PDA

View Full Version : Is my opponent just luckier than me?



Lord Inquisitor
22-04-2008, 23:02
Or... When I played 8 games of 40K in a row...

As part of my PhD, I'm taking a statistics class, and for this class I need to complete a project that needs to be completed quickly from experimental design through data collection and analysis. This needs to be a new study, and cannot have anything to do with my research. So for my project I decided to do something related to 40K.

I've a friend of mine who I play regularly against, usually 40K. And we've always joked that somehow he seems to have trademark good luck (particularly with his Eldar) while I typically show appalling luck. So I decided to test it.

For those interested in the stats, the design is a fully crossed 3-Factor ANOVA. One factor is the player (me and my opponent), another is the dice roll needed (3+, 4+ or 5+ ... other rolls [2+ and 6+] crop up too infrequently to be useful and contested rolls, difficult terrain rolls and leadership tests also don't fit the analysis). The third factor is importance of the dice rolls (high or low, agreed upon by both players at the time of the roll).

As for armies (from memory) - 500 points
My opponent:
Eldar
Autarch (Warp-jump pack, fusion pistol and lots of power weapon attacks)
10 Striking Scorpions (Exarch, power claw, infiltrate & move through cover)
10 Dire Avengers (Exarch, shimmer shield, defend & bladestorm)
10 Dire Avengers (Exarch, shimmer shield, defend & bladestorm)

Me:
Chaos Space Marines
Sorcerer (doombolt, Mark of Slaanesh)
6 Noise Marines (sonic blasters, blastmaster)
6 Noise Marines (sonic blasters)
6 Lesser Daemons

We played 8 games total (multiple games required as replicates - hence the small points size) on a 4x4 board with about 25-30% terrain. Every 3+, 4+ and 5+ roll recorded. Note that the actual outcome of the game is not a factor in the analysis (just how good the dice rolls are), but has been included for your interest.

Game 1: Cleanse
Eldar win, absolute miserable slaughter. None of his units under 1/2 strength.

Game 2: Take & Hold
Edar win, much closer game. Scorpions & autarch dead, handful of avengers survive due to lousy saving throws on my part and the fact that distract makes them such a damn tarpit in combat.

Game 3: Loot
Eldar slaughter (again). Bladestorm is a bitch. Lost an entire squad of marines to one salvo.

Game 4: Annihilation
Eldar eliminate all Chaos forces (seeing a pattern?). Put up a bit of a struggle this game, killing the autarch and reducing all of his squads below half strength.

Game 5: Recon.
Eldar slaughter all Chaos forces.

Game 6: Annihilation
Yep, eldar kill all chaos forces again. Highlight of the game was my sorcerer charging a squad of Dire Avengers (clipping them, only 3 in the kill zone) and being killed outright (see what I mean about my trademark luck?). By this stage I was getting a bit knarly about this, and checked his list as he just seemed to be having his cake and eating it. Yep, about 100 points over. He drops the warp pack and I added in another squad of daemons to compensate.

Game 7: cleanse
Chaos win! Only one squad of daemons and one squad of noise marines left. But all Eldar dead!

Game 8: by this stage we really didn't care too much. I think it was loot again.
Eldar win, but only a handful of Eldar left.

So, 7-1 to the Eldar, but fortunes for the Eldar changed in the last two games when actually forced to engage in a fair fight! :rolleyes: Damn those sneaky Eldar...

Now... what's the results of the analysis? My opponent did, indeed, score significantly higher on his dice rolls than me (p=0.001)! Not only that, but he scored significantly better than me when the rolls were important (regardless of what he needed to score).

So there you go. Perfectly justified in claiming that my lousy win record is due to my opponent being luckier than me! :D (Or maybe I need to have a look at his dice? :eek:)

Epicenter
22-04-2008, 23:10
Try switching to Las Vegas dice and see how you do. ;)

Kaoslord
22-04-2008, 23:14
Makes for an interesting read. I firmly believe there are some people who are just hideously unlucky, myself being one of them. This doesn't stop me from enjoying the game though.

I remember my last tournament, when I would finish my games on average half an hour ahead of other people. I asked one of my friends why they thought that was, what I wasn't doing that others were. His response...?

Making armour saves..... :cries:

kesofcom
22-04-2008, 23:31
switch armies lol, having a more numerous army means you get more average rolls right? or what Epicenter said. there was a forum a while ago that spoke of dice making a difference. When I read it I bought 41 square d6 about 5mm in width :P.

or this is just a silly one though... play against your self take two squads equal points and play a game (yes I realize this violates foc). either you or you will win right? unless..... cc results in a tie lol

Iron Father
23-04-2008, 01:45
I have horrid luck as well, but dice metter, I used chessex dice, and they do roll better than GW's dice..... hell ive seen dollar store dice roll better than GW dice

TheOverlord
23-04-2008, 01:55
Sneaky Eldar git :P lols

TheDarkDuke
23-04-2008, 02:19
Are there not 3 flaws in measuring the "luck" factor. 1) You are not rolling the same dice as your opposition and not the same amount of rolls. 2) You are not using the same stat lines, therefore again where is the balance in rolls? You roll for 50 3's, 75 4's and 30 5's while he rolls for 60 3's 60 4's and 60 5's... 3) How can you determine what is a high or low importance roll. That one to hit, to wound, to save, to anything could equally result in the difference anywhere.

Just my thoughts.

Norsehawk
23-04-2008, 02:23
The lists on their face look unbalanced too. You have all of 19 guys, he has 31, 6 of your guys are lesser daemons, which means they have no shooting ability at all.

If you want to test luck, swap lists, play 8 games with his list against your list, I would be willing to bet that you would win the majority of games. To me, it doesn't come down to anything random or luck, his list frankly is much more solid than yours.

Better yet, play 2 armies that are exactly the same, but then it can come down to small decisions as to what to do. Hell, each of you roll the same set of dice 5000 times, note the results, and then see if he in fact rolls luckier than you.

kesofcom
23-04-2008, 02:52
Norsehawk lol wow I have never thought about playing someone else's army before.

