# What does it do?

I’ve very often been asked the question of what I do and when I tell someone I teach mathematics and do mathematics research, I am invariably asked what I research. For many of the things I spend my time on, I have yet to be able to communicate to someone that doesn’t speak in my jumbled mathematics tongue. Everyone once in a while, areas that my research relates to comes up in the news. Here’s a great example of an application for the surface fitting and smoothing techniques I explored in my Master’s Thesis:

Spline-Enhanced 3D Surface Visualization of the Levees Around New Orleans

Take a look, it is very fascinating. Some work I am currently doing with variable knot splines also relates, indirectly.

# Solitaire Odds

I have finally taken the time to answer a question that has bothered me for some time. There is a solitaire card game that I learned while I was a Sojourner (high school summer missionary) in Bakersfield, California. I don’t know any sort of official name for the game, which means I can’t refer you to any site that describes it. I’ve called it either One in a Million or Bozo (a name provided by a Jennifer (Taylor) Mykitiuk while she was in Junior High.)

There is no strategy at all and so, winning is pure chance. I wanted to know what chance. Here is the approach to the game.

1. After thoroughly shuffling, hold the deck face down.
2. One at a time draw four cards from the bottom of the deck and place them on the top of the deck each face up.
3. Looking at the fourth card and the first card, if they are the same suit, discard the middle two cards. If they are the same denomination, discard all four. Otherwise, move on to the next step
4. Draw the next two cards (or four if all have been discarded) from the bottom of the deck, placing them face up on the top. Comparing the top card and the fourth from the top, repeat step 3.
5. Continue drawing and discarding until all cards have been drawn.

The goal is to discard all the cards. In playing an awful lot since I learned the game in ’94, I imagine I have won around 5 or 6 times total.

So, whis is the actually likelihood of winning. My first attempt of deriving an exact probability distribution for the outcomes failed miserably. Thus, I moved on to a “Monte Carlo” simulation approach.

I designed a computer program that played the game and determined the remaining number of cards after randomizing a deck. Using the program, I can play the game up to 100,000 over the timespan of about 5 minutes. The following is the outcomes from 100,000 random simulations:

 Number Left Frequency Approx. Probability 0 5,966 5.966 % 2 20,261 20.261% 4 22,494 22.494% 6 10,988 10.988% 8 12,201 12.201% 10 5,921 5.921% 12 6,903 6.903% 14 3,295 3.295% 16 3,732 3.732% 18 1,836 1.836% 20 1,967 1.967% 22 945 0.945% 24 1,086 1.086% 26 518 0.518% 28 590 0.590% 30 285 0.285% 32 300 0.300% 34 172 0.172% 36 170 0.170% 38 84 0.084% 40 93 0.093% 42 42 0.042% 44 56 0.056% 46 21 0.021% 48 18 0.018% 50 16 0.016% 52 40 0.04%

From this, we can determine that the expected value (average outcome) is 7.3712 cards and a standard deviation of 6.57 cards. It seems that the real challenge of the game is not to get rid of all of your cards but to maximize the number of cards left behind. I have never had a hand where no cards could be discarded. That’s my new goal. You know, in my free time, that is, the time I am not spending programming monte carlo simulations.

# I am that guy

So, in any other day and age the following story would vanish into obscurity, yet now, I feel compelled to document my complete descent into that professor I never wanted to be. You know the one, the one that is apparently focused on some deep problem, like the convergence rate for a three field finite element method or the derivation of a pseudo-rotation matrix that satisfies the Eckart conditions in a roto-vibrational molecular model, and so much so that he can’t keep track of his keys or his car or a simple little receipt he needs for reimbursement. Its this stupid little piece of paper that vexed me yesterday.

I am at Sam’s buying the vasts amounts of supplies our division needs to host a cookout for all our majors and minors and their families. We’re splitting the cost among the budgets of each division so I need to keep the receipt. After the purchase is made, I “carefully” place the receipt in my wallet. Oh and by the way, I also forgot to use the taxfree ID so I am going to have to pay the sales out of pocket (no reimbursement for sales tax). Now, if you been to Sam’s you know that you must also show your receipt at the door so I remove the receipt, show it, then “carefully” replace the receipt in my wallet. On the way home, I have a craving for Gardetto’s so I stop to buy a bag. I pull out my wallet, pay the lady and I am on my way.

It is at about the 35th mile marker on I27, I realize that I completely forgot to have the sales tax waived, so I pull out my wallet to check for how much tax I was in for. What the! Where’d it go? By the time I arrived at home I am in a panic. I just spent a pretty penny and I am not going to be reimbursed. I cleaned out the car from top to bottom (no small task considering how much stuff I had just purchased). Okay, I settle down and realize I can try calling Sam’s. They say they’ll print me a new one and I can pick it up anytime. I fill in my lovely wife on this set of details and we realize that it will be a while before we have a chance to go to Lubbock again. So we pack up and go right down to Lubbock. (Man, I love these gas prices.)

We pick up the receipt and it’s dinner time. Off to IHOP we go. For no particular reason I pull out this reprinted receipt to look it over. It’s not until we are driving back home that I realized it stayed on the table. ARGHH!! Sam’s is closed, so the only option is to head back to IHOP. Our very kind and patient waiter helps me find it in the garbage, still mostly intact but I am definitely going to make a copy and throw away this one. Once in the van, I “carefully” stick the receipt in the pocket of the door and close the door. You’ll never guess what happened next. We arrive back at the house a good 45 minutes later and check the door. ARGHHH! Now, this one perplexes me the most. We clean the van from top to bottom and look everywhere. Lori even watched me put it in the door. The ONLY thing that could have happened was that it blew out as I close the door.

I am that absent minded professor except I had no deep problems to solve so the only possible explanation is that I have no idea what it means to put anything anywhere, “CAREFULLY”.

Anywho, Sam’s faxed me the receipt this morning (yeah, I wish I thought of that last night). It is taped to my wall at work. Tomorrow, I will make 400 copies and stick them in every nook and cranny I can find.