For my own amusement I also wanted to figure out the probability of an 18 on 4d6 with a throwaway, but it's a friday afternoon and my brain hurts.)
It's fairly easy.
And 18 on 4d6 results from rolls 6-6-6-x where x is anything. Therefore, there are 6 possible rolls to get an 18. Divide that by the number of possible rolls and voila!
For my own amusement I also wanted to figure out the probability of an 18 on 4d6 with a throwaway, but it's a friday afternoon and my brain hurts.)
It's fairly easy.
And 18 on 4d6 results from rolls 6-6-6-x where x is anything. Therefore, there are 6 possible rolls to get an 18. Divide that by the number of possible rolls and voila!
noooooooo
There are 21 possible rolls. 6-6-6-x, 6-6-x-6, 6-x-6-6, x-6-6-6, and 6-6-6-6 (where x is 1 to 5). For the same reason that there are 3 ways to roll a 10 on 2d6: 4-6, 5-5, 6-4.
EffStarStarStar on
0
Options
Mr_Rose83 Blue Ridge Protects the HolyRegistered Userregular
For my own amusement I also wanted to figure out the probability of an 18 on 4d6 with a throwaway, but it's a friday afternoon and my brain hurts.)
It's fairly easy.
And 18 on 4d6 results from rolls 6-6-6-x where x is anything. Therefore, there are 6 possible rolls to get an 18. Divide that by the number of possible rolls and voila!
noooooooo
There are 21 possible rolls. 6-6-6-x, 6-6-x-6, 6-x-6-6, x-6-6-6, and 6-6-6-6 (where x is 1 to 5). For the same reason that there are 3 ways to roll a 10 on 2d6: 4-6, 5-5, 6-4.
Right, so 21 ways to get triple sixes from 6^4=1,296 possible rolls gives 1,275:21
Divide both sides by 21 to give odds of ~61:1 or 1 in 62 which easily beats 1 in 216 from 3 dice...
Which would still mean that only every 8-9th character rolled would have any 18s to start...
I always find it helps immensely in most games to get a good understanding of probabilities involved in D6s. For example, in Warhammer 40K a unit with a twin linked weapon firing at BS2 (EG: a Tau gun drone) is actually better than a unit firing non-linked at BS3. A lot of people over / underestimate the value of units because of things like this.
.
Something very similer was the reason for the Portent thread I mentioned before. It was stated that the Machine Spirit firing the Twin linked HB on a Land Raider was as good as a Space Marine firing one. 2/6+2/6 (BS2 TL) = 4/6(BS4). But it was pointed out by math that the TL BS 2 to hit Probability is actually 5/9 not 4/6(or 6/9). So a Space Marine still has a slightly better Probability to hit than the Machine Spirit.
The thing that I really took away from this article is that since no artificial random number generator(including Dice) is truly random, than the Statistics of a system can vary from the Probability of a system. This means that if you prove Statistically that your Machine Spirit is actually better than your Space Marine, it doesn't mean you are wrong, it means your dice roll more 5s and 6s than Probability dictates. This of course also means that basing your decisions on Probability isn't absolute as your Statistics CAN vary based on the bias of the dice you are using.
Moral of the story: ITS A GAME, stop worrying about abstract math and play to have fun.
The thing that I really took away from this article is that since no artificial random number generator(including Dice) is truly random, than the Statistics of a system can vary from the Probability of a system. This means that if you prove Statistically that your Machine Spirit is actually better than your Space Marine, it doesn't mean you are wrong, it means your dice roll more 5s and 6s than Probability dictates.
I don't think I follow you. How do you prove something statistically? If I were to take a d6 and roll it 60 times, could I say "A roll of 2 came up 12 times when it should have only come up 10, therefore I have proven that this die rolls 2s more often than the other numbers"? Of course not. We all know that a perfectly random die can get 12 of the same number on 60 rolls. In fact, the odds of that happening are pretty decent. Calling a die not "truly random" is a bit of a copout.
If someone says "I did 100 attacks with the Machine Spirit and 100 attacks with a Space Marine, and the Machine Spirits did better", that person isn't wrong. But if someone uses that example to try to prove that the Machine Spirits are better, then yes they are wrong. They can be mathematically proven wrong. And it doesn't prove that there is anything wrong with their dice either. It is improbable but not impossible for the Spirit to outperform the Marine given a finite number of trials. Naturally, the more trials you do, the lower the probability that the better unit will lose to the other one. But there is no point at which the probability becomes zero... no point at which you can say "I have proven it."
I think what he was trying to point out is that there's no such thing as an absolutely perfect dice; it always has imperfections that affect the outcome. Heck, just the differing number of dots per side screws with it. Of course, these differences are so imperceptibly small that they don't really matter, but all probability problems, mathematically speaking, use a hypothetical perfect dice that you wont' find in the real world.
I think what he was trying to point out is that there's no such thing as an absolutely perfect dice; it always has imperfections that affect the outcome. Heck, just the differing number of dots per side screws with it. Of course, these differences are so imperceptibly small that they don't really matter, but all probability problems, mathematically speaking, use a hypothetical perfect dice that you wont' find in the real world.
Correct. My whole point was that using Statistics of real world dice to infer a universal conclusion about a units effectiveness is flawed. Even if there was a large enough data set and a significant deviation is observed to draw a conclusion from, it is only applicable to the system used to generate the data. Any significant deviance from the expected Probability must be attributed to a flaw in the data set, the likeliest flaw is the bias of an imperfect random number generator.
Conversely, using Probability to to infer a universal conclusion about a units effectiveness is also flawed. First, Probability assumes a perfect radomness, which does not exist in the real world. Second, Probability is only useful in predicting trends with large data sets, and not particually applicable to a game in which you roll a d6 typically less than 1000 times. Your example only reinforces my point that using math as an absolute to base your unit selections on is a flawed premise.
