SpielByWeb

[TheKeck]

I'd just like to chime in that from what I remember of my statistics class in college, saying that you need 100,000 or 1,000,000 data points in order to get something statistically significant is ridiculous.

But I could be wrong.

[Golux13]

I don't know what the number is. It could be merely in the thousands. Given the variables involved in the real-world tower -- which makes it not really a purely probabilistic tool anyway -- I think the number would have to be pretty high to have any sort of confidence that the SbW probabilities accurately reflect how the tower really works. Similarly, I think you'd have to have a lot of data before you can say that the SbW implementation is not a reasonable approximation of the real-world tower. A thousand, ten thousand, a million... whatever. The point is, a handful of adverse outcomes is meaningless.

[nearsider]

With good data collection, 1000 data points should be more than sufficient to set up a reasonable model.

For collecting the data, all you need to do is record number of cubes put into the tower and number of cubes out of the tower. You can then calculate at each step the number of cubes that were in the tower and determine how that had an effect on the cubes coming in or out. I'd think this should be sufficient to determine if what is done is approximately good or bad, and give a clue as to how to make it better. If you wanted to be excessively detailed, you could record whether the cubes in the tower came out or not by using different colored cubes, but that would take much more time since every time you used all the colors you had you'd have to empty the tower of at least one color.

In my experience of one play IRL, the chance of a cube getting stuck seemed to be lower than 30%, and the chance of a lodged cube being dislodged started at about 50% for the next throw and decreased after that with each subsequent throw, but I have no measured data to back that up.

[Alashar]

I put in a call to a professor of statistics whom I know at the university where I work. He should be able to give us an accurate assessment of the number of data points required to be statistically sound, though I may not hear from him till after the holiday weekend. He may have some suggestions too about how to best set up a study. I'll keep you posted.

[HappyProle]

I looked at an old post where this came up and milksheikh seemed very open to changing the algorithm if someone could come up with a case for a more accurate model.

http://www.spielbyweb.com/forum/viewtopic.php?t=8&highlight=tower

Assuming we can come up with a reasonable alternate tower model, it certainly seems reasonable to implement the choice of model as game option for the game creator to choose.

I think it'd be cool to do some true experiments with the tower to come up with a reasonable model. The first step is obviously for everyone to find a lab partner...

[Kanga]

I've not played the game before, but generally speaking it is unlikely that you would need a particularly large database to get an accurate formula. Even 100 would be enough if it was a straight probability calculation. I'll go have a look at the game sometime soon, and work it out.

Rob (statistics major)

[Papperlapapsch]

Just as Rob said (while I seem to be far less qualified than he is), we don't need a thousand test runs. And even if we needed that many - I'd do 50 or so without a problem, and we should find some others willing to do that as well. The real problem will be to take these results and make an accurate model out of it. If we really want an accurate model.
As a non-purist, I dare to ask the question if we really only want to perfectly reflect the tower. What if the red cubes fell out easier because of smoother painting? Would we want to reflect that? I think we should really ask ourselves if we want such a large probability of completely inexpectable attack results. If we want more or less luck than is the case right now, we could adopt the numbers. And I think that while randomness should be present, the chit tower has the sole reason of existence to even out luck througout the game...which doesn't really work that well right now, as he "eats" too many stones.

[Raven]

In all this talk of statistical models, we've ignored another important fact. As Golux13 wrote "shit happens"... especilly in war. In 1588 the Great Spanish Armada, also known as "the Invincible Fleet" sailed against England and was defeated by a combination of brilliant tactics by Sir Francis Drake and really bad weather. After conquering most of Europe, Napoleon was forced to retreat from Russia because of the harsh winter. A few hundred years before that, a band of "barbarians" led by a guy named Ganghis conquered most of Asia. There are thousands of other examples where the army (or navy, or whaterver) that was supposed to win a battle or war lost because shit happens.
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"What is it about slime that chicks don't dig?"
-Milhouse Mussolini Van Houten

[nearsider]

Raven, I don't think people are advocating eliminating randomness entirely, I think they're complaining that the probabilities online are different than those offline.


In terms of data collection, the first thing is to determine the variables that might affect the results of the cube toss. Things that I can think of are: number of cubes in the tower, number cubes going into the tower. Both of these can change the probability of a cube getting stuck and a stuck cube getting dislodged.

