AWOL
40 Point Warrior
Warning: Kissing Chihuahua On Head Causes Sporadic Pooping, Urination, and Biting
Posts: 820
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Post by AWOL on Oct 24, 2007 10:51:08 GMT -5
"Hokey religions and ancient weapons are no match for a good blaster at your side, kid" Stats... I mean stats, not blaster... Where did that come from? LOL!! I was just waiting to see how long it would take someone to throw out that very famous Solo-ism!
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Post by YodaBreaker on Oct 24, 2007 12:09:45 GMT -5
While I appreciate statistics (and I understand that stats are simply a passion for some people), herein lies the problem of taking statistics too seriously when you're dealing with plastic little toys in a real world that will do none other than behave as plastic little toys. All the stats in the world won't determine if this figure or that figure will be white. Actually, that's demonstrably false. If I've painted all the wheel spaces black or white on a particular figure, the single statistic of proportion of spaces white or black will determine (as in absolute determination, not just probabilistic determination) whether my figure ends up white or not. Even in the more restricted case (where not every space is black or white), the stats certainly influence the likelihood of something occurring. Thus, if you're willing to abandon a dichotomous view of determination, the stats do certainly determine whether a figure comes up white or black in the weaker sense of determination as "influencing" as opposed to "definitively causing" a particular outcome. The classic demonstration of the strength of one's conviction that stats don't matter is the thought example in which a person is forced to choose to put one of two 6-shooters to one's head and pull the trigger just once: one that's loaded with 5 blanks and 1 live round, and another that loaded with 1 blank and 5 rounds. If "all the stats in the world won't determine" if the bullet to be fired is live or a blank, then you might as well pick the gun with 5 live rounds. After all, it's a one-time thing, right? Yes, some of us learned that it's just a movie, and that the real world doesn't operate according to Lucas's fantasies If it did, murder cases might be completely unworkable, given that we'd never know whether one assailant ever shot or not
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AWOL
40 Point Warrior
Warning: Kissing Chihuahua On Head Causes Sporadic Pooping, Urination, and Biting
Posts: 820
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Post by AWOL on Oct 24, 2007 13:23:30 GMT -5
YB - I love your Spock-ish answers!! Stats have a time and place, and I heartily see the value in them. But I'm going to say that the difference between winning and losing a game, and all points of conflict for that matter, is based on some things that are completely immeasurable - ingenuity, wisdom, patience, and persistence. These things are the "stuff" that beat the odds and throw numbers and stats to the wind. While I find all that statistical stuff curiously fascinating, I can guarantee you that I can figure out a way to beat any team with the crappiest, or "statistically challenged," group of Attacktix figures. (Unfortunately - and conveniently! - I won't have the opportunity to demonstrate this next year since I cannot make it to the Tixcon) But I do understand your perspective and absolutely love the presence you give to this forum (I know this was discussed a while ago in another thread, but now I'm really caught as to whether you or Grievous resembles Spock the most!).
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Post by Cona Chris on Oct 25, 2007 8:04:29 GMT -5
YB - I love your Spock-ish answers!! Stats have a time and place, and I heartily see the value in them. But I'm going to say that the difference between winning and losing a game, and all points of conflict for that matter, is based on some things that are completely immeasurable - ingenuity, wisdom, patience, and persistence. These things are the "stuff" that beat the odds and throw numbers and stats to the wind. While I find all that statistical stuff curiously fascinating, I can guarantee you that I can figure out a way to beat any team with the crappiest, or "statistically challenged," group of Attacktix figures. (Unfortunately - and conveniently! - I won't have the opportunity to demonstrate this next year since I cannot make it to the Tixcon) But I do understand your perspective and absolutely love the presence you give to this forum (I know this was discussed a while ago in another thread, but now I'm really caught as to whether you or Grievous resembles Spock the most!). Fascinating.
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Post by superflytnt on Oct 25, 2007 11:11:03 GMT -5
Ok guys, the statistics are fallacious to begin with, and let me point out why:
The statistics WOULD be applicable provided that the wheel only turned when moving, and only in one direction, AND if the spots were evenly distributed, such as White, Black, White, Black OR White, White, Black, White, White, Black.
