SpielByWeb

[freduk]

Does it really matter?
The poll results are still 70% to keep it as it is.
Why are the minority going to get to change it, when they probably won't agree on the new figures anyway?

[Bkruppa]

Not to sound unfeeling, but who really cares either way. Its a game, hashing and rehashing this same issue over and over takes away from the point of games. Social interaction using a common enjoyable activity.

[HappyProle]

I was just nudging this apparently dead issue to ensure it was truly dead... I must admit I was looking forward to someone performing cube tower experiments.

FWIW I doubt we would ever have eliminated the current tower model, I think we would have just added the new one as a variant.

[nearsider]

It's on my (overly extensive) list of things to do.

I might get together with a friend in early January some time and toss a bunch of cubes into the tower and see what happens.

If/when I do, I'll be sure to post my results here so people can tell me how I'm wrong.

[HappyProle]

Make sure you wear labcoats.

[thyrza]

there's 1% missing
_________________
Thyrza

[nearsider]

Sadly, I don't think I still have my lab coat.

Maybe I'll see if I can raid the chemistry building first.

I do have safety glasses, though. Those are a must - don't want to lose an eye to an errant army.

[Alashar]

I never heard back from the Statistics professor I know. I thought about hiking over to his office and hitting him over the head with my Wallenstein box to get his attention, but I didn’t.

I’m glad to hear that a Variant to the current game is a consideration. The percentage of people voting for a change in the chit tower has picked up in the last few weeks to 31.7%. That’s close to a third, so that’s a significant number of less than happy campers. And we do want to be happy when we’re out on a campaign!

Anyway, I too will be happy to throw some cubes in the tower to get some stats—probably in January. In thinking how to approach this, I’ve come up with a simple model and would prefer to get feedback on it BEFORE the testing, not after. So, please shoot it full of holes now so that I can revamp it before the 200 throws.

I think that testing the tower with 3 colors of cubes will suffice. Using only 2 colors would probably hang too many cubes of any 1 color up in the tower. Using 4 colors would add perhaps too much complexity to data management. I’ll be using Red, Yellow, and Blue as I’ll want to abbreviate them as R, Y, and B (using black and brown would confuse that!).

In order to track the rate that cubes are released from the tower, I’ll have to deface my chits and paint numbers on them. I’m thinking that 20 chits in each color will be enough. I’ll do some practice runs with that many first without recording data to verify that it will suffice.

After seeding the tower with 7 chits in each of the 3 colors, recording which ones are still in the tower, and returning those that fell into the cup to their respective lots, I’ll begin testing. I’ll run it in sets of 3 battles: R vs. Y, Y vs. B, and B vs. R, each with differing amounts of chits. I’ll run 10 different sets and call it a round, which will consist of 30 separate battles. I’ll work it out so that those 30 battles run the gamut from ties (2-2, 8- to lopsided (10-1, 3-9) and everything in between. I think I’ll cap the highest number of chits at 10 just to keep the data manageable. Sure, some battles use more chits in SBW and the real world, but I think it’s relatively rare and statistically insignificant. After the 30 battles, I’ll shake all the chits out of the tower, reseed the tower, and begin a new round.

Each battle will yield 4 data points (DPS). For instance, in the first battle of red vs. yellow, how many reds fell out of the reds put in is the first DP. Likewise the yellows falling out is the second DP. The third DP is the number of reds that have been knocked loose from the cup divided by those still left in the tower (e.g., 1 out of 3 = 33%). The fourth DP is the same for yellow. Another DP possibility is the third color (blue in this case) not involved in the battle which are knocked into the cup. But as these will immediately be funneled back into the tower for the next battle, I think it’s best to regard them as remaining held in the tower and not track this as a DP.

Thus, each set of 3 battles will yield 12 DPS. For each round of 10 sets, 120 DPS. I expect to run at least 4 rounds (yielding 480 DPS), and preferably 6 rounds (720 DPS). If someone else runs a similar test, we should have close to a thousand data points, which should generate fairly accurate statistics.

Anyway, pipe up now so that I can make some adjustments to the model, or be stuck with it after! Thanks to HappyProle for nudging the experiment forward and to nearsider for joining in on it.

[nearsider]

Well, I'm in the process of typing up a full reply, but that's going to have to wait a little bit because of an unexpected illness.