Sounds like a sound plan to me.

xAlpha
23-04-2008, 04:28
My dice used to fail me all the time, so I just decided to drop marines and pick up the Imperial Guard. I love their fluff, and I figured if I can't roll for crap anyway, I may as well play an army I have some attraction to.

They have done far better than other armies I've used. I think maybe enjoying the game makes me roll better.

Although I've still only ever won 2 games. :(

Lord Inquisitor
23-04-2008, 04:57
I have horrid luck as well, but dice metter, I used chessex dice, and they do roll better than GW's dice..... hell ive seen dollar store dice roll better than GW dice
Dice would be an interesting factor to have a look at. Anyone actually done a statistical analysis? If anyone wants to roll different types of dice I'll run the analysis...


Are there not 3 flaws in measuring the "luck" factor. 1) You are not rolling the same dice as your opposition and not the same amount of rolls.
No, I'm not rolling the same dice - that could certainly be an explanation. This does not, however, explain why he rolls better when the roll is more important! Even if his dice were loaded it wouldn't explain it...


2) You are not using the same stat lines, therefore again where is the balance in rolls? You roll for 50 3's, 75 4's and 30 5's while he rolls for 60 3's 60 4's and 60 5's...
Not a major issue - I designed the study that the replication was equal. The actual number of replicates used for each game is the proportion of, say, 3+ rolls of high importance. Exactly how many rolls represents only how much subsampling within each replicate. Even if there were insufficient subsampling, it would increase variance, which would obscure an effect, not create one (essentially, it would underestimate any effect, not overestimate). He did roll slightly more dice than me overall, but that actually strengthens the conclusion.

Not only that, but the data is normalised against the expected distribution, meaning that the 3+, 4+ and 5+ can be compared - and there was no overall significance difference between needing a 3+, 4+ or 5+ if you don't consider any other factor. So this definately isn't an issue.


3) How can you determine what is a high or low importance roll. That one to hit, to wound, to save, to anything could equally result in the difference anywhere.
It is subjective, true. However, that's no less valid. Any experienced 40K player knows that some rolls are pivotal to the game. To give an example, when attacking with his Dire Avengers, we assigned low (i.e. default) importance to the Dire Avengers but high to the Exarch's power weapon attacks. As long as the importance is agreed by both players and, critically, assigned before the roll is made, no problem there.

The test is going to tell us if he succeeds more often in situations we deem to be important. And he does!


The lists on their face look unbalanced too. You have all of 19 guys, he has 31, 6 of your guys are lesser daemons, which means they have no shooting ability at all.
I've not differentiated between dice rolls. A 3+ roll is a 3+ roll, whether from shooting or combat. If I were trying to say he's more lucky at shooting, that would be an issue, but I'm not.


If you want to test luck, swap lists, play 8 games with his list against your list, I would be willing to bet that you would win the majority of games. To me, it doesn't come down to anything random or luck, his list frankly is much more solid than yours.
And he won 7 out of 8 games. But the stats isn't looking at the outcome of the games - only the dice rolls themselves. Excepting that differing subsampling may affect things (which can be discounted as I've discussed before) you seriously think that the fact that he's rolling dice relating to pieces of plastic in eldar shapes affects the probability of, say, rolling a 4+ on one dice compared with if it related to a bit of plastic shaped like a chaos marine? ;)


Hell, each of you roll the same set of dice 5000 times, note the results, and then see if he in fact rolls luckier than you.
Ah, but I wanted to see if the importance of the dice roll in game had an effect - and it did!


They have done far better than other armies I've used. I think maybe enjoying the game makes me roll better.
Na, I had good fun and still rolled atrociously. You think positive attitude affects the dice rolls?

If I've time I'll also run a different analysis comparing our rolls with the theoretical predictions to see which sets of dice rolls differed significantly from the expected distributions. This analysis simply looks at whether I differ from my opponent.

I've some theories about what could be causing this, but those can wait for tomorrow! :o

xinsanityx
23-04-2008, 06:29
I know that the effect that the mind has on Random Number Generators has long been stuided, and many studies have found that the mind has a small impact on them.

I'm completely open to the idea that a person's mental state, attitude, or even brain structure can affect dice rolling. I don't believe in it steadfastly, but i certainly believe it could be a possibility.

It could also be a possibility that when your dice were cast they cooled down differently and the weight distribution was off.

I actually had one di that came with a blood bowl game that would consistently roll 6's. So, i sat down and counted the number of 6's it rolled over the course of 500 drops. Over those 500 rolls that di rolled 203 6's. Needless to say something went wrong when that di was cast.

Or maybe its even a combination of the 2, who's to say why the dice come up the way they do.

Malachai
23-04-2008, 06:55
I know one thing: Dice hate me.

tk7
23-04-2008, 10:44
Hmm the Eldar list looks way more then 500 points to me, that would explain why you were beat so often.

Smokedog
23-04-2008, 10:54
If for 6 games he had 100 points more, what is the point in posting wether he won or not?
If you have more points you are at an adavantage.

Maybe I should try having a 5th more points than my opponent next 1500 point tourney i'm going with 1800 points.. lets see if anyone notices...

Santiaghoul
23-04-2008, 10:58
Being of what I like to think is a rational mind, I hate to say this, but, yah, I do think a positive outlook has a bearing on dice rolls. :) I cant explain it. I at least feel like I roll better if Im upbeat and believe that the dice will roll the way I want/need them to roll. So much so, that I wont roll a die unless its sitting on the table showing a high/low number as needed. Silly, I agree. Totally irrational.

Also, of the regular people I play. One of them normally out rolls me. And I normally out roll another player. But, when they play each other, it seems they both roll average. I do not have any statistics to back that up. Just perceptions.

alphastealer
23-04-2008, 11:11
I had some issues with a friend of mine a while back.

He had this knack of rolling just what he needed at the right time be it a 3/4/ or 5+, so I got curious and watched him.

Eventually it came out that he has a dice rolling technique that (while not guaranteed) does tend to give him what he wants 8/10 times. Something about the number he wants he places to the left in his palm, then he curls his hand as he rolls the dice on a flat surface.