The reason I say this is as follows: Take a figure with 50% like Tion Medon. He is theoretically to come up white 50% of the time. If this was evenly distributed, then it is possible to plot when he will come up, and at what point, based upon linear, one-way tixing. His actual spaces are B,W,B,B,W,B,W,W,B,W,W,B,B,W,W,W,B,W,W,W,B,B,B,W,B,B. Although there are indeed 13 White and 13 Black spaces which indicates on PAPER that he will come up 50% of the time, this ONLY assumes that he is moving in one direction and there are no changes in the order of tixing.
The problem with the statistic is that the spaces are NOT evenly distributed, and even though there are 26 set TIX spaces this is not the case in gameplay. There are INFINITE tix spaces, as you may move forward or backwards, and there are cases on some figures (recover) that when they come up white the tix wheel is randomized. Hence, if one wanted to move forward 3 tix, then spin the figure 180 degrees, move 3 tix, rinse and repeat, there are in actuality only 3 tix spaces (on the bottom) that ever see the light of day and there is no way of actually knowing the chance of it coming up, hence each space has a 1 in 3 (33%) chance of coming up. In a figure that was evenly distributed, you'd have a 33% chance of one color, and a 66% chance of the other.
Another problem is that since the figures are randomized at points in the game and DO NOT generally have an evenly distributed pattern on the wheel, there is no finite start point and finite end point to the tix wheel. If you start at "0" and take 50 steps during the game, in a straight line, you STILL do not know what the percentage truly is as you'd have to know what color the space was originally, the order of the distribution to determine what percentage of the time the figure will come up white. In an evenly distributed figure, you could say easily that if you start on white and end on black in 26 turns, you could extrapolate which color will come up at the end of 50 steps, assuming they were in a straight line. In the REAL WORLD, unless you know the order and only move in one set direction you can never truly have an accurate representation of the percentage.
The only TRUE way of getting a percentage of probability is to play an entire game out, and at each tix step you take turn the figure over and count the times that it comes up white and divide it by total tix steps taken.
So, all that being said, there is no true way to know what the percentage is, only what it's theoretical potential percentage is, which is a good guideline to follow to determine feasability of useful power activation, no more, no less.
We all know that Obi Wan has a 69% white, but how many times has he recovered 1 times in a game, proving that he really only came up 50% of the time (once white when he recovered, and once black when he died) and conversely came up 4 times white in a row, proving his percentage is indeed 80% (4 whites to recover, 1 black when he died). I've even had him come up (much to the chagrin of Chris) 6 times in a row, giving him a whopping 85+% white ratio, better than Yoda!
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Whiz Kid
30 Point Captain
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Posts: 237
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Post by Whiz Kid on Oct 25, 2007 13:21:18 GMT -5
I always feel left out when geek talk turns to math. When math comes up, I generally differ to others or use a humorous excuse when I (invariably) get an equation wrong. Something in the nature of "I'm an English major. We don't DO math!" or "Hello? English major! Numbers scare me!" Lucky for me the sig other is in marketing, and between that and my aversion to the topic, will likely never ask me to balance the checkbook.
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Post by superflytnt on Oct 25, 2007 14:29:07 GMT -5
LOL, me too. I majored in English lit, then education, then childhood pschology. Now I'm a salesman. WTF.
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Post by YodaBreaker on Oct 25, 2007 22:43:19 GMT -5
YB - I love your Spock-ish answers!! *arching eyebrow* Indeed. No, wait...wrong universe... At any rate, just wait - you won't be disappointed. I swear, composing this answer over the course of a few hours was probably not quite worth the ire of my students at having their papers be another day late. Oh well - I justify this to myself by realizing I'll have to teach stats next semester, so this helps me iron out some probability theory. I agree that they may alter the local probabilities, but they won't change the figure's global probability a whit. Only painting the underside of the Tix wheel will do that. I'd say that you listed your "immeasurable" variables in roughly reverse order from their actual measurability, though wisdom and ingenuity should likely be switched. I could measure persistence rather easily - either using Cloninger's TCI (in which persistence is theorized - incorrectly, as the data turn out - to be a character trait) or something more defensible, like the time a person takes to give up on a series of various unsolvable or nearly unsolvable tasks. More time spent = more persistence. Patience might be measured across a series of various delay of gratification tasks, assuming that the active ingredient in patience is the ability to delay gratification. More frequent