One of the baseline assumptions here about die rolling is that the value for any given die is 1-x, where is is the number of sides (such as 1-6, 1-8, or 1-20).
for most die, this is the case- but some games do different things. Betrayal at House on the Hill, for example, has these really need six-sided die with two 2s, two 1s, and two blanks. Part of the reason for doing this was to allow people to occasionally take "zero points of mental damage" without having to start adding plus and minus modifiers (such as "take two d4 of mental damage, minus two").
Not that this affects the probability discussion much here, but when I hear stuff like 10d2, it seems like an interesting compromise (allowing you to have values from 0-10).
On 10d2 where a die has a 1 or 2 value, the odds of a 20 would be (1/2)^10 (roughly 1 in 1 000 times). On 10dBetrayal, where a die has a 0, 1, or 2 value, the odds of a 20 would be (1/3)^10 (roughly 1 in 10 000 times). I have not enough brain to work out the numbers for, say, 18 or 19.
I think what he was trying to point out is that there's no such thing as an absolutely perfect dice; it always has imperfections that affect the outcome. Heck, just the differing number of dots per side screws with it. Of course, these differences are so imperceptibly small that they don't really matter, but all probability problems, mathematically speaking, use a hypothetical perfect dice that you wont' find in the real world.
Actually, with good dice (eg: in casinos) they drill the holes to different lengths and use a little bit of lead to ensure that it is very well balanced indeed depite the number of holes.
A really good set of d6s is, if rolled properly, so close to truely random that you are not going to notice the difference in the context of a game.
A really good set of d6s is, if rolled properly, so close to truely random that you are not going to notice the difference in the context of a game.
Right but gamers aren't going to do that, in fact they are going to do the opposite: Intentionally find dice that are flawed to roll more 6s. Over the course of their gaming career most gamers keep the dice that roll above average and stop using dice that roll below average.
ElderCat on
0
Options
RankenphilePassersby were amazedby the unusually large amounts of blood.Registered User, Moderatormod
A really good set of d6s is, if rolled properly, so close to truely random that you are not going to notice the difference in the context of a game.
Right but gamers aren't going to do that, in fact they are going to do the opposite: Intentionally find dice that are flawed to roll more 6s. Over the course of their gaming career most gamers keep the dice that roll above average and stop using dice that roll below average.
Damn right. There are a huge number of rituals associated with dice. I have my own set that I use and nobody gets to touch them. I recently found a set of antique stone dice at a local antique shop that have taken over for my old clear blue d6es, and I love them to death. They have a set of genuine antique ivory d6es there that I covet madly, but they are $10 a pop, so maybe after christmas or something...
And in my gaming circle, if anyone misses a session where they were expected to be, the next time they show up they have to use the dreaded pink dice. Nobody wants to use the pink dice. They roll like shit, and they are completely fagtacular.
Rankenphile on
0
Options
INeedNoSaltwith blood on my teethRegistered Userregular
A really good set of d6s is, if rolled properly, so close to truely random that you are not going to notice the difference in the context of a game.
Right but gamers aren't going to do that, in fact they are going to do the opposite: Intentionally find dice that are flawed to roll more 6s. Over the course of their gaming career most gamers keep the dice that roll above average and stop using dice that roll below average.
I suppose I'm a bit of an exception to that; I simply learned how to roll dice to increase the probability of my numbers coming up. Subtle control of the conditions you roll under can seriously affect how well (or poorly) you roll. Why do you think craps tables have high sideboards all around instead of simply at one end?
I'm especially good with d6s (I'm banned from playing Russia in Axis & Allies after I decimated Germany with my infantry), but I can do pretty well with d10s and d8s, too. d20s are a bit too spherical for precision rolling, but you can roll them to increase the odds you'll roll over 10.
I think what he was trying to point out is that there's no such thing as an absolutely perfect dice; it always has imperfections that affect the outcome. Heck, just the differing number of dots per side screws with it. Of course, these differences are so imperceptibly small that they don't really matter, but all probability problems, mathematically speaking, use a hypothetical perfect dice that you wont' find in the real world.
Correct. My whole point was that using Statistics of real world dice to infer a universal conclusion about a units effectiveness is flawed. Even if there was a large enough data set and a significant deviation is observed to draw a conclusion from, it is only applicable to the system used to generate the data. Any significant deviance from the expected Probability must be attributed to a flaw in the data set, the likeliest flaw is the bias of an imperfect random number generator.
Conversely, using Probability to to infer a universal conclusion about a units effectiveness is also flawed. First, Probability assumes a perfect radomness, which does not exist in the real world. Second, Probability is only useful in predicting trends with large data sets, and not particually applicable to a game in which you roll a d6 typically less than 1000 times. Your example only reinforces my point that using math as an absolute to base your unit selections on is a flawed premise.
I refute your claim that a die cannot be a perfect random number generator. I roll a die with a variable amount of force, at a variable height and variable angle to the ground. Can you predict what the outcome will be? No, not at all? Then it is perfectly random.
You say "a significant deviation is observed to draw a conclusion from", but that is a mistake. There is no such thing. There is no deviation so significant that a conclusion can be drawn. For any data set, there is a chance that a perfect random number generator could come up with that data set. For example... I flip a coin 5 times and heads comes up each time. Can I conclude that the coin must come up heads more often than tails? No. There is a possibility (1 in 32) that a perfectly fair coin would come up heads 5 times in 5 trials. Not even by flipping the coin 50 times could I definitively come to a conclusion about its fairness.
So as I was saying above, a die can be a perfect random number generator. If you test a die by rolling it 1000 times, and your data set has a "significant deviation" that shows 2s coming up more often than average, can you conclude that the die is imperfect and is more likely to come up 2? There's a chance that it is perfectly fair and that 2s came up more often as just an improbable fluke. There's a chance that it is unfair and comes up 3s most often, and that 2s came up more often as a very improbable fluke. You can't ever prove yourself right or wrong based on a data set.
