Space Marines - Redesign/Rules Development

[Sigoroth]

The reason I chose the methodology that I did was that, due to the aforementioned inability to determine the precise bias of the die, each toss should be treated as a single case, though there are only a handful of possible outcomes.  In each case, I took the most likely favorable outcome, and used it as the basis for the next state.  

In the case of four Aboats flying into four turrets, the most likely favorable outcome is two Aboats get through, and so on.  

 While the methodology may or may not be independent of the 'fairness' of the die, the accuracy of it's outcome is absolutely dependent on how biased the die actually is.  A die with a very strong bias toward rolling a six in the hands of the attacker can turn even a single ship into an unstoppable juggernaut.  A strong bias in the hands of the defender can make a ship invincible.  Since we cannot pre-sample the die to make an educated guess as to the nature of it's bias, broadly speaking, using frequency, we have to treat it as a single case.

Utter utter utter utter load of crap! According to this method a non-locked Gothic will never get through a cruiser's shields.

Firstly, as a system, when we say a 5+ roll is needed, we are stipulating a 1 in 3 chance. Not an "oh, maybe 1 in 2 or 1 in 6, depending on your dice" chance. The assumption is perfectly fair and balanced dice, because it's a system. There is nothing to suggest that any bias in the dice would be systematic and nothing to suggest that this bias would favour one player or race. So any variation caused by bias will be around the mean anyway. This is unless someone is deliberately cheating. How do you suppose we come up with a system that assumes that people will not only cheat, but get away with it? That's tantamount to ordering someone to cheat. Therefore, all thought of bias should be expunged as irrelevant.

Nevertheless, it remains that 4 THs have over four times the chance of destroying a 4 turret braced escort than 2 lances do. The only real difference between BC and lances against escorts is the possible loss of 1 WB dice if you're smart enough to ignore that bullshit simultaneous fire crap from the new FAQ.

Therefore SMs do not need lances to handle escorts.

[Dark Depths]

It's complete nonsense BI, sorry.  Yes, some dice may indeed not be truly random, but we have to assume they are for our sanity and the game mechanics.  Otherwise it all falls over. 

[Eddie Orlock]

So, shall we give you the benifit of the doubt for a bit and allow you to post some more complete math rather than gainsaying middel school math with what appear to be crude approximations.

...

Maybe you could summon up some links to some authoritative works on 'propensity theroy' for the edification of your peers around here, as my cursory studies suggest that while the philisophical constructs are different, the math is the same.

You want links, we have links:

Hájek, Alan "Fifteen Arguments Against Hypothetical Frequentism".  Erkenntnis (March 2009) 211-235.

http://philrsss.anu.edu.au/people-defaults/alanh/papers/fifteen.pdf


However, I'll also admit that almost all probability methodologies have problems: the single case problem for frequency probability, Humphery's Paradox for propensity interpretation, and so on.

Due to the fact that frequency interpretation requires perfect repeatability to generate accurate results, and that no two die throws are the same due to sensitivity to initial conditions, it is impossible to determine exactly how biased a die is in a given throw.  (Indeed, I've seen many of our 'peers' spend hours trying to determine a die's bias [though they don't call it that] before purchasing one at a FLGS, only to have it roll poorly in another setting).

The reason I chose the methodology that I did was that, due to the aforementioned inability to determine the precise bias of the die, each toss should be treated as a single case, though there are only a handful of possible outcomes.  In each case, I took the most likely favorable outcome, and used it as the basis for the next state.  

In the case of four Aboats flying into four turrets, the most likely favorable outcome is two Aboats get through, and so on.  

 While the methodology may or may not be independent of the 'fairness' of the die, the accuracy of it's outcome is absolutely dependent on how biased the die actually is.  A die with a very strong bias toward rolling a six in the hands of the attacker can turn even a single ship into an unstoppable juggernaut.  A strong bias in the hands of the defender can make a ship invincible.  Since we cannot pre-sample the die to make an educated guess as to the nature of it's bias, broadly speaking, using frequency, we have to treat it as a single case.

Endevouring to the be fair sort I aspire to be, I've spent some time slogging though the fillibuster you linked to to see if it might genuinely enlighten me. So much of it seems so flawed I struggle as to where to begin. Round about page twelve the author pulls what looks like a strawman wherein he mentions a thought experiment in which an allegidly fair coin is tossed a thousand times and comes up with one outcome 471 times rather than the anticipated 500. The author then goes on to proclaim this an unresolveable paradox. It's not. There are several solutions, some he suggests, like the coin not truely being fair, and that the empierical result is a measure of the true probaility, or that the trial was insufficiently lengthy and rigourous. My initial reaction upon reading the trought experiment was that this was well within the bounds of the pseudo normal behaviour and close to the peak of the curve of likely outcomes and that if further thousand iteration trials were conducted we might see some with more and others with less than 500. Maybe this falls in the catagory of an insufficiently lengthy and rigourosus trial, but, if I'd tossed a coin a thousand times and recored the results, I'd honestly be suprised to get 500 of any one result, the modal result is really just a small portion of the solution space and 471 is right close by.

