Precision Dice

[von Marwitz]

I am not sure that statement is accurate. I remember reading about how the dice bot statistically produces more 3,4, 10 and 11 than would be expected. Skewing the bell curve ever so slightly

Back then, the ASL Scenario Archive website had a log-analyzer function. Into which you could copy/paste VASL logs. The function would provide the DR average, count Snakes & Boxcars, your best/worst DR average in all sessions recorded (with more than 50 DRs per session).

The nice thing was, that you could do this cumulatively and not only limited to one session as is currently possible with VASL.

Before the function no longer worked, because VASL used pictures of pips instead of normal numbers, I habitually pasted my logs in there for more than 100,000 rolls.

While the function did not record the number of particular pip-outcomes, it gave the overall average. Unsurprisingly, this was not exactly 7.0 for those 100,000+ rolls but it was within bounds of that chi-something test-thingy.

Bottom line:
Again, more fuss about the VASL dice bot going on than is warranted.

von Marwitz

 

[DVexile]

I am not sure that statement is accurate. I remember reading about how the dice bot statistically produces more 3,4, 10 and 11 than would be expected. Skewing the bell curve ever so slightly

No, just no. Random.org has absolutely no skew (or kurtosis as it appears the claim is) and anyone who wrote that it did simply didn’t understand what they were doing.

Also, it absolutely should not be a bell curve in the first place. Two dice summed give a triangular distribution.

VASL dice are the one set of dice you don’t need to worry about!

 

[Wayne]

[One reason we (all) get so antsy about our dice -- we remember our pains about 5x as long as our ecstasies (that's human nature).

Upshot -- if equipped w/hypothetically perfect dice, we'll never-the-less perceive they are skewed against us.

And (emotionally) perception trumps reality, almost every time it's tried...]

 

[Jwil2020]

In an effort to do my part to keep this eternal thread going, I offer the following tongue-in-cheek, and completely unoriginal, ruminations.

Assuming a pair of dice are not obviously lopsided or misshapen, it seems to me the only benefit to using precision dice is that they provide a subjective 'peace of mind' factor that the final roll was the result of pure, completely random, luck and not some imperfection in one or more of the speckled messengers of fate. If that peace of mind is worth the exorbitant price of said dice to a particular player, I say more power to him.

But even removing the quality of the dice from the equation may not be sufficient to allay all fears. As others above have noted, there is conceivably an endless list of other variables to the DR besides the quality of the dice. Are we using a dice tower? If so, does it matter if it is a tall one or short one? Should I gingerly drop the dice into the tower or violently throw them? If I throw them, does it matter if I first hold them up to my ear and shake them like a mariachi? Is the number of direction-change obstacles in the tower important? What about the material of the landing area: slick or non-skid? Is there an advantage to using a dice glass? What about the guy who likes to use a dice cup?

Are we sitting near a window in the daytime and the rays of the sun have heated my solid color die to be slightly warmer than the white die? Will all those excited atoms cost me the game on my final CC roll to capture that VC building? What about that AC unit right above my head in the hotel game room that is blasting a cold wind down my back? Will I fall victim to an unforeseen gust of air just as one of my dice was about to land with a 'one' showing?

Does talking to my dice help? Maybe the sound waves of my voice bouncing off the little cubes as they come to their final rest will save me from the dreaded 6,6. Okay, this last one I can categorically assert makes no difference: my dice have never listened to me. But just to be safe, I think we should give consideration to forbidding all talking during the dice roll.

Should I forbear eating at the game table? Is it possible the grease and salt from that bag of chips I am munching on will get on my precision dice and that one microgram of oil is the reason my MG did not make rate? Maybe I should run to the restroom to wash my hands before every roll to rule that out.

Setting aside my feeble attempt at comedy, I think it is safe to say we all want to feel the DRs in a game (whether for or against us) were arrived at fairly. And, as I said at the outset, if using a set of dice that have been sold under the 'precision' label, achieves that sense of fairness, then so be it.

Nevertheless, regardless of the dice used (including digital dice-bots), we have all experienced rolling streaks that seem to defy all statistical logic: a SW that goes on an extended rate tear and turns half my OB into a quivering mass of broken units; a whole turn where I rally every DM'd squad and pass every MC- even the 4MC one!

