistant starch beforehand, or a ton of time in the ice tub, but I just had the craziest dream the other night.

I dreamed I was with my friends, and the "Birthday Problem" came up.  That is the one that many quant-y folks have run into in a statistics class.  It goes like this: 

There are 23 people in a classroom.  What is the probability that at least one of them has the same birthday?

The probability is astoundingly high by most people, because the natural inclination is to think that this is very very rare.  My students mouths always dropped open when the answer was revealed, and it really got them thinking that maybe statistics wasn't so useless after all.

I had one student who was a real go-getter, and in her spare time, she liked to rent roach coaches, create interesting menus and hang around the local sports stadiums for a quick buck.  Unfortunately, many other folks in the restaurant biz hadn't run into the problem.

Anyway, where was I?

Oh yeah, the dream.

I decide to explain the birthday problem in great detail to my quant-y friends.  We arrange for a short presentation at a hotel we're staying at.  Other hotel guests get wind of the presentation, and by the time I am ready to start, the room is full of people with all sorts of interests and levels of understanding.  It gets quite comical.  I decide to start with some basics, and somehow I get into a discussion of the history of industrial statistics.  My new students are enthusiastic, but needy and time-consuming, so I remind myself and them what the talk is really about.  As I go back to the technical discussion of the birthday problem, most of the lecture-crashers leave, and I am left with my original presentation and my original friends.

As most dreams go, I never get to the presentation.  I wake up to my house-flipping neighbor's construction crew jack-hammering their front porch, and I sit there for awhile with my day-brain, wondering how I could actually describe the birthday problem more easily, and for that matter, why did this dream even come up?

Earlier I was reading about the percentage of celiacs, which is now around 1 out of 100 people if you include the folks who don't know they have it yet.  I had also gotten off the phone with a family member.  We were planning another mandatory multi-day get-together.  I was told I was "on my own" with the food situation, but also that we weren't going to make it a big-deal food-prep week like many of our gatherings.  Basically, it was, "You can't eat and you can't cook."  I was pretty mad about this.  (Said relative has now thought, back-tracked, and decided better accommodation was a good idea.)  But it got me thinking about how places like Starbucks and Panda Express pretty much say, "Hey Celiacs!  You're on your own here.  If you have some sort of problem, then don't eat ANY of our food."

And I thought, they probably think that there isn't much celiac to accommodate, right?  Isn't it like they are going to lose around .1% of their customer base by flipping celiacs the bird?

Like the birthday problem, the actual consequences of their decision are much larger.  The way to solve the birthday problem is not to look at how many people have the same birthday, it is to look at how many ways the students in the classroom CANNOT have the same birthday divided by the total possible ways that they can all have birthdays.  That is pretty easy to do, and then you just subtract that from one to get the answer.

So here's the restaurant problem.  It is not that they will lose even 1 percent of business.  People usually go to restaurants with other people.  So in order to see impact on restaurants, you have to calculate the probability that NONE of the dining party has celiac and then subtract from 1.

I have done the calcs, and put together a little table, showing the reduction in business if a typical table of 4 or 6 decides not to eat there if the restaurant refuses to provide workable gluten-free options.   The various percentages of celiac or wheat intolerances are also shown based on estimates by Drs. Fasano and Davis.  Of course, this calculations assumes independence, and we all know by now that this is not really the case with dining families, since it is an inherited disease.  So if one person has celiac, the others are much more likely to have it as well.  But, the table does work for friends.

Percentage C or WI                   Table of 4                  Table of 6
1%                                                 4%                                6%
7% (Fasano est.)                            25%                             35%
37%  (Davis est.)                            84%                             94%

You can see that the lost business starts to get pretty high.  Currently, it is pretty easy to ignore the celiacs, either by not offering appropriate menu choices, or improper preparation.  But it is getting pretty hard to ignore the gluten-intolerant.  This is probably what is going on with Lean Cuisine, bread stores, and even places like Red Lobster.                     


  1. I think the 37% number accurately describes the number of people who should abstain from gluten intake due to sensitivity issues. To avoid major chronic disease such as celiac or diabetes. With gluten it's definitely easy to eat yourself sick. But good luck selling that to most Americans. When people see how much weight I've lost they are very curious about what diet I'm on. When I tell them they can't have bread or pasta, and no sugar, they say that they would rather die an early death. And there not interested any more. At all. They don't even want me to keep talking. Even my own family has told me it's to hard to avoid those foods. It's going to take ten years before the government even acknowledges there may be a problem. Probably another ten before they stop putting it in everything just because it's a cheap filler.

  2. Rick, I was that way too. I am thinking that if I could change, anyone can. Thanks for visiting!

    1. :-) the only trouble with that hypothesis is, you're a lot stronger and smarter than the average!

    2. My relative is 10 times smarter AND she could actually read Hyperlipid if she would. Sometimes people "know things that ain't so" too well. I think it really depends on the specialty. If you are coming at Paleo coming off researching aspects of a meat-laden SAD diet, it may be more difficult. As for me, I was just trying to find out what was up with me, and coming from diabetes research, it made it a bit easier to read and understand how all the low-carb plans can help diabetics.