Haven't used them yet, but I'm still trying to come up with a reason to pull them out for the party I'm GMing for.
You're GMing, and you didn't invite me?
You dick.
And also, people are stupid when it comes to numbers. Ask 10 people what the average roll on 1d6 will be...I'm sure at least two will tell you "three."
Last week, our GM rolled four consecutive ones on a d20. In front of his screen. 1 in 160,000 odds, there.
I'm just running a game for a few buddies every Friday, trying to get familiar with the game again since it has been about 12 years since any of us have played a real around-the-table RPG. Wait a while until we get shit settled and finish this campaign, I'm sure I'll end up throwing an all-nighter or two for the PA doodz.
I'm just running a game for a few buddies every Friday, trying to get familiar with the game again since it has been about 12 years since any of us have played a real around-the-table RPG. Wait a while until we get shit settled and finish this campaign, I'm sure I'll end up throwing an all-nighter or two for the PA doodz.
On 10d2 where a die has a 1 or 2 value, the odds of a 20 would be (1/2)^10 (roughly 1 in 1 000 times). On 10dBetrayal, where a die has a 0, 1, or 2 value, the odds of a 20 would be (1/3)^10 (roughly 1 in 10 000 times). I have not enough brain to work out the numbers for, say, 18 or 19.
For 19 I believe it would be 10*[(1/3)^9]*(1/3), but then again, what limited understanding of probability I had while taking the course has mostly faded away by now.
That sounds like cheating in the same way counting cards is cheating.
I can do that, too. But I prefer to win poker games on the strength of my reputation as "totally unpredictable." I actually won a $2,000 pot with a 7-2 off-suit when I rivered a 7 to make a full house (I flopped two pair, but would have lost to a better two pair). My friends prefer that I be more or less hammered if we play for large sums now.
I refute your claim that a die cannot be a perfect random number generator. I roll a die with a variable amount of force, at a variable height and variable angle to the ground. Can you predict what the outcome will be? No, not at all? Then it is perfectly random.
You say "a significant deviation is observed to draw a conclusion from", but that is a mistake. There is no such thing. There is no deviation so significant that a conclusion can be drawn. For any data set, there is a chance that a perfect random number generator could come up with that data set. For example... I flip a coin 5 times and heads comes up each time. Can I conclude that the coin must come up heads more often than tails? No. There is a possibility (1 in 32) that a perfectly fair coin would come up heads 5 times in 5 trials. Not even by flipping the coin 50 times could I definitively come to a conclusion about its fairness.
So as I was saying above, a die can be a perfect random number generator. If you test a die by rolling it 1000 times, and your data set has a "significant deviation" that shows 2s coming up more often than average, can you conclude that the die is imperfect and is more likely to come up 2? There's a chance that it is perfectly fair and that 2s came up more often as just an improbable fluke. There's a chance that it is unfair and comes up 3s most often, and that 2s came up more often as a very improbable fluke. You can't ever prove yourself right or wrong based on a data set.
I took debate, I know what you are trying to do. So your straw man arguments are not compelling to me. Your refutations are based on attributing an indefensible position to your opponent that was never stated by him.
Your statment : "There is no deviation so significant that a conclusion can be drawn." Simply tells me that you did not read the article that I linked to, as one of the pages was about determining when a random event generator was biased or when it was simply expected deviations due to random chance.
Before you claim that something can't be done, you should really be sure you aren't jumping in on a discussion about an guide on how to do it.
I took debate, I know what you are trying to do. So your straw man arguments are not compelling to me. Your refutations are based on attributing an indefensible position to your opponent that was never stated by him.
Your statment : "There is no deviation so significant that a conclusion can be drawn." Simply tells me that you did not read the article that I linked to, as one of the pages was about determining when a random event generator was biased or when it was simply expected deviations due to random chance.
Before you claim that something can't be done, you should really be sure you aren't jumping in on a discussion about an guide on how to do it.
So, you can yell "HIGH SCHOOL DEBATE TEAM STRAW MAN STRAW MAN" like anyone else who has ever found themselves on the losing side of an argument. Good show. (<-- This might ad hominem, but I feel okay about that.)
On the other hand, what you are doing is an appeal to authority, which is also a fallacy. You're implying that because my argument is contrary to what the article states, I must necessarily be wrong. Even if my statements were incompatible with the statements made in the article that you linked to, that would not make me wrong because the article's author is also capable of being wrong.
But what's even worse is that I don't disagree with the article. I admit that I didn't read it until just now. I said, "There is no deviation so significant that a conclusion can be drawn", and in the original context, 'conclusion' meant mathematical conclusion. In the article's example of Orc Nostril Hair drops, he says flat out "If out of those sessions, players are finding ONH a lot less or a lot more than 10% of the time, then you probably have a bug that is affecting your reward rates." Note the use of the word 'probably'. You simply cannot say that the random event generator MUST have a problem based on the statistical data; it can only be increasingly likely that the program is not performing correctly. Is it likely that a programming error is to blame? Is it a good idea to debug the program? Absolutely. I agree.
I'd like to know how you got your idea that no artificial random number generator is truly random. As far as I can tell, that isn't even remotely implied by the article. There is a brief mention of using CPU temperature as a random number seed instead of the CPU clock, and the note that no digitial random number generator is truly random, in the sense that there will eventually be a pattern after thousands or millions of repetitions from a CPU clock seed. He mentions that using a different method for generating a random number is done for the players' peace of mind... not because a pseudo-random number generator's statistics vary too greatly from what probability formulas dictate.
Out of what you've said so far, the statement that gets me the most is "since no artificial random number generator(including Dice) is truly random, than the Statistics of a system can vary from the Probability of a system." If you are implying that an imperfect random number generator is the cause (and here, I am pointing at the word 'since') of statistics deviating from the most probably outcome, I must continue to disagree.