It is scary how often that number comes up, using that technique. Obviosuly this applies to a single dice roll on a smooth hard flat surface.

So be careful, sometimes what looks like luck is actually something else.

wickedvoodoo
23-04-2008, 12:16
I saw this on a TV show not too long ago. A guy had trained himself to be able to throw doubles whenever he wanted. he was playing backgammon so the doubles were winning it for him. Like alphastealer said, the trick is down to always holding the dice a certain way so there is more chance it just skims on the number you want rather than rolls over onto another side.

toymaker
23-04-2008, 12:53
I was thinking about this thread. I wonder if you went with Plague marines rather than Noise marines you'd have better luck. T5 and FNP would definately make things interesting

Lord Inquisitor
23-04-2008, 15:08
I know that the effect that the mind has on Random Number Generators has long been stuided, and many studies have found that the mind has a small impact on them.
Really? That's interesting. Bit of a long shot, but you wouldn't happen to have any references for that, would you? I'll certainly look it up as part of my write-up.


Hmm the Eldar list looks way more then 500 points to me, that would explain why you were beat so often.
Yep. About game 5-6 I checked his list and discovered he was over. Games 7 & 8 should have been equal points.


If for 6 games he had 100 points more, what is the point in posting wether he won or not?
If you have more points you are at an adavantage.
Well, clearly it had an effect .... I was just listing the games because I thought people might be interested - the outcome of the games was not in any way a factor in the analysis.


Maybe I should try having a 5th more points than my opponent next 1500 point tourney i'm going with 1800 points.. lets see if anyone notices...
People probably wouldn't... I sure don't check my opponents' lists at tournaments, even when they seem to have got a lot for their points.


I had some issues with a friend of mine a while back.

He had this knack of rolling just what he needed at the right time be it a 3/4/ or 5+, so I got curious and watched him.

Eventually it came out that he has a dice rolling technique that (while not guaranteed) does tend to give him what he wants 8/10 times. Something about the number he wants he places to the left in his palm, then he curls his hand as he rolls the dice on a flat surface.

It is scary how often that number comes up, using that technique. Obviosuly this applies to a single dice roll on a smooth hard flat surface.

So be careful, sometimes what looks like luck is actually something else.
Also interesting, I've been wondering about this.

Here are my theories (any other theories welcome - I can use it for my write-up! :) )

Pure random chance
It's possible there is no pattern and these things have simply cropped up by chance. Well, the analysis has calculated this probability - there is a one in a thousand chance of that. That's a very low chance (well within what's scientifically acceptable as non-random) and completely not what I was expecting! Not only that, but the reason for the study in the first place was anecdotal suggestion that he rolls better than me.

Loaded dice
Not necessarily loaded, but quite possibly uneven in some way. While differences in dice might explain the differences between us, it doesn't explain why he rolls better for important dice rolls.

One possible explanation would be that he has certain "lucky" dice. For regular rolls, he just grabs any old dice. For important rolls he (conciously or unconciously) may prefer to use certain dice. This may not even have anything to do with favourite dice - for example, if his 3 blue dice roll better, if he uses them to distinguish his power weapon attacks, he's consistently going to be using them for important rolls.

Still, there are some dice rolls like scatter dice where we do use the same single dice and he does seem to do better for them. And it doesn't explain Ld tests which require low rolls! Out of those 8 games, he made somewhere between 3-6 leadership tests (morale or pinning) per game. Not one single failure. Unfortunately I didn't record how many exactly, or I could run the numbers on that too...

Rolling technique
I seriously doubt he has a magic technique he's not telling me about, but most wargamers have stupid supersitions about the dice. For example, I tend not to roll dice that have rolled well again - I pick up new dice. Probably stupid, but it is possible something like this could be affecting the dice roll - particularly if there is some non-random likelihood of getting a given roll dependent on the type of dice being rolled.

Coragus
23-04-2008, 15:43
Dice have been discussed on another thread around here somewhere. I remember that a researcher with minions to command in a lab forced them to roll GW dice, regular dice, and Vegas dice a bunch of times and keep track of the results. The claim made, if I remember, was that the GW dice averaged a full pip lower than the other two types, which didn't show any statistical variance.

I know that my miserable dice luck went away the moment I threw away every single of the Gods-blessed little GW dice I owned and bought dice. Nothing fancy, just ten normal black dice with white pips, specifically for my Imperial Guard. They do what I ask from my dice, which is just to keep the improbabilities to a minimum.

Rirekon
23-04-2008, 15:56
If you have infinite monkeys with typewriters one of those monkeys will type the complete works of Shakespear, it could well be argued that monkey is luckier than the other monkeys. It's my theory, that out of the billions of people on Earth some of them will just happen to be consistently in the right place at the right time (or hitting the right keys in the right order).

Lord Inquisitor
23-04-2008, 17:53
I was thinking about this thread. I wonder if you went with Plague marines rather than Noise marines you'd have better luck. T5 and FNP would definately make things interesting
Again, the analysis had nothing to do with who won or lost, so unless you think that worshipping Nurgle would bring me better dice rolls... ;)

Besides, something people don't seem to be realising - I wanted to run this analysis using our usual armies... I did want to run it with our usual forces and dice.

One oddity, is that his trademark good luck doesn't seem to apply when he's using his guard. Might need to test it sometime! (That would blow every theory of mind out of the water!)


Dice have been discussed on another thread around here somewhere. I remember that a researcher with minions to command in a lab forced them to roll GW dice, regular dice, and Vegas dice a bunch of times and keep track of the results. The claim made, if I remember, was that the GW dice averaged a full pip lower than the other two types, which didn't show any statistical variance.
I'll have a search. Got a link to that, by any chance?

Well, I might add that neither of us use GW dice any more. However, mine are small (very similar to GW dice and uniform) while his are large and a variety of hard and curved edges.


If you have infinite monkeys with typewriters one of those monkeys will type the complete works of Shakespear, it could well be argued that monkey is luckier than the other monkeys. It's my theory, that out of the billions of people on Earth some of them will just happen to be consistently in the right place at the right time (or hitting the right keys in the right order).
Heh. Well, like I said, that makes him one wargaming monkey in a thousand. I'm going to have to start shouting "flukey monkey!" at him.