  3. Since my diagnosis a couple of weeks ago, I have inspired one person to give up wheat entirely, and another person to investigate celiac in her family. Unfortunately, I have not inspired anyone in my family to get tested, but my mother is going to speak to her doc about it. She is getting RA symptoms again after a 30+ year remission.

  4. RA is no joke, however my former mother-in-low while suffering terribly from it, can't push herself to try the diet changes I recommended - which she thinks would be too disruptive for her life. She has no doubt it could be helpful because she keeps commenting regularly on how she glad for me that I found a diet regiment eliminating my eczema.
    Imagine the sound of evil laugh, please - Whoa-Ha-Ha ! - I am the family culinary authority, and my position allows me to abuse my decisions making power .

    When talking about the cost of business for restaurants, we have to remember that people there are payed a minimal wade, and the business model in a food industry is based on using barely trained but eager to work people who are often dead tired because in order to meet ends meet they work two jobs, unless they are teens who live with parents and need gas and entertainment money. I guess the owners of fast-food places can't risk possible litigations and declare their places to be safe for celiacs with severe reactions while relying on tired over-worked people or children.

    1. very good points! ...but i had to reply because i LOVE the vision of you "abusing your power" to feed your loved-ones more health-building foods! :-)

    2. Thank you, Tess. I am also careful not to cause a rebellion among my subjects.

    3. Galina, I am the poster child for what RA does to families. RA has shaped my life in so many ways. My mom was basically an invalid when I was young. We were all moved around. I stayed with relatives. I had tons of "grandmas". As a little kid, if I wanted to wear something, I would have to run downstairs and do the laundry myself. If we wanted to eat, we had to go defrost something ourselves. When I was around 7, one teacher was appalled at how I was dressed. Mismatched clothing, weird hand-me-down underwear. Untucked. She pulled me aside and tucked everything in, muttering about who dressed me. My parents lied all the time, putting on a brave front. Of course, I dressed myself with what was available. We didn't have money for clothes that fit. Money was for buying all the drugs.

    4. I am sorry, wow! I have been dealing with allergies all my life, but RA is thankfully not my problem so far. My former mother in-law got diagnosed in her 50-s, she is now 74, many of her joints are visibly deformed and she has pains. They have no history of allergies in their family, but many family members are treated for mild neurological disorders, and amazingly for me many in their family now have psoriasis (I sort of want to say - "Wait for a minute, it is my privilege to suffer from allergies", many years ago my then mother-in-low saved my life when she called 911 when I was having anaphylaxis reaction on I don't know what, and I didn't want her to call an emergency - in illness people are often irrational ), sinus problems of allergic origin, my former husband definitely has IBS. I would gladly put all them on a gluten-free diet, but it, of course, out of question. You know - it would be the end of the world for the most, besides, it must be hard to comprehend how on of main staples in a diet which many seemingly consume without any problem became on the list of suspected poisons. My former MIL is very educated and intelligent person, there are many professional scientist in their family, she has a master degree in Chemistry. She admits that many of things I say make sense and follows some of my recommendations.

    5. I think the consensus is that all AI diseases have to have some sort of trigger. But regular allergies can even be more life-threatening. It usually takes awhile for AI to kill someone, but for people with allergies, they can get into real trouble. My family seems to have both types of immune response.

    6. The tough thing about AI is that it is often not seen by others, and variable. If you are walking around in a cast, people get that. I have one relative who takes great precaution with her kids' severe allergies, when I got dx'd with lupus, she told me to suck it up.

    7. sooo.......my version of sucking it up is to stay fairly low carb. It is so much less inflammatory compared to a higher-carb, higher GI diet. I had even forgotten what an autoimmune flare felt like, and it took me awhile this time to put two and two together. But my pattern for the past several years is to get really out of whack in the fall. It starts with Halloween, where I am out late with the same group of people every year, and candy, chili and sandwich wraps are always served. Then a week later was a yearly retreat where only vegetarian food was served. These two events really threw me off, and I would get back into balance right before Thanksgiving. Then turkey-snd-stuffing day would really throw me off. I would get better by Christmas, but then sometimes go off track with that. I think that this season I didn't eat one single Christmas cookie.

  5. I do think my mom is celiac. Her RA symptoms lessened when she started an old version of weight watchers. Much lower carbs and bread. Then they invented Motrin. This was the first real RA drug available, and she was one of the first to be on it, when it was still investigational. That drug really changed our lives.

  6. Maybe it was good to be woken from your dream by "my house-flipping neighbor's construction crew jack-hammering their front porch," ?

    It never ceases to amaze me how little effort some restaurants (and families) put into the thought of others with food allergies, health problems etc. Since Eddie's Type 2 diabetes diagnosis the family are far more aware what food's can be better tolerated than others and do cater for a reduced carbohydrate intake.

    It never ceases to amaze me the added cost that the so called gluten free or diabetic foods cost. In fact be careful when buying foods that say this especially pre-packed because when you read the small print what may look harmless isn't.

    If we do not all fit into round pegs and we are in fact a square peg then life and it's food choices are made that more difficult.Unfair yes but that is how it is ...which is why we must continue to speak out about it.

    Hope things sort themselves out for you ...life is never easy.

    Take Care

    All the best Jan