It would appear that there is some schools of thought I've not been made privy to yet, but so far the link provided has failed to provide that I'd hoped to get in thei initial request, which is, in a nut shell, what is 'propensity' theroy, and how does it differ from 'freaquentism'. As right now, the whole thing feels like the kind of hogwash literature students attempt to pull when faced with a math challenge, and I'd dearly like to think this isn't the case.

To second 'Dark Depth' even if your dice aren't fair, the game idesign is predicated on fair dice, and without this initial assupmtion, the whole thing collapses. I might sugggest that the use of 'fair' random number generators is an implicite rule of the game and that to not is to cheat.

[BaronIveagh]

Endevouring to the be fair sort I aspire to be, I've spent some time slogging though the fillibuster you linked to to see if it might genuinely enlighten me. So much of it seems so flawed I struggle as to where to begin. Round about page twelve the author pulls what looks like a strawman wherein he mentions a thought experiment in which an allegidly fair coin is tossed a thousand times and comes up with one outcome 471 times rather than the anticipated 500. The author then goes on to proclaim this an unresolveable paradox. It's not. There are several solutions, some he suggests, like the coin not truely being fair, and that the empierical result is a measure of the true probaility, or that the trial was insufficiently lengthy and rigourous. My initial reaction upon reading the trought experiment was that this was well within the bounds of the pseudo normal behaviour and close to the peak of the curve of likely outcomes and that if further thousand iteration trials were conducted we might see some with more and others with less than 500. Maybe this falls in the catagory of an insufficiently lengthy and rigourosus trial, but, if I'd tossed a coin a thousand times and recored the results, I'd honestly be suprised to get 500 of any one result, the modal result is really just a small portion of the solution space and 471 is right close by.

It would appear that there is some schools of thought I've not been made privy to yet, but so far the link provided has failed to provide that I'd hoped to get in thei initial request, which is, in a nut shell, what is 'propensity' theroy, and how does it differ from 'freaquentism'. As right now, the whole thing feels like the kind of hogwash literature students attempt to pull when faced with a math challenge, and I'd dearly like to think this isn't the case.

To second 'Dark Depth' even if your dice aren't fair, the game idesign is predicated on fair dice, and without this initial assupmtion, the whole thing collapses. I might sugggest that the use of 'fair' random number generators is an implicite rule of the game and that to not is to cheat.

The problem is that there is no such entity as a 'fair' random number generator using a physical object.  We would have to require a digital generator and expel anyone who thought their dice were 'lucky' for cheating as it implies a bias to the die. 

Unfortunately Hájek was the best source I could find a link to.  Most of the rest are in books, though if you can stomach his prose style, there's plenty of Hájek's work available online.  I would suggest Objective Single-Case Probabilities and the Foundations of Statistics by RN Giere or Philosophical Theories of Probability by Gillies. 

A die does not actually have to be 'loaded' per se, to be unfair and have a tendency to roll a certain result.

[Dark Depths]

Just to repeat myself:  yes, you may be right, but how are we meant to factor the unfairness of dice into a simple table top game?  Without resorting to complicated maths.  We have to assume die are fair.  And to be honest, has anyone here ever complained of always rolling the same number, all the time, in every game they play, with the same dice?  Its never happened to me. Sometimes in a game you'll get poor dice rolling, in another you'll get great dice rolling, so overall it works fine for me, so why all this fuss about dice not being 'fair'?

[horizon]

BaronI, you can also just accept the fact your maths are not "right" to determine the outcome of these events.

[Sigoroth]

Endevouring to the be fair sort I aspire to be, I've spent some time slogging though the fillibuster you linked to to see if it might genuinely enlighten me. So much of it seems so flawed I struggle as to where to begin. Round about page twelve the author pulls what looks like a strawman wherein he mentions a thought experiment in which an allegidly fair coin is tossed a thousand times and comes up with one outcome 471 times rather than the anticipated 500. The author then goes on to proclaim this an unresolveable paradox. It's not. There are several solutions, some he suggests, like the coin not truely being fair, and that the empierical result is a measure of the true probaility, or that the trial was insufficiently lengthy and rigourous. My initial reaction upon reading the trought experiment was that this was well within the bounds of the pseudo normal behaviour and close to the peak of the curve of likely outcomes and that if further thousand iteration trials were conducted we might see some with more and others with less than 500. Maybe this falls in the catagory of an insufficiently lengthy and rigourosus trial, but, if I'd tossed a coin a thousand times and recored the results, I'd honestly be suprised to get 500 of any one result, the modal result is really just a small portion of the solution space and 471 is right close by.