Trickle
23-04-2008, 19:04
Take one of the 2 dire avenger squads away and you are now close to 500pts for the Eldar.

Spook101
23-04-2008, 20:52
try this.
write up two lists just like before.
play eight games just like before
but
play two games with your army and your dice
play two games with your army and his dice
play two games with his army and your dice
finaly two games with his gear.

this should determine if the dice are a factor, some predetermined mindset of 'luck with this army', or luck in general.
Also, try to keep track of all rolls, not just the 'important' ones. you may find that the average 'bad' rolls happen when you dont pay attention. Also, use percentage rather than numers(ie. i passed 5 more 5+ saves than him becomes he passed 10% more than me)
(my luck is usualy very poor because i can save and pass ld 75%+, but i cannot hit or kill if i try)

also, that profesors studies are that dice with round corners roll under averege, while dice with square corners roll average.

Eulenspiegel
23-04-2008, 21:17
Well Lord Inquisitor, shame on you, you made two basic errors:

- both players not using the same dice

- not using a cup to roll and throw the dice

;)

Did your Chaos guys really make that many die rolls? It seems to me you were thrashed the first games, so youŽd propably made much less rolls to hit / to wound than your opponent (granted, more saves perhaps ;) ). So the statistical variability would be much higher, and the result much less tellling.

Lord Inquisitor
23-04-2008, 21:49
try this.
write up two lists just like before.
play eight games just like before
but
play two games with your army and your dice
play two games with your army and his dice
play two games with his army and your dice
finaly two games with his gear.

this should determine if the dice are a factor, some predetermined mindset of 'luck with this army', or luck in general.
Would indeed be a better study. But I'd need to play at least eight, probably many more, of each game type, not just two...


Also, try to keep track of all rolls, not just the 'important' ones. you may find that the average 'bad' rolls happen when you dont pay attention.
I did... all rolls were accounted for...


Also, use percentage rather than numers(ie. i passed 5 more 5+ saves than him becomes he passed 10% more than me)
Again, that's exactly what I did...


also, that profesors studies are that dice with round corners roll under averege, while dice with square corners roll average.
Interesting, although it was more like I rolled average with round corners and he rolled over average with square...


Well Lord Inquisitor, shame on you, you made two basic errors:

- both players not using the same dice

- not using a cup to roll and throw the dice

;)
Both would have been interesting factors, but I did want to simulate our normal gaming environment - i.e. the dice we usually use and the method of throwing them that we normally use.

Maybe using the same dice, a cup and a box for dice would have ironed out the "luck" factor - but that's not how we usually play!

Would be worth investgating in my own time, perhaps, to see if that solves the issue - perhaps we should use a dice box, cup and homogenous dice...


Did your Chaos guys really make that many die rolls? It seems to me you were thrashed the first games, so youŽd propably made much less rolls to hit / to wound than your opponent (granted, more saves perhaps ;) ). So the statistical variability would be much higher, and the result much less tellling.

Oh, and my Chaos guys roll plenty of attacks. 6 Noise Marines get 18 attacks when shooting or when charging! But as I said, there was plenty of variability and the variance (and differences therin) is part of the analysis. I can assure you, checking assumptions of homogeneity of variance for a 3-factor ANOVA is like having teeth removed - just trust me, it's accounted for!

whitehat51
23-04-2008, 22:04
Or... When I played 8 games of 40K in a row...
As for armies (from memory) - 500 points
My opponent:
Eldar
Autarch (Warp-jump pack, fusion pistol and lots of power weapon attacks)
10 Striking Scorpions (Exarch, power claw, infiltrate & move through cover)
10 Dire Avengers (Exarch, shimmer shield, defend & bladestorm)
10 Dire Avengers (Exarch, shimmer shield, defend & bladestorm)

Me:
Chaos Space Marines
Sorcerer (doombolt, Mark of Slaanesh)
6 Noise Marines (sonic blasters, blastmaster)
6 Noise Marines (sonic blasters)
6 Lesser Daemons

Here's the problem. His list is not nearly 500 points.

10 Dire Avengers with an Exarch with Bladestorm, Shimmershield, and Defend is way over 150 points, and 2x that is 350, at least. 10 Striking Scorpions cost over 150 naked, and the Exarch with the Scorpion's Claw, Stalker, and Shadowstrike brings it over 200 points. The Autarch is over 100 points with that equipment.

That gives him a list that is far over your designated points limit. He's winning because he's either very dumb or he's cheating.

Oh, and Rirekon, that thing you wrote is very original. You didn't steal it from Family Guy or anything.... ;)

rintinglen
23-04-2008, 22:23
Here's the problem. His list is not nearly 500 points.

10 Dire Avengers with an Exarch with Bladestorm, Shimmershield, and Defend is way over 150 points, and 2x that is 350, at least. 10 Striking Scorpions cost over 150 naked, and the Exarch with the Scorpion's Claw, Stalker, and Shadowstrike brings it over 200 points. The Autarch is over 100 points with that equipment.

That gives him a list that is far over your designated points limit. He's winning because he's either very dumb or he's cheating.

Oh, and Rirekon, that thing you wrote is very original. You didn't steal it from Family Guy or anything.... ;)

AT ISSUE IS NOT WHO WINS, BUT WHO ROLLS "BEST."
Yeah, I know I'm shouting, but the point bares reiterating--they were not comparing lists, but rather die rolls, especially die rolls when they count most.
It was not who won, but who was "luckiest" that was being tested.

Oh, and the thousand monkeys riff is far older than family guy. I recall reading it in a Sci-fi story written back in the fifties (I was reading it in the sixties--I'm not THAT old). The lead character was explaining his improbable survival, (yet if I recall correctly, he finished his monologue by saying someting to the effect that he still keeps his rabbit foot).

centy
23-04-2008, 23:55
i used to be unlucky like that, then i left my girlfriend and brought new dice . NOW I'm lucky.