ability to delay gratification = more patience. One might also choose to include tasks that promise reward only after enduring aversive physical stimulation (e.g., electric shock) or social stimulation (e.g., heckling), though those might start tapping "persistence" as much as "patience". Ingenuity can be measured by the ability to solve correctly any number of " lateral thinking" puzzles, situational puzzles, or puzzles requiring the overcoming of functional fixedness that demonstrate divergent thinking. Wisdom could be measured by assessing the degree to which a person is able to draw knowledge from a number of different domains to form a unified whole that is more than the mere sum of its parts, though this could be challenging to assess. Hee...and I'd love to see ya try that out I won't argue that it's impossible to beat the "best" team in any situation with a crappy team for that same situation - I'll simply argue that at least 90 times out of 100, and probably more like 95-99 times out of 100, the crappy team will lose. I'm Captain Kirk! I'M...CAPTAIN KIRRRRK! But seriously, I enjoy hearing your intuitionist perspective, too, especially inasmuch as it's not how I think about things. Ok guys, the statistics are fallacious to begin with, and let me point out why: Or...not Simply put, nope. Especially if you have a random grind each time a figure is put into play - which is why the random grind is so important to this game. With that assumption, and some assumptions detailed below, the stats are applicable no matter how frequently or infrequently one moves, no matter what the distribution patterns of the white and black spaces on the bottom of the Tix wheel. I think the confusion here stems from a confusion between the naïve probability that a given event will happen (which is represented by the number of white spaces / 26 in this game and is all that's knowable about that probability from the standpoint of the honest player), an empirically derived probability distribution for a small number of samples around the entire distribution (such as might occur over the course of a game with a single Recover figure), and the probability that one any single Tix will actually yield a white space (which will empirically be 1 or 0). The first of these is knowable from the basic statistics and is a zero-to-one ratio. The second is a count (either of stand-ups or activations of a number of figures with identical special power ratios) that's essentially unknowable - though its value will tend to be centered on the ratio of white to black spaces, its actual value will be substantially influenced by the large sampling error inherent in small samples. The third is the outcome of a single dichotomous trial that can either be a 1 or a 0. The set of assumptions asserted in the last sentence are inaccurate, as I describe in the section below this. Again, with a random grind, even with a perfectly evenly distributed set of white and black spaces, and no other information, the end probability is still going to be 50%. The problem with a perfectly even distribution of white and black spaces is that on the top of the Tix wheel is another set of perfectly evenly distributed spaces that change in color from red to non-red. Thus, these probabilities are no longer independent. In fact, they're perfectly linked. Let's assume that the top and bottom of a Tix wheel goes like this: t: R W R W R W R W R W R W R W R W R W R W R W R W R W b: W B W B W B W B W B W B W B W B W B W B W B W B W BIt's relatively easy to see that every time the top side of the wheel is red, the bottom side is white; every time the top side of the wheel is white, the bottom is black. In the notation of conditional probability, P(bW | tR) = 1, P(bW | tW) = 0, P(bB | tR) = 0, P(bB | tW) = 1. Now, let's assume a more random distribution of white and black bottom spaces with the evenly-spaced red and white top spaces, though each still has a 50% independent probability. t: R W R W R W R W R W R W R W R W R W R W R W R W R W b: B W B B W B W W B W W B B W W W B W W W B B B W B BNow, P(bW | tR) = .38, P(bW | tW) = .62, P(bB | tR) = .62, P(bB | tW) = .38. However, it's still apparent that a special power activation is more likely (.62) when the top side of the wheel is white, and it's less likely (.38) when the top window is red. Thus, for the best possible outcome for the defender, the defender should always stop moving this figure when its top window has white text. For kicks and giggles, here's one of the best possible distributions to ensure that the top wheel provides as little information as possible about the bottom wheel (starting with a naïve probability of .50 white): t: R W R W R W R W R W R W R W R W R W R W R W R W R W b: B B W W B B W W B B W W B B W W B B W W B B W W B WNow, P(bW | tR) = .54, P(bW | tW) = .46, P(bB | tR) = .46, P(bB | tW) = .54. Thus, it'd be slightly better to stop this figure when its top wheel displays red text (.54 probability of being white) than when it displays white text (.46 probability of being white). It's only possible to have a completely uninformative Tix wheel top if the bottom wheel has an even number of white (and hence black) spaces. I call this a "well-designed Tix wheel" because it maximizes the randomness inherent in the game. For example, let's assume that there are 14 white spaces instead of 13 in the above example (for a