I'm gonna back off the testosterone here, I wasn't trying to enter into an endless debate with you. I was trying to clarify my statements so that we could move the dialog along. My conclusions are: A) Probability and Statistics can be different and using either to base your unit purchasing decisions on is not the best idea. If you agree with the article, and you agree with my conclusions, I don’t really care that you disagree with the wording of my explanation of my thoughts. I am not going to try to defend your interpretation of what I meant. Yes, I can see how you came to your interpretation, but it seems to me that you are choosing to focus on a single word in my explanations and ignore what my point is just so you can argue with me. That just distracts from furthering the dialog of this thread.
Now that you have actually read it, do you have a question or comment about the article?
Are you really interested in discussing whether or not physical dice are accurate as random number generators?
You get out of a die as much as you put into it. If you hold a d6 half an inch above the tabletop with the 6 facing up, and then "roll" it by letting go, it's not random at all. If you hold it 4 inches above the table and drop it, it's still not very random. But if you properly roll a die by shaking it around in your hand a bit and then letting go in such a way that it rotates in the air a few times and then several more times as it bounces across the table before coming to a stop, then yes I'd say it can be completely random.
The whole idea behind a faceted die is that any number of miniscule factors are going to change the outcome of the roll. It is basically impossible to properly roll a die exactly the same way over and over. The direction and rotation and force are going to change a little bit each time because we just don't have that level of control over our muscles. It'll go a bit farther, maybe do one less rotation, or rotate around one axis a bit less and another axis a bit more. It will hit the table at a different spot that might have a higher coefficient of friction, or perhaps a lower temperature by half a degree. Innumerable factors are going to influence what face the die ends up on. One small change in the initial velocity completely changes the end result.
Since nobody (not even the person holding the die and making the roll!) knows what the speed, rotation, and angle of the next roll are going to be, the result of the next roll can't possibly be known with any amount of confidence. Therefore, it is a random roll.
You can't ever prove yourself right or wrong based on a data set.
Simple question:
Do you renounce every scientific discovery ever made for the same reason?
His thesis is such:
"One can not gauge the randomness of a number generation method by a set of results."
You have criticized his thesis as if it were:
"One can not gauge anything based on acquired data"
This, my fellow forumites, is a true straw man argument, though I'm not certain if it's deliberate or accidental. He has criticized a point other than that which was made. Note that he removed his quote from context. Anyone who had read it in context would clearly see that the quote was in reference to probability and the data sets derived from testing a proposed random method. It is vital when criticizing the point to criticize the point in it's entirety to avoid accidently making such an argument.
Assuming the argument was deliberate, from here, if Eff were to respond in the negative, Marty would most likely accuse him of denying his own thesis. His goal would most likely be to paint Eff as a solipsist.
You can't ever prove yourself right or wrong based on a data set.
Simple question:
Do you renounce every scientific discovery ever made for the same reason?
Not really. That quote was in reference to proving things that are contrary to mathematical fact. If someone showed experimentally that 2+2 = 4 (99% of the time) or 5 (1% of the time), naturally I would not believe a word of it.
And even scientific laws are only generalizations, unless they are mathematical definitions. The scientific community doesn't automatically accept something as truth just because there's never been a data set showing it to be wrong. And anyway, even if a data set is not absolute proof, that doesn't make it useless. If I flip a coin 50 times and get 50 heads, I may not have proven that the coin is biased to come up heads, but I sure as shit will suspect it and will refuse to use it for future coin flips.
You can't ever prove yourself right or wrong based on a data set.
Simple question:
Do you renounce every scientific discovery ever made for the same reason?
His thesis is such:
"One can not gauge the randomness of a number generation method by a set of results."
You have criticized his thesis as if it were:
"One can not gauge anything based on acquired data"
This, my fellow forumites, is a true straw man argument, though I'm not certain if it's deliberate or accidental. He has criticized a point other than that which was made. Note that he removed his quote from context. Anyone who had read it in context would clearly see that the quote was in reference to probability and the data sets derived from testing a proposed random method. It is vital when criticizing the point to criticize the point in it's entirety to avoid accidently making such an argument.
Assuming the argument was deliberate, from here, if Eff were to respond in the negative, Marty would most likely accuse him of denying his own thesis. His goal would most likely be to paint Eff as a solipsist.
Hah, you give me too much credit :P
To be honest, I didn't even read the quote tree - I was just browsing quickly and saw that statement and was like, "WTF is that?!"
Anyway, part of the issue here is "What do you define as proof?" You can use the Central Limit Theorem to say that, when sampling a random variable, with a large enough randomly sampled data set, the chances that average value on the data set is +/- k% of the true average value are less than e% (where the size of the data set you need is dependent upon k and e, obviously). Most scientific experiments take k=3 and e=5 or thereabouts. Ie, the chances that the result of the experiment is off by more than 3% are less than 5%.
Eff just made it sound too much like "You cannot draw any conclusions, ever, based on a data set," and that's simply not true. A perfectly valid conclusion would be something like, "I'm 99% certain that the true average value is within 3% of whatever value."
Since nobody (not even the person holding the die and making the roll!) knows what the speed, rotation, and angle of the next roll are going to be, the result of the next roll can't possibly be known with any amount of confidence. Therefore, it is a random roll.
You can't ever prove yourself right or wrong based on a data set.
Simple question:
Do you renounce every scientific discovery ever made for the same reason?
His thesis is such:
"One can not gauge the randomness of a number generation method by a set of results."
You have criticized his thesis as if it were:
"One can not gauge anything based on acquired data"
This, my fellow forumites, is a true straw man argument, though I'm not certain if it's deliberate or accidental. He has criticized a point other than that which was made. Note that he removed his quote from context. Anyone who had read it in context would clearly see that the quote was in reference to probability and the data sets derived from testing a proposed random method. It is vital when criticizing the point to criticize the point in it's entirety to avoid accidently making such an argument.