Lord Raneus
24-04-2008, 00:08
If you can't roll, don't play an elite army; play one that won't hit on anything higher than a 4 in most any situations, and doesn't roll armor saves:
In other words, Orks. :D

GW dice do seem to roll an ungodly amount of ones, I'm considering either blessing mine with holy water (no joke- I have some from Knox, Ireland!) or buying some blue-and-white Chessex ones to go with my Ultramarines.

And even if who wins is not at issue, I'm sure he'd love not getting plastered in over 50% of his games because his friend is either bad at writing army lists or cheating. ;)

Lord Inquisitor
24-04-2008, 01:11
That gives him a list that is far over your designated points limit. He's winning because he's either very dumb or he's cheating.
Looking at it, I make it 691 points and even after I noticed the discrepancy he was still 100 points over me for the last two games. Going to have to mention that to him... :eyebrows:


Yeah, I know I'm shouting, but the point bares reiterating--they were not comparing lists, but rather die rolls, especially die rolls when they count most. It was not who won, but who was "luckiest" that was being tested.
Someone was paying attention!


I recall reading it in a Sci-fi story written back in the fifties (I was reading it in the sixties--I'm not THAT old). The lead character was explaining his improbable survival, (yet if I recall correctly, he finished his monologue by saying someting to the effect that he still keeps his rabbit foot).
While it predates it quite considerably, personally I always remember it from Hitchhiker's Guide...


i used to be unlucky like that, then i left my girlfriend and brought new dice . NOW I'm lucky.
But... but these were new dice... Pink and black to go with my army...

Hmmm... :eyebrows:

I seriously doubt I could make that grounds for divorce! :angel:


If you can't roll, don't play an elite army; play one that won't hit on anything higher than a 4 in most any situations, and doesn't roll armor saves:
In other words, Orks.
I run on the assumption that my Noise Marines are actually, in fact, Ballistic Skill 3. They always seem to hit with about 50% of their shots.


GW dice do seem to roll an ungodly amount of ones, I'm considering either blessing mine with holy water (no joke- I have some from Knox, Ireland!) or buying some blue-and-white Chessex ones to go with my Ultramarines.
If you want to bless some of your dice and keep others as the control, roll each set a bunch of times and record the rolls I'd be happy to run the analysis to see if blessed dice roll better! ;)


And even if who wins is not at issue, I'm sure he'd love not getting plastered in over 50% of his games because his friend is either bad at writing army lists or cheating.
Well, getting obliterated game after game did get a little onerous... He's a good guy, so I'm sure he wasn't cheating, but I'm going to have to make sure he checks his maths in future!

TheDarkDuke
24-04-2008, 03:42
Also interesting, I've been wondering about this.

Here are my theories (any other theories welcome - I can use it for my write-up! :) )

Pure random chance
It's possible there is no pattern and these things have simply cropped up by chance. Well, the analysis has calculated this probability - there is a one in a thousand chance of that. That's a very low chance (well within what's scientifically acceptable as non-random) and completely not what I was expecting! Not only that, but the reason for the study in the first place was anecdotal suggestion that he rolls better than me.

Loaded dice
Not necessarily loaded, but quite possibly uneven in some way. While differences in dice might explain the differences between us, it doesn't explain why he rolls better for important dice rolls.

One possible explanation would be that he has certain "lucky" dice. For regular rolls, he just grabs any old dice. For important rolls he (conciously or unconciously) may prefer to use certain dice. This may not even have anything to do with favourite dice - for example, if his 3 blue dice roll better, if he uses them to distinguish his power weapon attacks, he's consistently going to be using them for important rolls.

Still, there are some dice rolls like scatter dice where we do use the same single dice and he does seem to do better for them. And it doesn't explain Ld tests which require low rolls! Out of those 8 games, he made somewhere between 3-6 leadership tests (morale or pinning) per game. Not one single failure. Unfortunately I didn't record how many exactly, or I could run the numbers on that too...

Rolling technique
I seriously doubt he has a magic technique he's not telling me about, but most wargamers have stupid supersitions about the dice. For example, I tend not to roll dice that have rolled well again - I pick up new dice. Probably stupid, but it is possible something like this could be affecting the dice roll - particularly if there is some non-random likelihood of getting a given roll dependent on the type of dice being rolled.

Just to add to my earlier post/your response. I think you should play another couple of games, but use the same dice.. ie what you deem a high importance armor save, use the same dice as he would. Just to cut out the "different dice" aspect. I am now thinking that instead of you agreeing on important rolls... try tallying the difference in luck for hits, wounds, saves separately based on 3's,4's and 5's. See if that changes any of your stats.

Pure random, or "chance" is my bet, as GW do not make loaded dice, they probably do not have that same standard as say a casino... but that is something that is probably known. There is no "magic dice rolling technique" There are dice "sliding" techniques but these are very easily spotted as the dice do not roll but rather kinda rattle on a hard surface but never toss/turn. If you have ever played Yahtzee(sp?) using the plastic cup to roll the dice, you can see the "affect" of dice sliding, should the dice be set decently in the cup.

Rirekon
24-04-2008, 08:21
Oh, and Rirekon, that thing you wrote is very original. You didn't steal it from Family Guy or anything.... ;)

You're right, I didn't. I stole it from the same source Family - not an original idea in our bones - Guy did.


I am now thinking that instead of you agreeing on important rolls... try tallying the difference in luck for hits, wounds, saves separately based on 3's,4's and 5's. See if that changes any of your stats.

I think, please correct me if I've got the wrong impression, this study is taking into account that "being lucky" is measured by how much the outcome benefits you. This is actually a really interesting take as it ignores that any given die rolled any given number of times should result in a (roughly) equal number of each face. Instead it highlights that the for this particular person the values they want to come up do so more often when it's important to them.
What would be interesting is getting out a roulette wheel and wagering pennies with them (to given an importance to the event). See how often they get it right just using black/white. You then have a direct measure of importance (the more pennies - the more imporant).

xinsanityx
24-04-2008, 10:00
http://noosphere.princeton.edu/

Here's the reference on the ability of minds affecting random number generators. Sorry i didn't post it sooner, i've had a busy week.

They've been doing that for 10 years, theres quite a bit of stuff to read through. Regardless of what your conclusion is, it should be an interesting read.

