Shower Math

Family members often inquire as to what I could possibly be doing in the shower for 40 minutes each day. Sometimes I think about telling them, but then I realize these things are just better left alone. Does anybody really want to know what I do in the shower, besides apply soap to my wet, naked body?

But I don’t care what you think of me, blog readers! See? I just began a sentence with a conjunction. Oh, that feels dirty.

So I will tell you what I do in the shower for 40 minutes every day, because it really is amazing; just as penguins migrate miles and miles to mate each year, I go on my own sort of special adventure each morning as I strip down and lather up.

My attention span, some may say, is much like lightning. It’s a beautiful sight, but it’s always gone in a flash. That doesn’t apply only to class lectures and summer reading assignments though. Often, I get distracted in the shower during my daily routine. What could possibly distract me for a half-hour? Soap, shampoo, the various peculiarities of my own body, but most often, it’s my damned curiosity that threatens to make me late for school each morning.

One day, I had nearly remained focused for the entire shower cycle. I had gotten through the body wash, and I had already poured the shampoo into my hand when it happened. I was dumbfounded; a random question had taken hold of me, and at any cost I would know the answer:

What are the odds of rolling a yahtzee in Yahtzee?

Damn. Instantly, nothing was more important than knowing the answer to this, the question of all questions. I began to work it out in my head. What are the odds of rolling all the same number with five dice? Well crap. I’d better start small, I thought, the shampoo oozing off my hand. What about one die? That’s easy, it’s always all the same number with one die, so 100 percent. Sweet. One step closer. The shampoo slithered off the shower floor into the drain.

OK, how about two dice? Well, how many combinations are there? Steam began to rise around me. There should be six possibilities for the first die, and then six possibilities for its partner. Sweet. So that’s six times six? Duck? Wait, no – 36. Duck? Why would I think that? I saw a duck yesterday (figure 1). Wait. Focus.

Figure 1: A distracting duck.

OK, so 36 possibilities for two dice. Sweet. Wait, though, it seems too easy. More steam. HEY! One and two is the same as two and one! Shoot. I give up. If only I had a sheet of paper… but it would get wet…

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WAIT! The steam! The sliding glass door is caked with it! It’s practically a white board!

1 – 1 2 – 2 3 – 3 4 – 4 5 – 5 6 – 6

1 – 2 2 – 3 3 – 4 4 – 5 5 – 6

1 – 3 2 – 4 3 – 5 4 – 6

1 – 4 2 – 5 3 – 6

1 – 5 2 – 6

1 – 6

(If you’re wondering, “Did he really write all of this with his finger on the foggy sliding glass door in his bathroom while hot water rolled off his naked body?” then the answer is yes. I did.)

That’s 21 possibilities for two dice. Six of those possibilities are doubles; therefore, the odds of rolling doubles are 6/21. Wait, but that’s almost a third of the time. That doesn’t seem right. Scratch that. Since there are two combos for 2 and 1 and 1 and 2 it’s twice as likely to occur and should be counted twice, bringing the odds back to 6/36, or 1/6 (I have a way of making things more complicated than they actually need to be, which you’ve probably noticed by now).

This means all of the numbers are complete idiocy. I find that I’m often a victim of my own idiocy. Unfortunately, I had used the entire foggy space of the glass to write this large sequence of meaningless numbers, leaving myself no room to further study my complex problem. How, though, do I clean the sliding glass shower door?

Then I remembered how innovative I am, and my superior brain quickly dissolved the problem.

Moving out of the way of the water, I turn the knob to its hottest setting and cry out in pain as it burns the bottoms of my feet while it flows into the drain. Soon the pain ends though; a fresh blast of steam covers the above collection of nonsense numbers like the large, foreboding wave that washes away one’s pointlessly intricate sandcastle (figure 2).

Figure 2: A pointlessly intricate sandcastle.

After having figured out the odds of rolling doubles with two dice are 1/6, and the odds of rolling a yahtzee with three dice are 1/36, I found the pattern. With four dice the odds are 1/216, and with five dice the odds are 1/1,296. After covering my shower door with multiplication problems, I had found the answer.

My life could now continue, once I had de-pruned. I stepped out of the shower/laboratory and dried myself by shaking like a dog for approximately seven minutes. Damn, I am interesting. Anyway, I resolved to move on with my day, having satisfied my thirst for Yahtzee knowledge.

Regrettably, I later realized that my findings were useless because you don’t just get one roll in Yahtzee, you get three. You’d have to first figure out the odds of rolling it on the first try, then the odds of rolling the same number with four dice out of five on the first try, then the odds of rolling three dice the same on the first try, and so on and so forth multiplying and dividing and adding all sorts of numbers. It’s a question for another shower.

Hopefully, this has shed some light on what people, or at least what I do in the shower for 45 minutes each day, other than the usual cleaning and the drinking warm shower water and the drawing obscene things with my finger on the foggy sliding glass door. I hope this has brightened someone’s day.