Assuming the argument was deliberate, from here, if Eff were to respond in the negative, Marty would most likely accuse him of denying his own thesis. His goal would most likely be to paint Eff as a solipsist.
Hah, you give me too much credit :P
To be honest, I didn't even read the quote tree - I was just browsing quickly and saw that statement and was like, "WTF is that?!"
Anyway, part of the issue here is "What do you define as proof?" You can use the Central Limit Theorem to say that, when sampling a random variable, with a large enough randomly sampled data set, the chances that average value on the data set is +/- k% of the true average value are less than e% (where the size of the data set you need is dependent upon k and e, obviously). Most scientific experiments take k=3 and e=5 or thereabouts. Ie, the chances that the result of the experiment is off by more than 3% are less than 5%.
Eff just made it sound too much like "You cannot draw any conclusions, ever, based on a data set," and that's simply not true. A perfectly valid conclusion would be something like, "I'm 99% certain that the true average value is within 3% of whatever value."
I though it might have been accidental. I probably wouldn't have pinted it out except that false straw man accusations (see above) are a pet peave of mine and I thought an example of a true one would be appropriate.
Taken out of context in the way it is in your quote, I can see how one would draw that conclusion. The formula you propose is useful, but to get k at 3 and e at 5, you need a larger data set than is likely to be observed through normal play. even then, a perfectly random method can fall well outside of those ranges on occasion. In order for it to be useful, you need several sets each with a great many entries in each, so as to reduce the possibilty of a chance result. This still isn't absolutely certain, but is close enough to be reliable, but is already well outside what is practical in a gaming context. Would you collate a dozen sets of one thousand throws each for every one of your dice, and expect the rest of your group to do the same?
It's so much easier just to get a die spinner. If the variables you're putting into the throw (die balance, distance of throw, intial spin, aned s on) are fair, the die can be deemed random enough.
For k = 3, e = 5, the rule of thumb is just over 1000 random observations. This is why most nationwide polls happen to poll (randomly! or so they say) that amount of people. The same figure applies to dice rolls as well.
(edit - actually, that figure might have been for k = 5 and e = 5. It's been a while :P)
Yeah, and you'll never get that many consistantly recorded observations within a gaming context, much less enough sets like that to determine the status of possible outliers. Even then you'll get the occasional wonky result.
Probability studies are innately uncertain. As soon as you call a thing a probability study, you are admiting a rather large chance (as compared to most fields of scientific study) that you're data is a result of a fluke, especially when you're discussing things with as many required uncontrollabe variables as dice rolling, cpu clock-based number generaters, and the like.
As you increase the size of a data set, a given trend becomes more likely to be the result of a flaw, but it doesn't eliminate the possibility of a fluke. That's why an e value is necesary, and e doesn't get anywhere near zero until the number of results just get plain ridiculous. Even then all you've shown is that the method tends to give results similar to what one would expect in a random system, not that the system is truly random.
You could fund a small team of researchers to determine the fairness of a set of dice over the next six months and get a probable result, or spend five bucks on a die spinner and know to a similar degree of certainty right now. The methodology required to reach a reasonable degree of certainty using resultant data just isn't practicable. Testing a die for even weighting and enacting rules that increase the variables that determine the outcome evenly across all possible results is rather easily done and can grant a higher degree of certainty.
My friends and I were bored one day and we were trying to come up with a good system that incorporated aspects of point buy, with aspects of dice rolling, and best incorporated the D20 into the system. This is the crazy thing we came up with:
Roll a D4 and a D20. The D4 represents the numbers 13, 14, 15, and 16 (or 12+d4). The d20 represents the numbers between 1 and 20.
Multiply the result together. Hold this number. Once all stats have been rolled you can add up to and we usually say 8 points between your stats. This number is not choosen arbitrarily.
So A 1 and a 1 is 13. A 1 on the d4 and a 20 on the d20 is a 260, and you could choose to make the 13 into a 21, or the 260 into a 268, or some combination between them.
Take the square root of this number and round to the nearest integer. That's your stat.
It helps if you keep a copy of this table on hand, but a calculator also works. I recommend color coding the table and underlining combinations that can be upgraded. (So the first 7 numbers are all upgradeable, but a 2[d20]+4[d4] [32 total or an 8] is not)
I ran a computer program to work out average point buy, it actually isn't that bad, around 27ish iirc, Median is 12.5 but the Mode is 15. 3 values can score an 18 (so 3/80), but only a natural 20 and a natural 4 will get a pure 18. Further, no one is 'stuck' with a 4 as the lowest value you can get is a 4 upgradeable to a 5 (1, 1, with 8 points gives 21. 21^.5 is 4.58, rounds to a 5. This gives some people the ability to play with stats as low as 3, or bounce around with race and age combinations to achieve some interesting characters. You might want to set a final point buy limits of the system between say, 15 and 50, or 20 and 45 as the extremes are slightly more likely in this system.
Pretty neat system, most of the players seem to like it, though some just down right hate the complexity. Some people can get some wonky stats with it, but it's fun. Great when combined with "Roll for your strength, now roll for dex." I usually let players choose between a fixed point buy, this system, or 4d6.
I hope you all will tolerate my presense and questions. You are SO far over my head in all this, but I am writing a novel with a character who is having a statistics discussion about games. He's a genius kid whose Dad is a paid hacker to find holes in security for major corps and soem govt agencies. I only need a few comments in the exchange, but I'm thinking the kid is designing a game and talking to Dad and his partner, both computer wizards about either a problem or simply a few statistics.
I don't have to go into lots of detail as this is a romance and discussion is just for a dinner conversation in one scene. However, I would like it to sound intelligent/realistic, should someone well versed in this field read it.