I also believe that there was a study done in the late 80's early 90's on the ability of individuals to affect a random number generator. I can't find any information on the internet about it though, however i only really looked for 5 minutes. There was also a discovery channel piece on this subject that i watched in a statistics class back in high school. I don't recall its name however, and it might not have even been a discovery channel product, it could have been from the science, or history channel, or some other obscure company.

Souchan
24-04-2008, 10:24
I may be superstitious, but since I once heard of that study I gave a try to never using those tiny little dice, be they GW or other and I must say, I am never going back. I don't know what it is about the little ones, but they just rock at getting them 1's and 2's and my BT's never felt like they wore power armour with how quick they died.

Switching to the big red dice that come with poker sets(that had their recent popularity surge) has been bliss. I have always been able to be sure that I have only myself to blame. Unlucky spills happen, but they are now conuter balanced by some lucky ones(which were few and far between, I actually kept count) and no longer 1's are a common sight on my single roles. With the little ones, they managed to surprise me if I made a roll that didn't involve a 1 and while when rolling many dice, sure there are gonna be ones, but every time when rolling only one or 2 die getting a one is downright frustrating.(My plasma pistol assault marines, well, I came to rely on them dying if I shot so I just stopped shooting with them.(certain situations still we're better to try than not, only to stare again at 2 sudden holes in my formation)

Once again, some my friends think I'm paranoid, some have fallen in and agree(played a game against him, he used the small dice I used my big dice, easiest win I ever had against him, maybe the dice gods fueling our paranoia but hey :) )

Take it as you will, I haven't got the science to back it up, just the feeling that came with the switch :)

Smokedog
24-04-2008, 10:40
I have recently switched back to my "big dice" with square corners as my little dice seemed to be woeful. I'll see waht happens this saturday at the tournemnt.

Also interesting to note is all the best players (and GT winners) that I know use bigger dice, co-incidence?

Anyway back on topic - I found this link on the subject. You will ahve to read the comentaries at the bottom to get the bit on affecting dice rols.

http://www.intentblog.com/archives/2007/06/the_mind_outsid.html

xinsanityx
24-04-2008, 10:57
I have recently switched back to my "big dice" with square corners as my little dice seemed to be woeful. I'll see waht happens this saturday at the tournemnt.

Also interesting to note is all the best players (and GT winners) that I know use bigger dice, co-incidence?

Anyway back on topic - I found this link on the subject. You will ahve to read the comentaries at the bottom to get the bit on affecting dice rols.

http://www.intentblog.com/archives/2007/06/the_mind_outsid.html


went to that site and read a bunch of the comments and someone brought up string theory. That was something that hadn't crossed my mind. That's also another interesting subject to look up and read into. Physics is a crazy world.

cruise
24-04-2008, 11:25
I've always considered my self lucky. Freaked my maths teacher (and a lot of the class out) once, when I spent a night at home rolling a die to see if I got higher than average rolls. I didn't, but the next day in Maths we had to...roll a die a load of times and average the result, and I just pulled out my pad from the night before. Heh.

Anyway - very interesting results. I may start recording the types of rolls and their results in my games with friends - one particularly seems to have very good chances with the scatter die, but his tanks get immobilised driving through terrain on a regular basis.

It sounds like you know your statistics, but as a computer programmer here's how I'd approach "debugging" this problem:

All throws made by a third person, using the same cup and dice for all throws, without knowing the importance of the throw.
All throws made by a third person, using the same cup and dice for all throws, knowing the importance of the throw.
All throws made by a third person, using the same cup but each players dice for all throws, knowing the importance of the throw.
All throws made by the player, but both players using the same cup and dice.
All throws made by the player, using their own dice, but using the same cup.

That should help you track down what's generating the effect.

onlainari
24-04-2008, 14:04
Wow nice effort. I'm doing actuarial studies myself.

Nice effort. Well done.


If you have infinite monkeys with typewriters one of those monkeys will type the complete works of Shakespear, it could well be argued that monkey is luckier than the other monkeys. It's my theory, that out of the billions of people on Earth some of them will just happen to be consistently in the right place at the right time (or hitting the right keys in the right order).
When you have infinity to work with, a lot of things can happen.

When you have billions to work with, not so much can happen.

Rirekon
24-04-2008, 14:26
When you have infinity to work with, a lot of things can happen.

When you have billions to work with, not so much can happen.

If you have 1 die there is a 1/6 chance it will roll a 6
If you have infinite dice there is a 1/6 chance any given die will roll a 6, however you are more likely to see at least one of them roll a 6.

If there was a 1/9^99999999999 (whatever) chance that a given monkey will type the complete works of Shakespeare then it's possible for one monkey to achieve it.
This is why, in point of fact, that even though the odds of winning the lottery are so low people still win, and even then you occasionally get multiple people winning at once.

Lower samples don't mean it can't or won't happen, it's just less likely across the sample.

Lord Inquisitor
24-04-2008, 18:12
To give you guys some more info then, here are my actual results:

Me (small dice):
Low importance:
3+ 0.64 (expected: 0.67)
4+ 0.47 (expected: 0.50)
5+ 0.36 (expected: 0.33)
High importance:
3+ 0.63 (expected: 0.67)
4+ 0.47 (expected: 0.50)
5+ 0.35 (expected: 0.33)

Him (large dice)
Low importance:
3+ 0.66 (expected: 0.67)
4+ 0.57 (expected: 0.50)
5+ 0.34 (expected: 0.33)
High importance:
3+ 0.74 (expected: 0.67)
4+ 0.62 (expected: 0.50)
5+ 0.49 (expected: 0.33)

As you can see, the "large dice roll better" hypothesis can't be the whole story. I roll the same whether low or high importance, and typically about average (slightly less). He rolls about what is expected (I'll run an analysis at some point to check this) when low importance but the real jump higher than expected is when it is important.





Here's the reference on the ability of minds affecting random number generators. Sorry i didn't post it sooner, i've had a busy week.
No problem, thanks!

That's some good stuff there. Seems like it's pretty much bunk, but the debunking itself seems interesting.