My philosophy is to not get too excited when this happens. I've been rolling dice at the wargaming table across five decades. My experience, mixed with a little common sense, has taught me that in the course of most games, those hot dice will eventually cool down, and those two tiny blocks of ice might yet burst into flames. My only hope is that at game end I am the one who needs first aid cream for my blistered palms.









.

 

[von Marwitz]

Nevertheless, regardless of the dice used (including digital dice-bots), we have all experienced rolling streaks that seem to defy all statistical logic: a SW that goes on an extended rate tear and turns half my OB into a quivering mass of broken units; a whole turn where I rally every DM'd squad and pass every MC- even the 4MC one!

My philosophy is to not get too excited when this happens. I've been rolling dice at the wargaming table across five decades. My experience, mixed with a little common sense, has taught me that in the course of most games, those hot dice will eventually cool down, and those two tiny blocks of ice might yet burst into flames. My only hope is that at game end I am the one who needs first aid cream for my blistered palms.

Amen to that.

von Marwitz

 

[Bill Kohler]

Assuming a pair of dice are not obviously lopsided or misshapen, it seems to me the only benefit to using precision dice is that they provide a subjective 'peace of mind' factor that the final roll was the result of pure, completely random, luck and not some imperfection in one or more of the speckled messengers of fate. If that peace of mind is worth the exorbitant price of said dice to a particular player, I say more power to him.

Precision dice are manufactured to higher tolerances, both in dimension and density. It seems to me that higher tolerances--whatever the time of day or AC unit one is using--can't help but lead to more uniform probabilities.

And to the contrary, I've seen no convincing evidence in this thread that the lower tolerances of standard dice won't negatively affect the probability of dice rolls.

Now certainly, at some point, higher tolerances are only gilding the lily. But it doesn't seem like anyone knows what that tolerance threshold is--I certainly don't. But since higher tolerances are readily obtainable, I choose to use dice manufactured to those higher tolerances. It's true that the only benefit I'm gaining may simply be "peace of mind"--but it's also possible that I'm gaining "fairer" dice.

 

[Robin Reeve]

And I've seen no convincing argument in this thread that the lower tolerances of standard dice won't negatively affect the outcome of dice rolls.

The contrary hasn't been proven.
You don't seem to understand that the scale of an ASL scenario offers a much too low sample of dice rolls to establish that the difference between precision dice and well balanced non precision dice cannot be noticeable.
Imagine a game with only one die roll: how could you tell, within the scope of that game, that a die is more balanced than another one?

Many players don't use precision dice and don't seem to have noticed any significant unbalance in the results of their dice rolls, over hundreds of scenarios.

I am afraid that your insistence upon what everybody knows (i.e. that precision dice will be more balanced that lesser quality dice) constantly avoids the question of the sample of dice rolls.
I am sure, for an example, that a Ferrari will be a much more stable car than an old Volkswagen.
But when you are driving in a parking lot, you won't see the difference between them.
Until proven the contrary, using precision dice during an ASL scenario are like driving a Ferrari in a parking lot: they shine, their sound is nice, but usual dice work fine too.

 

[Faded 8-1]

Bill has thrown out 2% or 3% as the amount of difference he believes there might reasonably be between 'regular' dice and precision dice. If that is indeed true, that is significant enough to matter within a scenario - certainly within a CG.

To me though, that sounds high. I would be surprised if the difference was even a tenth of a percent. But the only way to know would be to conduct tests, removing all the other variables from the equation as much as possible. And, if the margin of difference really is minute, it would take a huge sample size to accurately reflect it. Like, 10 sets of a million rolls each, with both regular and precision dice. I don't have the math anymore to know how big the sample size actually should be, but this can be estimated mathematically given the expected degree of precision required/margin-of-error allowed.

It seems likely that this has been examined in detail scientifically by somebody, someplace, sometime. No doubt the companies that make precision dice have good data on this, but the actual numbers the CEO keeps in the safe in his office wouldn't necessarily match the public (marketing) numbers.

 

[Bill Kohler]

Bill has thrown out 2% or 3% as the amount of difference he believes there might reasonably be between 'regular' dice and precision dice. If that is indeed true, that is significant enough to matter within a scenario - certainly within a CG.

I agree.

I threw out the 3% value on the basis of Wayne's work: Testing Dice.