If anyone is willing to help me out or if I could even quote some debate on this topic, it would be great. Then whoever volunteers to help me out could read the short discussion in my novel and let me know if I've totally screwed it up:)
I think the Writer's Block has a sticky thread specifically for requesting knowledge from people well-versed in the particular area. You should check it out.
Posts
That distorts the will of the die.
It's hard enough to tell what facet you're landing on, and you want to roll on a surface notrious for cocked dice?
It's fairly easy.
And 18 on 4d6 results from rolls 6-6-6-x where x is anything. Therefore, there are 6 possible rolls to get an 18. Divide that by the number of possible rolls and voila!
noooooooo
There are 21 possible rolls. 6-6-6-x, 6-6-x-6, 6-x-6-6, x-6-6-6, and 6-6-6-6 (where x is 1 to 5). For the same reason that there are 3 ways to roll a 10 on 2d6: 4-6, 5-5, 6-4.
Divide both sides by 21 to give odds of ~61:1 or 1 in 62 which easily beats 1 in 216 from 3 dice...
Which would still mean that only every 8-9th character rolled would have any 18s to start...
Nintendo Network ID: AzraelRose
DropBox invite link - get 500MB extra free.
Something very similer was the reason for the Portent thread I mentioned before. It was stated that the Machine Spirit firing the Twin linked HB on a Land Raider was as good as a Space Marine firing one. 2/6+2/6 (BS2 TL) = 4/6(BS4). But it was pointed out by math that the TL BS 2 to hit Probability is actually 5/9 not 4/6(or 6/9). So a Space Marine still has a slightly better Probability to hit than the Machine Spirit.
The thing that I really took away from this article is that since no artificial random number generator(including Dice) is truly random, than the Statistics of a system can vary from the Probability of a system. This means that if you prove Statistically that your Machine Spirit is actually better than your Space Marine, it doesn't mean you are wrong, it means your dice roll more 5s and 6s than Probability dictates. This of course also means that basing your decisions on Probability isn't absolute as your Statistics CAN vary based on the bias of the dice you are using.
Moral of the story: ITS A GAME, stop worrying about abstract math and play to have fun.
I don't think I follow you. How do you prove something statistically? If I were to take a d6 and roll it 60 times, could I say "A roll of 2 came up 12 times when it should have only come up 10, therefore I have proven that this die rolls 2s more often than the other numbers"? Of course not. We all know that a perfectly random die can get 12 of the same number on 60 rolls. In fact, the odds of that happening are pretty decent. Calling a die not "truly random" is a bit of a copout.
If someone says "I did 100 attacks with the Machine Spirit and 100 attacks with a Space Marine, and the Machine Spirits did better", that person isn't wrong. But if someone uses that example to try to prove that the Machine Spirits are better, then yes they are wrong. They can be mathematically proven wrong. And it doesn't prove that there is anything wrong with their dice either. It is improbable but not impossible for the Spirit to outperform the Marine given a finite number of trials. Naturally, the more trials you do, the lower the probability that the better unit will lose to the other one. But there is no point at which the probability becomes zero... no point at which you can say "I have proven it."
Correct. My whole point was that using Statistics of real world dice to infer a universal conclusion about a units effectiveness is flawed. Even if there was a large enough data set and a significant deviation is observed to draw a conclusion from, it is only applicable to the system used to generate the data. Any significant deviance from the expected Probability must be attributed to a flaw in the data set, the likeliest flaw is the bias of an imperfect random number generator.
Conversely, using Probability to to infer a universal conclusion about a units effectiveness is also flawed. First, Probability assumes a perfect radomness, which does not exist in the real world. Second, Probability is only useful in predicting trends with large data sets, and not particually applicable to a game in which you roll a d6 typically less than 1000 times. Your example only reinforces my point that using math as an absolute to base your unit selections on is a flawed premise.
for most die, this is the case- but some games do different things. Betrayal at House on the Hill, for example, has these really need six-sided die with two 2s, two 1s, and two blanks. Part of the reason for doing this was to allow people to occasionally take "zero points of mental damage" without having to start adding plus and minus modifiers (such as "take two d4 of mental damage, minus two").
Not that this affects the probability discussion much here, but when I hear stuff like 10d2, it seems like an interesting compromise (allowing you to have values from 0-10).
On 10d2 where a die has a 1 or 2 value, the odds of a 20 would be (1/2)^10 (roughly 1 in 1 000 times). On 10dBetrayal, where a die has a 0, 1, or 2 value, the odds of a 20 would be (1/3)^10 (roughly 1 in 10 000 times). I have not enough brain to work out the numbers for, say, 18 or 19.
Actually, with good dice (eg: in casinos) they drill the holes to different lengths and use a little bit of lead to ensure that it is very well balanced indeed depite the number of holes.
A really good set of d6s is, if rolled properly, so close to truely random that you are not going to notice the difference in the context of a game.
Right but gamers aren't going to do that, in fact they are going to do the opposite: Intentionally find dice that are flawed to roll more 6s. Over the course of their gaming career most gamers keep the dice that roll above average and stop using dice that roll below average.
Damn right. There are a huge number of rituals associated with dice. I have my own set that I use and nobody gets to touch them. I recently found a set of antique stone dice at a local antique shop that have taken over for my old clear blue d6es, and I love them to death. They have a set of genuine antique ivory d6es there that I covet madly, but they are $10 a pop, so maybe after christmas or something...
And in my gaming circle, if anyone misses a session where they were expected to be, the next time they show up they have to use the dreaded pink dice. Nobody wants to use the pink dice. They roll like shit, and they are completely fagtacular.
That's not a flaw that's luck.
I'm especially good with d6s (I'm banned from playing Russia in Axis & Allies after I decimated Germany with my infantry), but I can do pretty well with d10s and d8s, too. d20s are a bit too spherical for precision rolling, but you can roll them to increase the odds you'll roll over 10.