The short of it is that you've got some good things and some bad thing about your experiment.

The most problematic is the assumption about cubes being knocked loose being counted as being "in the tower." This is a poor assumption, because what you're really testing is the chances of cubes in the tower coming out on cubes being tossed in, this really messes with that.

I think it's important to think explicitly about which variables you're testing and whether this test will work for that, and how you can turn your data into something useful to model that variable.

[nearsider]

Ok, here goes...

In order to determine an appropriate experimental design for our cube tower model, we have to figure out a couple things. First, what is our goal? Second, what variables are involved and which ones can we/do we want to test?

First, our goal. What we're after is the probability that on the event of cubes being thrown into the tower, a given cube comes out. So we want a function of several variables p(A) that we apply to a cube that represents the probability that that cube appears in the cup after a toss of cubes into the tower. Here A represents the set of variables upon which the probability depends.

Currently, we have a function for this probability. In the model now, A consists of one variable, specifically whether or not the cube is in the tower or not. If 0 is not in the tower and 1 is in the tower, then P(0)=.7 and P(1)=.3. A random number is generated for each cube, and compared to the probability function, and if the number is less than P(A) for that cube, it goes in the cup, if it's greater than P(A) for that cube it goes in the tower.

What we want to do now is identify other variables that affect this probability function and devise an experiment to test these variables to model the probability function better than it currently is modeled.

Some variables that I can think of that determine whether or not a cube exits the tower on a toss are:

Number of cubes in the tower
Number of cubes going into the tower
How long a cube has been in the tower
How the cubes are thrown in the tower
Where in the tower the cubes are located

Now, to determine how to model these variables.

The first 2 are in my opinion the most influential (besides simply whether or not a cube is in the tower), and thus should be the first ones tested. I'll describe a possible experimental below.

The 3rd is probably fairly important, but a little harder to test beyond simply in the tower or not. I'll get into that later.

The last 2 probably have some influence, but are very difficult to test and equally difficult to model. How the cubes are thrown in will likely average ittself out over repeated experimental trials, and where in the tower cubes are located will primarily be a factor in how long a cube is in the tower, and will likely show up as part of that model.

This leaves us with the goal of getting a function p(x, y, z) where x is the number of cubes in the tower, y is the number of cubes going into the tower, and z is how long a cube has been in the tower. These variables may or may not be independent of each other, so determining whether or not they are should be part of the analysis of any data that is acquired.

All that is needed to test the first two of these variables is a way to differentiate the cubes going into the tower from the cubes coming out of the tower. This can be done by numbering the cubes individually (which also allows full testing for length of time in the tower), but for those of us who don't want to mar our components, you can do this simply by alternating which color you toss in, recording which colors come out, being sure to only throw in a color that has no cubes currently stuck in the tower. This does require emptying the tower whenever there are cubes of all colors inside. This has a limitation in that you're artificially removing cubes from the tower sometimes, so that is data that is lost in terms of how length of time in the tower affects things, and might put a cap on number of cubes in the tower that we're testing.

So enough theoretical blabbering. What needs to be done to test?

We have cubes of 6 colors, say, A, B, C, D, E, F. All you need to do is toss N cubes of color A into the tower, record how many you put in (and which color) and how many came out (and which color.) Whenever you have a cube of all 6 colors in the tower, empty the tower. Note you will not have to empty the tower every 6 throws.

I've put together an excel spreadsheet that will allow you to easily record the number of each color that goes in and comes out, and will tell you which color you should throw in next.

If anyone wants this spreadsheet, let me know and I'll email it to you.

In another post I'll describe what to do with this data once you have it.

If anyone sees errors I've made (and I'm sure I've made them), let me know and we can fix it.

I wonder if anyone actually read that whole thing...

[Bkruppa]

Um, wow...I thought my math professors were major geeks, but I believe there might be a new candidate!

[nearsider]

FWIW, I was a math major and went to grad school in math for awhile.

I wear the label of "math geek" proudly.

[Bkruppa]

LOL--I have a secondary math teacher master's but unfortunately still feel the stigma from the title "math geek". Hopefully someday I will be able to shed the self-imposed feeling of shame and wear it with dignity like you!!

[JRamirez]

thank you