I think the point that the author was trying to get at was that there was no reason why someone holding to this particular theory of frequency probability would believe that the actual probability was .5 when empirically speaking it was only .471 and it is actually impossible to flip infinite times, therefore you can't show that .5 is the true value. Also it isn't terribly likely that heads would turn up exactly 500 times out of 1000, even in a fair system. So he was questioning the reason for the belief, not saying that it couldn't be true. Mind you, as with a lot of philosophy (and I'm speaking as a fan here) it's all so much wank.

The suggestion is that anyone that tries to make a prediction as to the general result is essentially wrong as you can't by definition predict the unpredictable. If you could then it wouldn't be a chance event. All nonsense of course. No one attempts to predict the outcome of a particular chance event, except as a wager (in which case the chance of being wrong is implicit). However, predicting the general shape of an outcome dependent on a large amount of minor random events for which the individual probabilities are known is not a case of predicting the unpredictable and therefore denying the possibility of being wrong. It is merely observation of the principle of regression to the mean. As N increases variance decreases. Taking this relationship to its logical end we find that as N approaches infinite the variance approaches zero. This is merely a logical extension of an observed principle and requires no rejection of inherently chancy events. In fact, it seems to be demonstrably true in physics, since at the subatomic level there is possibility of random events, whereas at the macro level things tend to be much more predictable (moons don't randomly lose their orbits and crash into their planets after all).

[Eddie Orlock]

The problem is that there is no such entity as a 'fair' random number generator using a physical object.  We would have to require a digital generator and expel anyone who thought their dice were 'lucky' for cheating as it implies a bias to the die.

...

A die does not actually have to be 'loaded' per se, to be unfair and have a tendency to roll a certain result.

The suggestion of a digital generator is interesting, or, rather it is more interesting that after all this that you'd make it as imply that it is superior. It is my experience and understanding that these are far more easily obfuscated and the obfuscations far more easily concealed than physical objects. Even when they're not messed with they display unfavourable traits. I have encountered people who would have us print up 72 cards, twelve of each number and shuffle them up and draw for all the rolls just to ensure an even distribution across the game. This leads to what in my ignorance I call the 'blackjack' problem. Just as it's possible to beat the house counting cards in that game, so is it possible to beat the curve with this system. The dice would cease to be independent events. My favoured solution, the horror of several people I've encountered, is when I think I see something funky with the dice, and sometimes just because, is to insist that everyone uses the same dice. If they roll high, we all roll high, if low, we're all low. The problem becomes something of a wash.

I think it’s more a question of intent anyway. Using a biased die is only really a problem if people intend to use biased dice or notice that they seem skewed.

[BaronIveagh]

The suggestion of a digital generator is interesting, or, rather it is more interesting that after all this that you'd make it as imply that it is superior. It is my experience and understanding that these are far more easily obfuscated and the obfuscations far more easily concealed than physical objects. Even when they're not messed with they display unfavourable traits. I have encountered people who would have us print up 72 cards, twelve of each number and shuffle them up and draw for all the rolls just to ensure an even distribution across the game. This leads to what in my ignorance I call the 'blackjack' problem. Just as it's possible to beat the house counting cards in that game, so is it possible to beat the curve with this system. The dice would cease to be independent events. My favoured solution, the horror of several people I've encountered, is when I think I see something funky with the dice, and sometimes just because, is to insist that everyone uses the same dice. If they roll high, we all roll high, if low, we're all low. The problem becomes something of a wash.

I think it’s more a question of intent anyway. Using a biased die is only really a problem if people intend to use biased dice or notice that they seem skewed.

I was precluding the possibility of premeditated cheating, which is I believe what you're referring to here.  I've actually considered the 'all parties use the same die' tack before, but I've found that, as with role players, TT war-gamers occasionally resist the idea of anyone but them touching their dice with a certain.... insistence.  (One subject actually became physically violent when an a female opponent asked to borrow a d6 [surprisingly, he was not cheating, but had rather unusual views on his 'lucky' dice])

As far as trying to anticipate outcomes of random events, almost every decision we make in this game is based on trying to anticipate the outcome of a random number based on what we believe to be averages. 

(as an oddity I just realized: we have a game where hitting a target is dependent on the target's armor, not on the ballistic skills of the crew or targeting system of the fireing ship.)