I refute your claim that a die cannot be a perfect random number generator. I roll a die with a variable amount of force, at a variable height and variable angle to the ground. Can you predict what the outcome will be? No, not at all? Then it is perfectly random.
You say "a significant deviation is observed to draw a conclusion from", but that is a mistake. There is no such thing. There is no deviation so significant that a conclusion can be drawn. For any data set, there is a chance that a perfect random number generator could come up with that data set. For example... I flip a coin 5 times and heads comes up each time. Can I conclude that the coin must come up heads more often than tails? No. There is a possibility (1 in 32) that a perfectly fair coin would come up heads 5 times in 5 trials. Not even by flipping the coin 50 times could I definitively come to a conclusion about its fairness.
So as I was saying above, a die can be a perfect random number generator. If you test a die by rolling it 1000 times, and your data set has a "significant deviation" that shows 2s coming up more often than average, can you conclude that the die is imperfect and is more likely to come up 2? There's a chance that it is perfectly fair and that 2s came up more often as just an improbable fluke. There's a chance that it is unfair and comes up 3s most often, and that 2s came up more often as a very improbable fluke. You can't ever prove yourself right or wrong based on a data set.
You dick.
And also, people are stupid when it comes to numbers. Ask 10 people what the average roll on 1d6 will be...I'm sure at least two will tell you "three."
Last week, our GM rolled four consecutive ones on a d20. In front of his screen. 1 in 160,000 odds, there.
Twitter | Facebook | Tumblr | Last.fm | Pandora | LibraryThing | formspring | Blue Moon over Seattle (MCFC)
I'm just running a game for a few buddies every Friday, trying to get familiar with the game again since it has been about 12 years since any of us have played a real around-the-table RPG. Wait a while until we get shit settled and finish this campaign, I'm sure I'll end up throwing an all-nighter or two for the PA doodz.
BTW, nice code work there, chief.
Twitter | Facebook | Tumblr | Last.fm | Pandora | LibraryThing | formspring | Blue Moon over Seattle (MCFC)
I took debate, I know what you are trying to do. So your straw man arguments are not compelling to me. Your refutations are based on attributing an indefensible position to your opponent that was never stated by him.
Your statment : "There is no deviation so significant that a conclusion can be drawn." Simply tells me that you did not read the article that I linked to, as one of the pages was about determining when a random event generator was biased or when it was simply expected deviations due to random chance.
Before you claim that something can't be done, you should really be sure you aren't jumping in on a discussion about an guide on how to do it.
So, you can yell "HIGH SCHOOL DEBATE TEAM STRAW MAN STRAW MAN" like anyone else who has ever found themselves on the losing side of an argument. Good show. (<-- This might ad hominem, but I feel okay about that.)
On the other hand, what you are doing is an appeal to authority, which is also a fallacy. You're implying that because my argument is contrary to what the article states, I must necessarily be wrong. Even if my statements were incompatible with the statements made in the article that you linked to, that would not make me wrong because the article's author is also capable of being wrong.
But what's even worse is that I don't disagree with the article. I admit that I didn't read it until just now. I said, "There is no deviation so significant that a conclusion can be drawn", and in the original context, 'conclusion' meant mathematical conclusion. In the article's example of Orc Nostril Hair drops, he says flat out "If out of those sessions, players are finding ONH a lot less or a lot more than 10% of the time, then you probably have a bug that is affecting your reward rates." Note the use of the word 'probably'. You simply cannot say that the random event generator MUST have a problem based on the statistical data; it can only be increasingly likely that the program is not performing correctly. Is it likely that a programming error is to blame? Is it a good idea to debug the program? Absolutely. I agree.
I'd like to know how you got your idea that no artificial random number generator is truly random. As far as I can tell, that isn't even remotely implied by the article. There is a brief mention of using CPU temperature as a random number seed instead of the CPU clock, and the note that no digitial random number generator is truly random, in the sense that there will eventually be a pattern after thousands or millions of repetitions from a CPU clock seed. He mentions that using a different method for generating a random number is done for the players' peace of mind... not because a pseudo-random number generator's statistics vary too greatly from what probability formulas dictate.
Out of what you've said so far, the statement that gets me the most is "since no artificial random number generator(including Dice) is truly random, than the Statistics of a system can vary from the Probability of a system." If you are implying that an imperfect random number generator is the cause (and here, I am pointing at the word 'since') of statistics deviating from the most probably outcome, I must continue to disagree.
Now that you have actually read it, do you have a question or comment about the article?
Are you really interested in discussing whether or not physical dice are accurate as random number generators?
The whole idea behind a faceted die is that any number of miniscule factors are going to change the outcome of the roll. It is basically impossible to properly roll a die exactly the same way over and over. The direction and rotation and force are going to change a little bit each time because we just don't have that level of control over our muscles. It'll go a bit farther, maybe do one less rotation, or rotate around one axis a bit less and another axis a bit more. It will hit the table at a different spot that might have a higher coefficient of friction, or perhaps a lower temperature by half a degree. Innumerable factors are going to influence what face the die ends up on. One small change in the initial velocity completely changes the end result.
Since nobody (not even the person holding the die and making the roll!) knows what the speed, rotation, and angle of the next roll are going to be, the result of the next roll can't possibly be known with any amount of confidence. Therefore, it is a random roll.
Simple question:
Do you renounce every scientific discovery ever made for the same reason?
His thesis is such:
"One can not gauge the randomness of a number generation method by a set of results."
You have criticized his thesis as if it were:
"One can not gauge anything based on acquired data"
This, my fellow forumites, is a true straw man argument, though I'm not certain if it's deliberate or accidental. He has criticized a point other than that which was made. Note that he removed his quote from context. Anyone who had read it in context would clearly see that the quote was in reference to probability and the data sets derived from testing a proposed random method. It is vital when criticizing the point to criticize the point in it's entirety to avoid accidently making such an argument.