naïve probability of .54 for white): t: R W R W R W R W R W R W R W R W R W R W R W R W R W b: B B W W B B W W B B W W B B W W B B W W B B W W W WNow, P(bW | tR) = .54, P(bW | tW) = .54, P(bB | tR) = .46, P(bB | tW) = .46. Thus, there is no way to predict whether the bottom window will be black based on the color of the top window (.54 bottom white probability if the top is red, .54 bottom white probability if the top is white) any more than the original naïve probability of .54. Hence, the 'bro should have always used even numbers of white spaces on the Tix wheel (and probably should have used a 28 Tix wheel to allow for a 50% probability to have an even number of white spaces) to ensure that the conditional white probabilities would be minimally different from the naïve white probability. Unfortunately, I doubt they give significant consideration to the distribution of white/black spaces on the bottom side of the Tix wheel with respect to the white/red spaces on the top side of the Tix wheel. I'd prefer that they create a single well-designed distribution of white/black spaces for each probability and just stick that on each figure. Not incidentally, this is why I think the addition of the “extra Tix” on the top wheel is a terrible idea, inasmuch as it dramatically increases the conditions to which conditional probabilities can be applied. Taking our marvelously well-designed Tix wheel with a .54 white probability, but fouling it up with a set of “2 +1 Tix, 1 -1 Tix” spaces: t: R + R W R W R W R W + W R W R W R W R - R W R W R W b: B B W W B B W W B B W W B B W W B B W W B B W W W WThe first + is red, the second is white, and the – is white. Now, we've got 12 – yes, 12! – conditional probabilities to consider instead of 4. Namely, P(bW | tR0) = .42, P(bW | tR+1) = 1, P(bW | tR-1) = X, P(bW | tW0) = .45, P(bW | tW+1) = 0, P(bW | tW-1) = 1, P(bB | tR0) = .58, P(bB | tR+1) = 0, P(bB | tR-1) = X, P(bB | tW0) = .55, P(bB | tW+1) = 1, P(bB | tW-1) = 0. Notice how the defender now knows there will always be a white bottom space when there's a top red “+1 Tix” space and the white “-1 Tix space”; s/he also knowns there will always be a black bottom space when there's a top white “+1 Tix” space. Technically, I suppose there are only 10 real conditional probabilities, because there's no red “-1 Tix” space, but dang, does it make it nasty. In this case, with good Tix mapping, once a defender encounters the red “+1 Tix” or white “-1 Tix” space, that defender could just keep moving the figure so that it always ends up on that space and hence always has its special power activated when it's defeated (barring being struck across the playing field and having its Tixer reset – or having the attacker grind the figure as soon as it's knocked over). Ah, but assuming a random grind and a well-designed Tix wheel, you'd never know whether the figure you chose started out on a white or a black space. Thus, you'd actually have a 50% probability of having a 2/1 white/black ratio, and a 50% probability of having a 1/2 white/black ratio. Averaging those out, you'd have a 3/3 ratio – which exactly corresponds to the 50% naïve probability. Assuming a random grind and a well-designed Tix wheel, similar results would be obtained, no matter how few or many Tix you grind, no matter how whites and blacks are distributed along the Tix wheel. Again, no. Assuming a well-designed Tix wheel and a random grind, you'll have no way of ever truly knowing anything more than the naïve probability. Recall the difference between the first type of probability I mentioned in the first section of my reply to superflytnt (ratio of white to total spaces) and the third type (outcome of a single dichotomous trial). If you take a limited frequentist approach to probability, then this statement is true, if not tautologous. However, a standard frequentist or a naïve Bayesian approach to probability (that is, with no posterior information to modify the initial prior probability) would say that the probability is always the ratio of white spaces to total spaces. Only if you substitute the second type of probability (count of events) for the more proper first type (ratio of white to total spaces) for the “true” probability. Well, the Poisson distribution (which is typically the appropriate distribution to consider for counts) would suggest that with Starter 2 Kenobi's mean of 2.25 activations per game (18 white / 8 black), the probability of having exactly 1 activation is 24%, of exactly 4 activations is 11%, and of exactly 6 is 2%. Again, it's important not to confuse activation counts that are strongly influenced by sampling error with the long-run probability.
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Post by superflytnt on Oct 26, 2007 15:32:10 GMT -5
Jeeeeez louise. You need to get another hobby besides higher level mathematics. Maybe spend time with the wife or something. Attempt procreation or something! ;D
You can 'intellectualize' this as much as you so deign necessary, but the fact remains that irrespective of the correleation of the TOP paint to BOTTOM paint (which I care absolutely nothing about) AND irrespective of the randomization, unless the figure has an evenly distributed W/B/W... set of spaces you will never know the probability of the figure coming up white because of the nature of the gameplay, variables in movement, and the distribution of spaces.