[Zelnik]

hey baron, now that the space marines are getting huge crack in IA10, you may have less to complain about.. have a peek at the IA10 thread in general.

[skatingtortoise]

to me the IA10 additions consist of character ships for SM chapters, a SC with improved thrusters which replaces BC's with torpedoes, and a battle barge which exchanges firepower for transoprt capacity.
the first is in line with a lot of the chaos god specific ships being put forward, the second and third are extensions of the current SC model of basic setup with optional upgrades/refits.
battle barge with an assault point value of 4? seems nice and fluffy to me.

lastly, i cant see it being a bad influence. at the worst, there will be more SM players out there getting spanked in fleet engagements and raids. at the best, we will see some new models on par with the GK cruiser (right after ive converted some as well  ). the first is dependent on people actually getting the book, which i cant imagine will happen just for the BFG goodies, or be widespread enough to 'ruin space marines'.

[Sigoroth]

I was precluding the possibility of premeditated cheating, which is I believe what you're referring to here.  I've actually considered the 'all parties use the same die' tack before, but I've found that, as with role players, TT war-gamers occasionally resist the idea of anyone but them touching their dice with a certain.... insistence.  (One subject actually became physically violent when an a female opponent asked to borrow a d6 [surprisingly, he was not cheating, but had rather unusual views on his 'lucky' dice])

Well, as it is impossible to predict any potential bias, and no reason to suspect that it is unidirectional bias or that it favours one particular fleet or player over another then there's no reason to bring it up.

As far as trying to anticipate outcomes of random events, almost every decision we make in this game is based on trying to anticipate the outcome of a random number based on what we believe to be averages. 

Here we're trying to predict the general shape of the event outcome not the outcome of a specific chance event. We do not use probability to say, "well, I've failed the past 4 braces saves therefore I have a 31/32 chance of passing this save!"

Firing 8 lances against a single escort might not even destroy it, but we'd likely be better off firing those lances against a cruiser at least. We might not do that well, but it's fairly likely that we'll have more impact than if we just shot at the one escort and it also allows for the possibility of rolling well. Hitting with all 8 lances against the 1 escort does nothing more than hitting with just 2. Against the cruiser the upper limit on the hits will be effective. So our predictions are valid, even when they're not right.

All of which conclusively proves that SMs don't need lances.

(as an oddity I just realized: we have a game where hitting a target is dependent on the target's armor, not on the ballistic skills of the crew or targeting system of the fireing ship.)

The accuracy of the shooting is represented in the gunnery table.

[BaronIveagh]

The accuracy of the shooting is represented in the gunnery table.

On the firing lances against an escort: No, but if you're firing it against a squadron of escorts, you'll likely do better then against the cruiser for purposes of reducing the enemies effectiveness. 

On the gunnery table: Only in a very broad sense.  Consider that, unless a special rule is in effect it means that highly trained crew and advanced cogitators are just as accurate as an ork using a set of crosshairs mounted on the barrel of the gun.  Very few ships, even ones that logically would, get a left shift. 

[Eddie Orlock]

On the gunnery table: Only in a very broad sense.  Consider that, unless a special rule is in effect it means that highly trained crew and advanced cogitators are just as accurate as an ork using a set of crosshairs mounted on the barrel of the gun.  Very few ships, even ones that logically would, get a left shift. 

As I mentally model it, a unit of fire power is not a unit of firepower. This is to say that some races generate their firepower units far more efficiently than others. The orks saturate a larger region of space than Imperial forces do for the same effective attack density. Modelling this is beyond the scope of the game and would really only come into play in the most obsessive/compulsive sets of campaign rules dealing with the tracking of munitions expendature.

Special rules and shifts are an aberation in what should be a simple system of just increasing the number. We really shouldn't add complexity when we don't have to.

[BaronIveagh]

On the gunnery table: Only in a very broad sense.  Consider that, unless a special rule is in effect it means that highly trained crew and advanced cogitators are just as accurate as an ork using a set of crosshairs mounted on the barrel of the gun.  Very few ships, even ones that logically would, get a left shift. 

As I mentally model it, a unit of fire power is not a unit of firepower. This is to say that some races generate their firepower units far more efficiently than others. The orks saturate a larger region of space than Imperial forces do for the same effective attack density. Modelling this is beyond the scope of the game and would really only come into play in the most obsessive/compulsive sets of campaign rules dealing with the tracking of munitions expendature.

Special rules and shifts are an aberation in what should be a simple system of just increasing the number. We really shouldn't add complexity when we don't have to.

Or if, god help us, we play with a system that takes a 3rd dimension into account.  That said: actually, supposedly it really is a unit of firepower now, if you follow the conversions from BFG to RT.