Assuming the argument was deliberate, from here, if Eff were to respond in the negative, Marty would most likely accuse him of denying his own thesis. His goal would most likely be to paint Eff as a solipsist.
Not really. That quote was in reference to proving things that are contrary to mathematical fact. If someone showed experimentally that 2+2 = 4 (99% of the time) or 5 (1% of the time), naturally I would not believe a word of it.
And even scientific laws are only generalizations, unless they are mathematical definitions. The scientific community doesn't automatically accept something as truth just because there's never been a data set showing it to be wrong. And anyway, even if a data set is not absolute proof, that doesn't make it useless. If I flip a coin 50 times and get 50 heads, I may not have proven that the coin is biased to come up heads, but I sure as shit will suspect it and will refuse to use it for future coin flips.
Hah, you give me too much credit :P
To be honest, I didn't even read the quote tree - I was just browsing quickly and saw that statement and was like, "WTF is that?!"
Anyway, part of the issue here is "What do you define as proof?" You can use the Central Limit Theorem to say that, when sampling a random variable, with a large enough randomly sampled data set, the chances that average value on the data set is +/- k% of the true average value are less than e% (where the size of the data set you need is dependent upon k and e, obviously). Most scientific experiments take k=3 and e=5 or thereabouts. Ie, the chances that the result of the experiment is off by more than 3% are less than 5%.
Eff just made it sound too much like "You cannot draw any conclusions, ever, based on a data set," and that's simply not true. A perfectly valid conclusion would be something like, "I'm 99% certain that the true average value is within 3% of whatever value."
Twitter | Facebook | Tumblr | Last.fm | Pandora | LibraryThing | formspring | Blue Moon over Seattle (MCFC)
I though it might have been accidental. I probably wouldn't have pinted it out except that false straw man accusations (see above) are a pet peave of mine and I thought an example of a true one would be appropriate.
Taken out of context in the way it is in your quote, I can see how one would draw that conclusion. The formula you propose is useful, but to get k at 3 and e at 5, you need a larger data set than is likely to be observed through normal play. even then, a perfectly random method can fall well outside of those ranges on occasion. In order for it to be useful, you need several sets each with a great many entries in each, so as to reduce the possibilty of a chance result. This still isn't absolutely certain, but is close enough to be reliable, but is already well outside what is practical in a gaming context. Would you collate a dozen sets of one thousand throws each for every one of your dice, and expect the rest of your group to do the same?
It's so much easier just to get a die spinner. If the variables you're putting into the throw (die balance, distance of throw, intial spin, aned s on) are fair, the die can be deemed random enough.
(edit - actually, that figure might have been for k = 5 and e = 5. It's been a while :P)
Probability studies are innately uncertain. As soon as you call a thing a probability study, you are admiting a rather large chance (as compared to most fields of scientific study) that you're data is a result of a fluke, especially when you're discussing things with as many required uncontrollabe variables as dice rolling, cpu clock-based number generaters, and the like.
As you increase the size of a data set, a given trend becomes more likely to be the result of a flaw, but it doesn't eliminate the possibility of a fluke. That's why an e value is necesary, and e doesn't get anywhere near zero until the number of results just get plain ridiculous. Even then all you've shown is that the method tends to give results similar to what one would expect in a random system, not that the system is truly random.
You could fund a small team of researchers to determine the fairness of a set of dice over the next six months and get a probable result, or spend five bucks on a die spinner and know to a similar degree of certainty right now. The methodology required to reach a reasonable degree of certainty using resultant data just isn't practicable. Testing a die for even weighting and enacting rules that increase the variables that determine the outcome evenly across all possible results is rather easily done and can grant a higher degree of certainty.
Roll a D4 and a D20. The D4 represents the numbers 13, 14, 15, and 16 (or 12+d4). The d20 represents the numbers between 1 and 20.
Multiply the result together. Hold this number. Once all stats have been rolled you can add up to and we usually say 8 points between your stats. This number is not choosen arbitrarily.
So A 1 and a 1 is 13. A 1 on the d4 and a 20 on the d20 is a 260, and you could choose to make the 13 into a 21, or the 260 into a 268, or some combination between them.
Take the square root of this number and round to the nearest integer. That's your stat.
It helps if you keep a copy of this table on hand, but a calculator also works. I recommend color coding the table and underlining combinations that can be upgraded. (So the first 7 numbers are all upgradeable, but a 2[d20]+4[d4] [32 total or an 8] is not)
I ran a computer program to work out average point buy, it actually isn't that bad, around 27ish iirc, Median is 12.5 but the Mode is 15. 3 values can score an 18 (so 3/80), but only a natural 20 and a natural 4 will get a pure 18. Further, no one is 'stuck' with a 4 as the lowest value you can get is a 4 upgradeable to a 5 (1, 1, with 8 points gives 21. 21^.5 is 4.58, rounds to a 5. This gives some people the ability to play with stats as low as 3, or bounce around with race and age combinations to achieve some interesting characters. You might want to set a final point buy limits of the system between say, 15 and 50, or 20 and 45 as the extremes are slightly more likely in this system.
Pretty neat system, most of the players seem to like it, though some just down right hate the complexity. Some people can get some wonky stats with it, but it's fun. Great when combined with "Roll for your strength, now roll for dex." I usually let players choose between a fixed point buy, this system, or 4d6.
I don't have to go into lots of detail as this is a romance and discussion is just for a dinner conversation in one scene. However, I would like it to sound intelligent/realistic, should someone well versed in this field read it.
If anyone is willing to help me out or if I could even quote some debate on this topic, it would be great. Then whoever volunteers to help me out could read the short discussion in my novel and let me know if I've totally screwed it up:)
My email is lindaw_1950@yahoo.com.
Thanks lots,
Linda W
Linda W