This is Dan and Andrew’s Gaming Place. We will be making posts on Tuesdays.

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# Dan and Andrew's Game Place

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## Welcome!

## Goofspiel

## Metropoluna, the Mercantile Moon.

## Realm of the Powers Core Rules.

## Printable Figures for Urns, Amphorae, and Potions

## Mighty Morphin’ Number Sentences!

## Hidden Maze Death Traps

## Advance By Factors

Dan and Andrew's tips, tools, and techniques for games and game theory.

This is the post excerpt.

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This is Dan and Andrew’s Gaming Place. We will be making posts on Tuesdays.

The game of Goofspiel is a simple two player card game. Humans can play it pretty well but it is hard to get AI to learn to play — because the good strategy is obscure. The game requires a standard deck of 52 cards, split up by suit. Player one gets all of the hearts, Player two gets all of the diamonds. The spades are shuffled and placed face down in between the players. The clubs are set aside. The cards are ranked as follows. An ace is worth 1 point, the two is worth 2 points, …, the Jack is worth 11 points, the Queen is worth 12 points, and the King is worth 13 points.

Here at Dan and Andrews, we proposed that you spice up your campaign with moons. These are celestial bodies with monsters, treasure, and even civilizations that show up in the skies above your campaign world whenever you want them to. So far we have released the Chimerical Moon. The rapacious capitalists of *Metropoluna* are mentioned in the source book for the Chimerical Moon. This week, we feature the Mercantile Moon including a 99-page sourcebook.

A very long time ago, Bill Underwood wrote a gaming system called *Beasts Men and Gods*. While the lab at Dan and Andrew’s Game place has a few copies, the rule system mostly died out in the gaming world. We wrote our own version which grew to more that 10,000 pages and required a master’s degree to play. The rules that we are reviewing in this post are the Stage II light-weight version with a number of innovations from decades of experience as fantasy game players and referees. Interested? Read on.

Steve Jackson’s original cardboard heros, published many moons ago, had some square tiles with treasure in them. A couple were bottles and they were all about the same scale. This week’s post tries to address the lack that happened in our gaming group long ago. In an act of mathematics, in the aid of gaming, we have made sixty printable potions. The subtext of this post is that knowing a lot of math gives you some abilities other than teaching algebra class.

If you print these, you will probably want to print these in landscape mode. As with our other printables, you can print on cardstock or print on white paper and then use a glue stick to attach it to thin cardboard of some sort. If you want a two-sided standee, make a reversed duplicate with your image editing software. The GIMP (which is free) can be used to do this.

**Potion Bottles**

Enough commentary! Here are the potion-sized version of the images.

**Whiskey bottles or maybe Urns and Amphorae**

These are the exact same images, but larger and broken into several images.

Image 2:

Image 3:

**Where did you get these?**

Elves. Wait, no, that was something else. These are very odd curves in the polar coordinate system filled with synthetic textures made at Dan and Andrew’s lab. The outlines were actually discovered by accident — they started as a code bug, and if you really want to know, drop a line to dashlock@uoguelph.ca and he will send you the math.

The colors are the result of making three crater-rich lunar landscapes and then dumping the height values into the red, blue, and green color channels of an image. We bias the height of the craters in each channel to get different shades. The ones that are not biased at all are the most multi-colored. We also have a blur control: the width of the crater rims. The broader the crater rims, the smoother the texture. The ones where you can see parts of circles are the least blurry while the smoother ones have a high blur coefficient.

This is **Dan** of Dan and Andrew’s Game Place. Let me know what you think about this post in the comments. If you have other image needs (we are bad a character figures) let us know!

This weeks post is about a whole class of puzzles called *edit puzzles*. The classic edit puzzle is turning one word into another by changing one letter at a time. For instance turn “STORM into SHADE” can be solved by STORM STORK STARK STARE SHARE SHADE. What is a little more interesting is that the words form a network (a fragment appears below) that contain huge numbers of puzzles. The fragment, for example, contains 190 puzzles, though some are pretty trivial. To make one of these puzzles, you start building a network and stop when two things that are the right number of steps apart in the network are also interesting to connect. This weeks post does something similar with *number sentences*.

Look at the maze shown to the left. The red squares are the beginning and end of the maze. Here’s the thing: given the top view this is a really easy maze. Too easy. It was created by computer search. The search algorithm was given a certain amount of wall. The computer was told to use walls to make the distance from the beginning to the end of the maze large (and it did). The cul-de-sac part way through wastes some wall, but for a search of the cosmically large number of ways to put down the walls this is pretty good. If you can see all the walls from the top, though, this is not a good *maze*. This comes under the heading of “computers do what you tell them to, not what you want them to”. This week’s post is about mazes where this search strategy *is* a good one.

This game was originally called Sum-48, and it was created by some students of mine in a game theory class I was teaching. Part of the criteria I gave to the class was to keep the rules simple, since it is often the case that simple rules can create fairly complex games, like Nim. Advance by factors is a game that can be used to teach younger (and older) students about factors of numbers, and developing some higher level game playing strategy.Advance by factors is a two-player game that uses the natural (counting) numbers (1, 2, 3, and so on), and is played as follows. There is a goal number that both players want to reach. In the original creation of the game, the goal was 48

- Player 1 starts the game by rolling a six sided die. Whatever the result is, that number is where the game starts.
- The two players take turns making moves.
- The player whose turn it is can advance to another number by adding one of the factors of the number she is currently at that is
*strictly**between*one and the number — unless the number is prime — in which case they may add any divisor of the number (itself or one). - The player than manages to arrive at the goal is the winner.

So, for example, if Player 1 starts at 4, that means she has only one option to add to her position, 2, and so she advances to 6. 6 has two available factors, 2 and 3, and so player two can advance to 8 or 9. Player two chooses 9 leaving player one with one option, 3, so player one advances to 12. Player two then has a rich set of options as the factors of 12, other than 1 and 12, are 2, 3, 4, and 6. The game continues.

The goal of the game is to be the first player to reach the agreed upon number, like 48. However, if you can force your opponent into a position where she cannot reach the goal, then you win. Here is an example of how the game might go:

P1 starts at 4, and chooses to move to 6.

P2 considers 6, and moves to 9.

P1 then moves to 12, using the factor 3.

P2 moves to 14, using the factor 2.

P1 moves to 21, using the factor 7.

P2 moves to 24, using the factor 3.

P1 moves to 30, using the factor 6.

P2 moves to 35, using the factor 5.

P1 moves moves to 42, using the factor 7.

P2 moves to 48, using the factor 6. **Winner!**

It turns out that 48 has an interesting property which was found by my student during their final project: Player 2 can always force a win for themselves, regardless of where the game starts! An interesting observation, and we aren’t sure how many other numbers have a forced win. It may take player 2 a while to figure out how to force a win. Look at all the possible games for 48, diagrammed here, as if we start from 2. This diagram shows shortest routes so the move from 40 to 48 isn’t shown, because it takes just as many moves to get to 40 as to 48.

Give this game a try, but don’t pick 48 unless you want to ensure the outcome 🙂 We used a computer to figure out the numbers that are a given number of moves away from 2, along the shortest path to reach them. This can help you decide which numbers you might want to play with. Notice that 5 (if you roll it on the initial die) goes to 6 or 10, so it joins the diagram above pretty quickly.

This is Andrew, of Dan and Andrew’s Gaming Place.