Wayne talks about considering a die as possibly being imbalanced (and needing further testing) if, after 100 rolls, it fails at the 5% level, which happens if any given dice face comes up fewer than 8 times or more than 25 times. (He calculates that properly balanced dice will exceed this threshold only 5% of the time.)

If all dice faces come up between 11 and 22 times, then that die has a better chance of being balanced. (Properly balanced dice fall within this range 80% of the time.)

The difference between those two zones (8-25 and 11-22) is 3 out of 100, which is where I got my 3% from, as a ballpark figure.

After 1000 DRs, Wayne's zones tighten to 151--183 and 143--191, which is a difference of 8, or 0.8%. I don't know how common it is for Wayne to find dice that fail the 5% level after 100 dr, or after 1000 dr--maybe he'll chime in here.

To my crude way of thinking, dice that fail at the 5% level after 100 dr might be 3% off from being balanced dice (and possibly 8% off, if you measure the delta from the expected value, 16.7), and those that fail after 1000 dr might be 0.8% off from being balanced dice (and possibly 2.4% off, if you measure the delta from the expected value, 167).

 

[bendizoid]

There is something to be said about some of the craftsmanship/engineering in these precision dice, functional little works of art.

 

[Faded 8-1]

Thank you. I was wondering where you got those numbers - I didn't think you were pulling them out of thin air.

Having not read Wayne's article, I cannot comment further.

Wayne is dead-on about people's perceptions though - even if we had completely perfect dice, we would never know or accept it, and after an odd run of luck we would be seeing Confederates in the Mist.

 

[Faded 8-1]

Just don't sit down at the table if you see this guy staring up at you, or if you do make sure he uses a big, convoluted dice tower and not just free-rolling into a tray.

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[von Marwitz]

Because I have the ambition to get this thread to at least 12 pages , I have dug up my old post giving hard facts & counted numbers of my personal standard-out-of-the-box AH/MMP dice and will paste this in below with a few amendments:


So, instead of speculating about AH/MMP dice, I did the work and provide hard facts.

Sample of 1000 DRs of my BV3 dice rolled the way I usually do (no dice tower, dice cup on desk):


DR number of times my dice number of times expected with "perfect" die
2 24 27.77777777
3 46 55.55555555
4 79 83.33333333
5 107 111.111111111
6 138 138.888888888
7 159 166.666666666
8 141 138.888888888
9 125 111.111111111
10 80 83.3333333333
11 72 55.5555555555
12 23 27.7777777777

My DR average in 1000 rolls is 7099, the "perfect" expected DR average would be 7000.

From here on, please, math-gurus, correct me if I have screwed up somewhere, as I am not much into math.

Emiprical variance for my dice would be:

24 * (2-7.099)² +
46 * (3-7.099)² +
49 * (4-7.099)² +
107 * (5-7.099)² +
138 * (6-7.099)² +
159 * (7-7.099)² +
141 * (8-7.099)² +
125 * (9-7.099)² +
80 * (10-7.099)² +
72 * (11-7.099)² +
23 * (12-7.099)² = 6199.82

6199.82 / 1000 (i.e. # of sample) = 6.19982 = Empirical variance for my dice @ a 1000 sample.

Now Empicial variance for "perfect" dice:

27.77 * (2-7)² +
55.55 * (3-7)² +
83.33 * (4-7)² +
111.11 * (5-7)² +
138.88 * (6-7)² +
166.66 * (7-7)² +
138.88 * (8-7)² +
111.11 * (9-7)² +
83.33 * (10-7)² +
55.55 * (11-7)² +
27.77 * (12-7)² = 5833.33

5833.33 / 1000 = 5,83333 = Empicical variance for "perfect" dice @ a 1000 sample.

Standard deviation would be the square root of Empirical variance.

√6.19982 = 2.48994 is the Standard deviation for my dice @ a 1000 sample.
√5.83333 = 2.41523 is the Standard deviation for "perfect" dice @ a 1000 sample.

The Standard Deviation for my dice with a sample of 1000 rolls is:

7099 +/- 2.48994% or in other words between 6998.26 and 7147.27.

"Perfect" dice @ a 1000 sample could expect to roll

7000 +/- 2.41523% or in other words between 6915.47 and 7084.53.

To put this into perspective:

Using "perfect" (not merely "precision") dice, with a 1000 rolls you can expect statistical differences of 169.06 pips in the overall total of expected 7000 pips.