I also believe that there was a study done in the late 80's early 90's on the ability of individuals to affect a random number generator.
I'll have a look. I'll post if I find it.


I may be superstitious, but since I once heard of that study I gave a try to never using those tiny little dice, be they GW or other and I must say, I am never going back. I don't know what it is about the little ones, but they just rock at getting them 1's and 2's and my BT's never felt like they wore power armour with how quick they died.
So, it is the size of the dice or whether they have round corners? Man, I may need to get some dice to test this! Take player and importance out of the equation and just test dice...


Anyway back on topic - I found this link on the subject. You will ahve to read the comentaries at the bottom to get the bit on affecting dice rols.

http://www.intentblog.com/archives/2007/06/the_mind_outsid.html
Cheers. Also useful!


Anyway - very interesting results. I may start recording the types of rolls and their results in my games with friends - one particularly seems to have very good chances with the scatter die, but his tanks get immobilised driving through terrain on a regular basis.
As I said before, this same opponent seems to have the devil's luck with scatter dice (>50% hits, I would say), while I seem to miss quite miserably ... using the same dice...


It sounds like you know your statistics, but as a computer programmer here's how I'd approach "debugging" this problem:

All throws made by a third person, using the same cup and dice for all throws, without knowing the importance of the throw.
All throws made by a third person, using the same cup and dice for all throws, knowing the importance of the throw.
All throws made by a third person, using the same cup but each players dice for all throws, knowing the importance of the throw.
All throws made by the player, but both players using the same cup and dice.
All throws made by the player, using their own dice, but using the same cup.

That should help you track down what's generating the effect.
Yeah, something like that would be good, although I wouldn't be sure about adding in a third person (how do we know they're a good benchmark?). The analysis would have to be different though, because an ANOVA like this would just make your head explode. A simple contingency table might work...


When you have infinity to work with, a lot of things can happen.
More than that. If you have infinity, anything possible WILL happen.


If you have 1 die there is a 1/6 chance it will roll a 6
If you have infinite dice there is a 1/6 chance any given die will roll a 6, however you are more likely to see at least one of them roll a 6.
If you have an infinite number of dice then you will roll an infinite number of sixes... ;)


If there was a 1/9^99999999999 (whatever) chance that a given monkey will type the complete works of Shakespeare then it's possible for one monkey to achieve it.
This is why, in point of fact, that even though the odds of winning the lottery are so low people still win, and even then you occasionally get multiple people winning at once.

Lower samples don't mean it can't or won't happen, it's just less likely across the sample.
Yes, but bear in mind that the probability of said event may be so low it is practically impossible. If your event is unlikely to happen even if you get all of the monkeys in the universe working for billions of years - then it is, for all intents and purposes, impossible. On the other hand, given an infinite amount of time it will happen.

D.B.
24-04-2008, 19:52
I'm curious as to what exactly an ANOVA analysis is (I've browsed wikipedia briefly, but still none the wiser - has your course any handy online notes?) and whether it assigns a probability of 1/1000 (and if so under what assumptions?) or a significance level of 1/1000?

Lord Inquisitor
24-04-2008, 21:25
Basically, it just works out whether two (or more) mean values are significantly different. So for example, if we're comparing me and my opponent rolling 20 dice and we can just see what the probability that these two samples actually are different (or, more exactly, what the probability that these samples aren't different and the difference in means is due to chance). So my p-value of 0.001 means there is a 1 in 1,000 chance that with that amount of sampling, the difference in mean value is purely due to chance. In our case, this is dead easy to conceptualise, since we know what the expected probabilities are (but note that I'm NOT using any probabilities relating to dice - purely comparing him versus me, nothing to do with expected values). So to answer your question significance and probability are the same thing - significant means less than 5% probability of getting this result by chance, given the variability in the samples.

Now, the actual analysis is much more complicated because we're comparing anywhere between two and twelve mean values in various different ways - not only whether, say, he rolls better than me, but under what conditions and whether the interactions are important.

Rirekon
24-04-2008, 21:35
If you have an infinite number of dice then you will roll an infinite number of sixes... ;)

Yeah, that was a silly mistake :p:D

Coragus
28-04-2008, 13:57
Dice have been discussed on another thread around here somewhere.

Found it! Right here:
http://warseer.com/forums/showthread.php?t=65531

Bunnahabhain
28-04-2008, 14:25
Just to check, you were deciding if dice were high or low importance before the roll, yes?

I've spent long enough in science to know when you get strange results, you check your equipment, your methods, and most importantly, your assumptions. 8 battles should generate enough dice rolls that the chance of it being a skewed data set is very small. How many dice rolls does your data set come from, by the way?

"Ford, there's an infinite number of monkeys outside who want to talk to us about this script for Hamlet they've worked out..."
Hitchhikers.

Lord Inquisitor
28-04-2008, 16:28
Just to check, you were deciding if dice were high or low importance before the roll, yes?
Yep.


I've spent long enough in science to know when you get strange results, you check your equipment, your methods, and most importantly, your assumptions. 8 battles should generate enough dice rolls that the chance of it being a skewed data set is very small. How many dice rolls does your data set come from, by the way?
Me: 1470. Him: 1808

That's a little misleading, however - the actual numbers used were the proportion of successful dice rolls, and these were not always constant number of dice (in particular, the 5+ rolls were rather under-represented).

If I've time, I'll run another analysis that WILL take the actual number of dice into account and compare our results to the expected distributions.

In the meantime, here's a graph of the data. My rolls are in blue, his in red and the darker colour indicated higher importance.

http://www.geocities.com/eoinwhelan/Graph.JPG

onlainari
02-05-2008, 03:11
I want to expand on what I said earlier.

When you have infinity to work with, anything possible will happen.

However the expected time it takes to happen might be infinity.

mchmr6677
02-05-2008, 13:06
Question 1: Are you using your opponent's dice to make the armor saves?
Question 2: Does your opponent use particular dice for power weapon attacks or AP2 attacks that seem overly lucky?

kaptin_blacksquigg
02-05-2008, 13:34
Cool, thread.

I've taken and taught some stats classes in my time and have some technical notes.