100 data points might not be enough because of the number of different cominations of cubes going in and cubes in the tower. I'd think that any number between 1 and 10 cubes in the tower should be tested, in addition to each number of cubes added between 1 and 10 (or more). Here, 100 data points would only be sufficient for 1 test per combination, which doesn't give good data.

Another thing that can affect the probability is how long a cube has been in the tower. That might be a little harder to test though.

Also, one might want to keep track of whether a cube that comes out was one that was put in or one that was stuck, but this is fairly easily tracked.

There's a lot to keep track of, but it's certainly something that could be done in a Saturday afternoon or 2.

[craw-daddy]

I think we all tend to remember the times when "weird" things (i.e. what we think are unexpected) seem to happen, glossing over all those many other times when what seems to be normal occurs.

I'm quite surprised that there are suggestions that you could base a reliable model on only 100 tries of the tower. That would be like trying to judge if a ten sided die (or a d6 for that matter) were really biased by throwing it only 100 times. I'll have to dig out one of my old books on statistical hypothesis testing. That is, if I can ever find the time in between "real work" (and taking turns of course).


Edit: And I was about to write some of the things that nearsider did, but I didn't, and now notice that I didn't have to anyway (but I'm not sure that "a Saturday afternoon or two" would suffice). I think you'd also need to test a larger range than 1-10 cubes in the tower. I haven't played Wallenstein much, but the few times I did there were certainly times when there were more than ten. And then would you want to test it when there are x red, y black, z yellow, etc. cubes in the tower? (And when I chuck in x' black, y' black, z' yellow, etc?)

[Big Bad Lex]

This thread has gone on longer than I expected, but for what its worth, I'd rather admin support spent what precious time they have on maybe a new game rather than burning hours throwing every permutation of cube number, angle and velocity into a real life tower to add +/- 5% onto the current model.
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It's not the winning, it's utter annihilation of your opponant that matters.

[HappyProle]

I'm certainly not going to throw any dice into the tower, but if someone else went to the work of coming up with an alternate tower model based on experiments I don't think it would take that long to implement that as a game option. Trust me, it's not going to take any time away from developing Maharaja or game #13.

[mrbass]

[Raven]

[Golux13]

One thing that has gotten lost in this discussion is that a straight %-stuck/%-dislodged probability scheme is far more predictable (in a casual game setting, at least) than the real-world tower, where the probabilities depend on the number of cubes, the interaction of the cubes, the shape of the tower (and the positions of the holes in it), the angles and velocity with which the cubes go into the tower, and if you want to get perfectly deterministic, even such odd factors as air temperature and humidity. No matter what is decided -- and I do recognize that 30/30 was at best a reasonable guess by Mikhael -- the SbW implementation is always going to be based on numeric probabilities and a pseudorandom number generator, not on the same variables that make the real-world tower the randomizing factor it is in the game.

So if your complaint is about apparent "arbitrary randomness" (whatever that might mean) making your planning and strategy less predictable, then you're actually better off playing on SbW, where you can figure exactly what your odds should be -- no matter what the numbers are -- and plan accordingly. As I noted, the current equation is (0.7*A1)+(0.3*A2)=At. Right now, for instance, I have a potential battle where I will be defending with 4 armies, 5 in the cup and 1 in the tower versus 3 attacking armies plus 5 in the cup and 2 in the tower. I calculate the attack as a 6.6 to 6.2 underdog, but it's so close that anything could happen. (From a strategy perspective, it is not an attack I would make, but it's the endgame and the player may be desperate enough to go for it.)

If we change the numbers to 25/50, as suggested in the original post, that just changes the odds, but may not change the strategy. In my current situation, the numbers become 7.25 (9*0.75 + 1*0.5) to 7 (8*0.75 + 2*0.5) against success. Even more of a coin flip, and the same strategic considerations presumably apply.

But in the real world, you can't really make the same calculation. You can estimate the numbers and calculate on that basis, but not with anywhere near the certainty that I have about the SbW version. How can you possibly predict the outcome when you don't know, for example, whether the cubes will all go in at the same time or in a stream; whether they will go into the center or down one of he sides as they go in; or whether any of the stuck cubes are pushed into a corner and thus almost certain not to be dislodged?

So if your complaint is about the unpredictability of the SbW implementation as opposed to the real-world tower, then I think you're looking at it backwards. And yes, you could do statistical testing on the real-world tower, but in order to derive accurate probabilities, I think you would have to run enough tests to "smooth out" the variability caused by all those physical factors.