Like I said, if you move forward 3 tix, then backward 3 tix after rotating 180 degrees, only 3 spaces are ever capable of being displayed. This makes the possibilities only 100, 66, or 33%. Period. Also, if the figure is not evenly distributed, if the figure moves 6 spaces and is killed, there are only 6 possible percentages of probability, and you'll never know them unless you know the start point and the distribution. Period.
Hence, it is safe to say that a 8 or 15% trooper will likely NOT come up white twice in the same game based upon the probability. It is also safe to say that a figure with a 69% percentage is MORE likely to come up than one with a lower percentage. It is NOT entirely safe to say that a figure with a 69% percentage will ever come up 69% of the time. The only safe, accurate assumption is that the published percentage is merely a GUIDELINE to help players determine what figures will THEORETICALLY be capable of producing a white spot upon defeat RELATIVE to other figures published percentages.
Hence, the percentages listed ARE INDEED fallacious in my view as there are so many distributions, variances in gameplay, and possible scenarios that basing your gameplay entirely upon them would be the height of absurdity as they are NOT accurate.
I guess, to simplify, my argument comes down to this: If you take a figure like S2 Starter Obi Wan with a 69% white ratio, and run him 26 spaces forward, YES, he has a 69% chance of coming up. If you run him 13 spaces forward, NO, he does NOT have a 69% chance of coming up because the spaces are not evenly distributed (nor can they be). If you take the figure and run him 5 forward, rotate him and move 5 backward (but in the same initial direction) he is still not 69% probable of coming up white.
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Post by YodaBreaker on Oct 26, 2007 17:27:28 GMT -5
I think the fundamental disagreement here stems from notions of what's knowable from the Tix that have gone by. Your simplified argument ignores the fact that you're sampling only a subset of the spaces on the figure - a subset whose composition can't be known in advance if you're using a random grind and a well-designed Tix wheel. Thus, unless you're looking at the bottom of the figure after each Tix and are actually constructing an empirical sampling distribution from the third type of probability I discussed above, you have no chance of knowing what part of your Tix wheel from which you're sampling. I refer you to this paragraph: You can expand that reasoning out to 13, 26, 429, or any number of Tix with any probability of white spaces coming up - it'll still converge on the true probability out of mathematical necessity. In fact, the example above shows that you won't even know the precise probability of a 50/50 figure coming up white, even if you know that the Tix are evenly distributed. In essence, your example above assumes that the precise distribution of Tix is knowable to the player; if one plays the game in a standard fashion with random grinds and well-formed Tix wheels, it isn't. Thus, in the standard condition of ignorance about the precise spaces Tixing by on the bottom surface of the Tix wheel, the probability of Starter 2 Kenobi coming up white is 69%, whether you move no Tix throughout the entire game or 829 Tix, whether you move all in one direction or jigger him forward and backward randomly, and whether the white and black spaces are relatively evenly distributed along the Tix wheel or completely clumped. I never argued that the special probabilities should be used as direct arbiters of how many special power activations a given figure must have in a game. Indeed, if one were to do that, one would completely negate the notion of random game mechanics, and you might as well just use counters to determine when or how often a particular figure should be allowed to activate its special power when knocked down. The argument to which I object is that the statistics are somehow fallacious or inaccurate. To me, this is like arguing that casinos operate on a fallacious or inaccurate business model because some people win the big jackpot. Over the long run (and in probability theory, the long run is typically infinitely long, though a sufficiently large sampling distribution might profitably substitute for infinity), the house still wins because the probabilities and adjusted payoffs are not fallacious or inaccurate ;D Also, if you didn't "care absolutely nothing about" the top part of the Tix wheel, I doubt you would have denounced it with such vehemence. I brought up the whole conditional probability argument to demonstrate another limit on the assumption of the random grind being sufficient to make the naive probability one's best estimate as to the likelihood of a given figure coming up white on a single defeat.
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Post by superflytnt on Oct 26, 2007 20:22:08 GMT -5
LOL. You misunderstand me completely. In relation to this discussion, the discussion of the realistic probabilities versus the published ones, I am assuming that the player cannot know the correlation between the top and bottom tix wheel and "Care nothing about the top wheel". When looking at cheating, and the ability to do so, then I believe most of us care about the correlation to top and bottom, and 'preloading' figures. But in the purview of this discussion, the top wheel is not a factor in my argument.