Firstly and most importantly, did you decide on measuring a significance level of P<0.001 before carrying out your analysis? If you did not, then I'm afraid your choice to test this level of significance is capitalizing on chance. This is a very common mistake, especially when using software that give exact points where significance can be obtained.

That said I'm amazed that your data from under 3.3k rolls would give you a small enough variance to get anywhere near p:001, especially when using a random number generator (dice), this suggest a huge variation in the dice you where using.

What really interests me is the analysis of the importance factors, how does your sample size break down by importance?

On a more general note, I imagine the main difference effect is caused by dice. A applied mathematician will explain to you the extent that slight deviation in weight distribution can have a big effect on dice rolling (especially dice with rounded edges).

Another thing to note is that rounded edges will not effect the rolling of a balanced dice, but will emphasis the effect of any uneven weighting.

Lord Inquisitor
02-05-2008, 14:35
Question 1: Are you using your opponent's dice to make the armor saves?
No, my dice.


Question 2: Does your opponent use particular dice for power weapon attacks or AP2 attacks that seem overly lucky?
Yep, probably. I didn't take any notes on dice when we played the games, but he has lots of white dice and a few red and blue dice - it is very likely that certain dice were persistantly being used for important dice rolls. That's my favourite theory to explain the whole buisness. Not only does it explain the low/high importance thing, but a couple of dodgy (coloured) dice which are disproportionately used would explain how such a big difference could come about.


Firstly and most importantly, did you decide on measuring a significance level of P<0.001 before carrying out your analysis? If you did not, then I'm afraid your choice to test this level of significance is capitalizing on chance. This is a very common mistake, especially when using software that give exact points where significance can be obtained.
Hmmm. I've checked this. Now, my critical value for significance is 0.05. This was assigned prior to data collection (I peformed a preliminary power test so I really did assign this first).

Now, my result of p<0.001 is obviously significant. Beyond that it is okay to report the best estimate of the exact probability (I'm reading this out of my stats textbook "Biostatistical Analysis,") which gives you more information.

What I can't do is look at the data and try and decide whether p=0.08 is significant after the fact - if I assign alpha=0.08 then that would be significant, but that would be naughty!

Or am I missing something here?


That said I'm amazed that your data from under 3.3k rolls would give you a small enough variance to get anywhere near p:001, especially when using a random number generator (dice), this suggest a huge variation in the dice you where using.
Remember I was using the proportion of successes over total dice rolls as my response variable - so the variance is going to be a lot smaller than if I were actually looking at the average scores of the dice (which are largely irrelevant anyway - noone cares if you score a 4 or a 6 on a 4+ roll, just whether you pass or not).


What really interests me is the analysis of the importance factors, how does your sample size break down by importance?
The sample size was equal for every combination of factors. However, the subsampling did vary, but there wasn't really much less subsampling for the important rolls (1982 low importance and 1296 high).


On a more general note, I imagine the main difference effect is caused by dice. A applied mathematician will explain to you the extent that slight deviation in weight distribution can have a big effect on dice rolling (especially dice with rounded edges).

Another thing to note is that rounded edges will not effect the rolling of a balanced dice, but will emphasis the effect of any uneven weighting.
Yeah, I think it has to be the dice too. I'm still surprised there was such a big difference!

mchmr6677
02-05-2008, 15:01
No, my dice.


Yep, probably. I didn't take any notes on dice when we played the games, but he has lots of white dice and a few red and blue dice - it is very likely that certain dice were persistantly being used for important dice rolls. That's my favourite theory to explain the whole buisness. Not only does it explain the low/high importance thing, but a couple of dodgy (coloured) dice which are disproportionately used would explain how such a big difference could come about.




When my usual foe (my brother) and I play, we use the actual dice that rolled the wounds to roll the saves. This would eliminate the chance that the dice are fouled (he needs high rolls to hit and wound and he needs me to roll low rolls to fail the saves), and verify weither it is my hand or his that is luckier.

That being said, my brother uses 8 black dice for his lascannons and assault cannons (SM). These dice could be loaded (not likely) or just slightly uneven, and therefore roll high numbers more often. Again, this can be counterbalanced by our using the actaul wounding dice to roll the saves because if a die is more likely to roll sixes, then while it is more likely to scores hits and wounds, it is also more likely to allow cover and invulnrable saves.

Therefore, my recommendation to eliminate the possibility of the dice being the cause is to roll saves with your opponent's dice. Then it is up to your luck alone.

Deadmetal
02-05-2008, 15:14
I used to use certain dice for important rolls, they just seemed "luckier". I also seemed to be really lucky with my amour saves, but with my Vindicare Assassin I could never wound with him, id hit every time but never ever get a 4+ for the wound roll.
Mabey this whole study proves that luck is a relevant factor in life?

onlainari
03-05-2008, 03:00
I must say on Sunday at gaming there was a player caught with a dice that had a dot painted on the 2.

He had a 5/6 chance of 3+ (still 1/2 chance of 4+ and 5/6 chance for 2+ though).

kaptin_blacksquigg
04-05-2008, 10:58
Hmmm. I've checked this. Now, my critical value for significance is 0.05. This was assigned prior to data collection (I peformed a preliminary power test so I really did assign this first).

Now, my result of p<0.001 is obviously significant. Beyond that it is okay to report the best estimate of the exact probability (I'm reading this out of my stats textbook "Biostatistical Analysis,") which gives you more information.

What I can't do is look at the data and try and decide whether p=0.08 is significant after the fact - if I assign alpha=0.08 then that would be significant, but that would be naughty!

Or am I missing something here?



Yeah, It's ok to say that your results are significant at the 0.05 level and ok to report you best estimate of exact probability, all I was saying is that you can't say that you have denied the null hypothesis at the 0.001 level.
In effect the exact probability is basically an interesting aside that will be useful to guide further research.
You get me?

It's a bit of a nit-pick really, but an important mistake to avoid (that is often made even in professional journals).

Also, personally I would have used non-parametric measures if you're working with probability of success (or even straight dice rolls), but that's a debate for a stats forum!

By the way I'm not trying to shoot down your work, I think this is great, just trying to help you with your report :)