Using "my lowly dice", with the 1000 rolls I can expect a difference of a (surprisingly lesser) difference of only 149.01 pips in the overall total of expected 7099 pips.

This is a difference of 169.06 - 149.01 = 20.05 pips for "my lowly dice" compared to "perfect dice" in 7000 pips in a sample of 1000 rolls.

Thus you can specify the difference of "perfect" (not merely "precision") dice to "my lowly standard MMP BV dice" at 20.05 / 7000 = 0.29% in a sample of 1000 rolls.

Note, that the total number of pips of "my lowly dice" in a sample of 1000 rolls was 7099, while those of "perfect dice" would be only 7000. In other words "my lowly dice" roll worse than "perfect dice".

Let's take hard numbers a little bit further looking at DR averages:

Worst result within Standard Deviation for my dice with a sample of 1000 rolls is:
7099 + 2.48994% = 7147.27 pips => DR average of 7147.27 / 1000 = 7.147

Best result within Standard Deviation for "perfect dice" with a sample of 1000 rolls is:
7000 - 2.41523% = 6915.47 pips => DR average of 6915.47 / 1000 = 6.915

So, the worst that could conceivably be expected to happen to me within the range of the Standard deviation of "perfect" dice pitted against my low production process BV3 ones is a

DR average of 6.916 against 7.147 in 1000 DRs to my disfavor.

I am crushed. Oh, the injustice of it. It must have turned the game against me. Seriously?

But what lies within the limits of statistics the other way around?

Best result within Standard Deviation for my dice with a sample of 1000 rolls is:
7099 - 2.48994% = 6998.26 pips => DR average of 6998.26 / 1000 = 6.998

Worst result within Standard Deviation for "perfect dice" with a sample of 1000 rolls is:
7000 + 2.41523% = 7084.53 pips => DR average of 7084.53 / 1000 = 7.084

At the same time within statistical expectations it could have optimally turned out for me to be a

DR average of 6.998 against 7.085 in 1000 DRs to my favor.



At this point, I find it very hard to understand people insisting upon precision dice making a significant difference.

Of course, it can make a difference, but it is highly unlikely to make a significant difference.
As you would not base your plan of attack depending on your killer-stack rolling consecutive snakes, it is in the same way nonsense to base the assessment of your chances to win on the difference of 'precision dice' or even 'perfect dice' compared to standard MMP dice.

So if any of you "dice-superstitionists" is playing me in a tournament and should feel harrassed by my dice and call me out to change them: If I were to give in to your capers (which I would not unless precision dice were mandated by the tournament's rules), you would harm yourself based on statistical hard tested facts on my set of standard dice.

If you consider me a cheater in the first place for using standard dice, of course, you would suspect me lying about my having tested my dice or claiming that - by stroke of luck - my standard dice happen to be pretty precise while all others are not. I'll provide you with that perfect recipe to make your world "whole" again...

Instead of "claiming" and "assuming", I challenge everyone in doubt to more productively do the work and test your dice.

Even those for whom standard dice are anathema own that box of 'Beyond Valor'. Prove me wrong or simply provide more data by rolling your lowly standard dice - and your precision dice, too, while you are at it.


von Marwitz

 

[Tuomo]

2 24 27.77777777
3 46 55.55555555
4 79 83.33333333
5 107 111.111111111
6 138 138.888888888
7 159 166.666666666
8 141 138.888888888
9 125 111.111111111
10 80 83.3333333333
11 72 55.5555555555
12 23 27.7777777777

We need to have a talk about significant digits.

 

[Vic Provost]

No, just no. Random.org has absolutely no skew (or kurtosis as it appears the claim is) and anyone who wrote that it did simply didn’t understand what they were doing.

Also, it absolutely should not be a bell curve in the first place. Two dice summed give a triangular distribution.

VASL dice are the one set of dice you don’t need to worry about!

Yes indeed, me and Tom Morin do almost all Dispatches playtesting via VASL, whether when we play together or play any of the playtesters that help us out, VASL dice are what they are, sometimes they make you suspicious but always totally random rolls are right around the corner. I would rather roll my Battleschool dice and always do so when playing ftf but the vast majority of my play in the past 5 years has been via VASL, since we have the random.org virtual dice we don't worry about it. With dice, you roll what you roll. I have never known of an opponent I played who tried to use funny dice, if they did, I'd offer to use some of my precision dice instead, if they refused, I'd never play them again.