So, essentially we'll agree to disagree on some points, and agree to agree on others. My point is simply that if there WERE no top red/black wheel, and you had a figure with "X" percentage, that percentage is only valid if the figure moves it's full 26 tix. If the figure moves more, or less, than the 26 tix, then you are not taking advantage of the full field of possibilites and thus the probability of the spaces coming up white is not as published. No more, no less. And on this, I think we'd disagree. ;D I completely see how you're looking at it, logically and mathematically, and I am looking at it from a nearer point of view. Yes, the global percantage will always be "X", and I agree. Where we differ is that I believe that the local percentage is not necessarily that same "X" percentage if you have a figure that does not move the full 26 rotation term. It may be more, it may be less, it may even be "X", but it is not predictable and is not necessarily as published. That's all I'm saying.
My reasoning is this: If you take the entire set of 26 spaces, and only move 7, there could be anywhere from 0-7 white spaces in that slot on the wheel. When looking at the entire wheel, YES INDEEDAROONY there would be a "X" percentage of hitting that jackpot. But is the probability still "X" percent for that subset of 7 spaces? I would argue not that it isn't, but that it is unknowable, and not finitely "X". I hope you see where I'm coming from and I'm being clear.
Either way, kudos on the statistical analysis! And when I was speaking of "choosing figures based upon %", remember that I am not only talking with you YB, but the entire audience who may read this. The debate is indeed open to all, not just us old folks! There was no implication that you had said that, just a word of advice to the readers.
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Post by Turkish Van Cat on Oct 27, 2007 3:06:02 GMT -5
I'll try . I haven't taken stats yet, and YB is obviously quite significantly more knowledgeable in the subject than me, but I am good at math and I know a little bit about probability, so I'll try and add myself to this conversation. My theory is that in the end, the overall probability is the one that matters. Here's my reasoning: Suppose that S2 Starter OWK gets to move 0 tix, so he only has one window to choose from. It can only be white, or not white, so it's easy to see where the probability comes in. For all we know, that window can be any of his 26 windows, of which 18 are white, so there is a 9/13 probability that he will be white. On a subset of 7 (from your example), the possible ratios of white windows to all windows are indeed 0, 1/7, 2/7, ..., 7/7. If you move that figure only on that set, those are indeed the only possible ratios for that OWK in that instance. However, each of those seven windows has a probability of being white itself. From my first example, the probability of any random window is 9/13. Since I don't know OWK's tixmap, each of those seven windows is pretty much random to me. So there's a 9/13 probability of the first window being white, 9/13 for the second window, 9/13 for the third window.... So for any of those seven windows, the probability of any one of them being white is 9/13. The same goes for any number in a subset of tix, since they are all random. Now I think I do understand what you're saying Superfly. For the previous example, none of OWK's white/all ratios in a subset of 7 are equal to 9/13. In a subset of three, the only possible ratios would be 0, 1/3, 2/3, and 3/3. The ratios are not the probabilities though. The probability is still 9/13; it's just that for that particular trial, the outcomes would be restricted to those ratios, but with more trials, it would average out to 9/13. Even if a figure doesn't move the full 26 tix, for all a player knows, the current window could be any of the 26, so the overall ratio still holds. Because of all this, in the end, its the overall probability that matters and that affects gameplay, which I believe is the crux of the matter. I concur. You said it took you several hours to do that? I'll send kudos to both of you for the nice debating that's kept me entertained, occupied and up till 1:00 this evening. ;D
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Post by Radar on Oct 27, 2007 15:00:40 GMT -5
To me, the overall probability is the significant number, but to be complete honest, some of what is being discussed is over my head.
I will add though that I assume (I haven't made a tix map) that once the figure is defeated, and we know the bottom wheel is white, it would make sense that once could alter the likelihood of getting another white by moving a certain # of spaces. An analysis of the tix map may show that (theoretically) moving 9 spaces after a white has a higher probability of returning a white than moving 10. But without making a tix map, it is just a theory.
Just my 2 cents.
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warlordofmars
30 Point Captain
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Post by warlordofmars on Nov 3, 2007 15:03:52 GMT -5
Isn't the real point that S4 Vader kicks S1 Vader's rear end?
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Post by superflytnt on Nov 7, 2007 10:09:01 GMT -5
I like S1 better because it gives me a reason to play a sith squad.
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