Sarah’s Reflection Week 1

September 9, 2010
By

You never know exactly what will happen... unless you've got 100% probability. Or just crazy luck.

When we learned about the “Josephus game” and how skipping people and leaving a winner had strategies, I wondered, was there a pattern? I wanted to know if there was some kind of formula or method to quickly find out how to win those kind of eliminating games, like Josephus would have had to do in his dire situation. I became puzzled, as I couldn’t find any patterns to use. Then I found a concept.

At first it was hard to express. I had the idea in my mind, but I found it hard to write out. It’s like when you’re looking for the right word, but you don’t know what it is or how to describe it really. The idea was that with p people in a circle and a skip rate of s leaving the winner the rth person, then with p+1 people in a circle and a skip rate of s, the winner could be determined by eliminating the sth person, then counting r people from that person. So, the winner would be the (s+r)th person for a game of p+1 people with a skip rate of s.

I had been frustrated with trying to find a pattern for the Josephus game, and I tried all I could on my calculator; ExpReg, PwrReg, LinReg, and so on. None really did what I wanted to do, so I abandoned that idea. But I tried to solve a problem relating to the pattern of the Josephus game and tried to understand the solution. Then it clicked, and I arrived at the aforementioned method. I think that this elimination pattern could probably have one explicit formula; I’ve only found a recursive formula. But when I do find an explicit formula, it would be really interesting to use in real life when such elimination games like ”Eeenie meenie minee mo” or “Bubblegum, bubblegum” are used, and I could expect who would win and lose.

Math is all around us in life, but games are too. Games provide entertainment. They create environments, moods, cooperation, friends, money, losses, among many things. You’ve probably heard somewhere that “Life is just a game”, but whether that’s true is another story in itself. I think it will be quite interesting to learn about games with math. Lately games have been broken down to mere tricks of strategy. Even poker is being filled with “math nerds” who calculate odds and play precisely, quickly and accurately. Players of luck or skill are few, and so gaming is becoming an increasingly more mathematic, scientific type of endeavor.

This change interests me a lot; I’m the type of person who just plays, usually without a strategy, mostly because I don’t know how to find a strategy efficiently. Strategies can be hard to find without good logic, and strategies can be quite complicated the more complex the game is. I’m not good at remembering things, but I think that if I can better understand the logic and patterns behind games in general, I won’t have to memorize strategies. I’ll be able to “derive” them and have fun. This week’s just the beginning, and it’ll get more and more interesting from here on out. Cheers!

p.s. Sorry this was such a long post. I kind of write as if I was talking when I blog. It’s a lot of fun though! :)

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One Response to Sarah’s Reflection Week 1

  1. Mrs. Krummel
    September 13, 2010 at 8:50 AM

    We’ll be studying the mathematics of games a lot this year. It is fun to think about them in this new way!

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