 

[Bill Kohler]

Thank you for posting this, von Marwitz. It's great to see actual data--I mean that.

Since you said they were BV3 dice, I take it they're MMP dice (e.g., the ones that have often come with a purple die)--and not the older, lighter, rounder AH-style dice.

I think you have effectively demonstrated that your dice, and the way that you roll them, betray little probability imbalance. They look to fall within Wayne's 20% threshold: e.g., the threshold that balanced dice will meet 80% of the time.

And as I've said above, I gladly play with players whose dice aren't obviously chintzy or misshapen or have missing chunks.

I still would like to read more about Wayne's experience, if he cares to share it, as to approximately what percentage of dice he has tested have failed his tests and how badly they failed. From the quoted post, it appears that he has failed some.

And I still have greater confidence in my precision dice than I do in any non-precision dice that I own, due to their higher manufacturing tolerances. But your data leads me to believe that my MMP BV-dice are likely pretty good--and I'm glad to know that.

 

[Bill Kohler]

We need to have a talk about significant digits.

Obviously an engineer . . .

An old jibe from my college days--and pretty accurate at the time--about how engineering students simply typed in [oops, an anachronism] wrote down every digit that showed in their calculator displays. (For you younger readers, a "calculator" was a cell phone that only did mathematical calculations.)

Or, how do an engineer and a physicist and a mathematician count to a googol?
Engineer: 0.0000000000, 0.0000000001, 0.0000000002, . . .
Physicist: 1, 10, 100, 1000, . . .
Mathematician: Let N stand for Ɐx in the set of whole numbers, then ⱻx such that when the value 1 is added to each X in N a corresponding . . .

 

[von Marwitz]

Since you said they were BV3 dice, I take it they're MMP dice (e.g., the ones that have often come with a purple dice)--and not the older, lighter, rounder AH-style dice.

This is the 'kit':

Leather dice cup, not a dice glass.

The black and white die to the left were the ones of the sample of 1000 rolls.
I use these as my 'standard dice' along with the red one (the latter for SAN only, that one has not been tested). I don't know if they are Avalon Hill or MMP, but they are of the more 'pointed' variant.

For comparison, to the right, you can see a standard Battle School precision die (the larger black one) and another standard AH or MMP one with more rounded corners, which I have not tested.

von Marwitz

 

[Martin Mayers]

View attachment 24896

This is the 'kit':

Leather dice cup, not a dice glass.

The black and white die to the left were the ones of the sample of 1000 rolls.
I use these as my 'standard dice' along with the red one (the latter for SAN only, that one has not been tested). I don't know if they are Avalon Hill or MMP, but they are of the more 'pointed' variant.

For comparison, to the right, you can see a standard Battle School precision die (the larger black one) and another standard AH or MMP one with more rounded corners, which I have not tested.

von Marwitz

NONE CONSISTENT DICE SIZES

You utter fiend.

 

[Bill Kohler]

Thank you for the picture, von Marwitz.

Yes, the center black and white dice are what I think of as the MMP BV dice. The small white one far to the right looks like the style of the old AH BV dice.

Comments about the leather cup:
--Super--it has to be much quieter than glass cups! (ASLers who use glass cups should never be permitted to claim the Stealth drm.)

--Do you spill the dice from the cup onto the table, or do you keep the dice in the cup? (From your earlier post, it sounded like you kept them in the cup.) If the latter, how does your opponent see the outcome? Do you occasionally have head-on collisions? (I'd be tempted to don a bicycle helmet.)

--And if you keep the dice in the cup, that's interesting:
• I think leather, being more yielding than glass or even felt-covered wood, would tend to reduce the tumbling of the dice once you stop actively shaking them (which could dampen the effect of imbalances),
• And the small surface area at the base of the cup could reduce any density-impacted rolling onto a heavier dice face (which could dampen the effect of imbalances),
• And you use MMP dice which are sharper edged (which could also dampen the effect of imbalances, as discussed up-thread).
• I wouldn't like to use the larger precision dice in that cup since the base area looks a little too confining for two of the larger dice. A vigorous shake might be needed to ensure they spin around at least a couple of times between rolls so that there's not a roll-to-roll correlation in the outcomes.