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Is my opponent just luckier than me?
ragnarok
 Post subject: Is my opponent just luckier than me?
PostPosted: Fri May 02, 2008 5:10 pm 
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Lord I.

Have you chcked to see if your luck balances out?

I have found that if I am having really horrible luck (all 1s and 2s) then my opponent will be getting all the 5sand 6s.

Thus in the game the luck and unluck cancel out.

I have also noticed, on rarer occasions, when the luck is on one table, we both always roll sixes, whilst on the next table their dice don't believe in numbers above 2.

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Lord Inquisitor
 Post subject: Is my opponent just luckier than me?
PostPosted: Fri May 02, 2008 5:52 pm 
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That's simply a matter of increasing your sample size until it all balances out ...

But what we're talking about is a systematic bias over a large number of games. No, it doesn't cancel itself out! Here are the overall deviations from the expected frequencies (so 0=no deviation from expected):



Vanvlak: no, 1 in 1000 isn't impossible. I've seen someone have their character killed in Inquisitor by a 1 in 10,000 chance (needed two "100" rolls on a D100 in a row!). But it is small enough chance that it can be accepted that there must be something else going on here. Typically anything below p=0.05 (1 in 20) is the scientific benchmark that we don't just have random effects. In the final analysis, the actual value was p=0.0003. Plus don't forget that the reason for the exercise in the first place was that we had observed that he tended to be more "lucky!"
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vanvlak
 Post subject: Is my opponent just luckier than me?
PostPosted: Fri May 02, 2008 6:56 pm 
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Interesting, this :)
How is 'lucky' defined, then? Getting more than 4 on more than 50% of the die rolls? Getting a certain % of 5+?
Or just getting the required number?

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Lord Inquisitor
 Post subject: Is my opponent just luckier than me?
PostPosted: Fri May 02, 2008 7:10 pm 
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I didn't define "lucky" that's just a convienient muddle-word.

The test was to see if he scored, on average, proportionally more successes per game than me. It can also be taken as a test to see if our dice rolls scored significantly more or less than expected assuming the dice are truly random (only the big red bar - high importance - was significantly different from 0)
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vanvlak
 Post subject: Is my opponent just luckier than me?
PostPosted: Fri May 02, 2008 7:47 pm 
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Umm, one thing I still don't quite grasp (I always was slow to get these probability things) - the first chart indicates the number of successes when a 3+ is needed; getting less when 4+ is needed, and still less when 5+ is needed (which is expected). I assume that if you needed 5+ rolls and he needed 3+ rolls this was taken in account, correct? Otherwise it would be obvious that he would have more success than you (although I for one regularly fail 3+ rolls).

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Lord Inquisitor
 Post subject: Is my opponent just luckier than me?
PostPosted: Fri May 02, 2008 8:03 pm 
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Yeah, the analysis was designed so I could pick out which factor I wanted to look at (so I can examine what effect, say, importance has and the computer will compare all the 3+ values with the other 3+ values, the 4+s with the other 4+s and so on).

But as it happens I also normalised the data by subtracting the expected result.

So, for example, game 7 I rolled 69 "low importance" dice that required a 4+ result. Of these, 39 scored a success. So, for that game, for my low importance dice rolls, the result was 0.57. Then I deducted 0.5 (the expected value for frequency of successes of 4+ rolls) so the final result for that data point was 0.07. That way it can be compared with other types of rolls with no problems. And that's what it shows in the second graph - the total averages for the importance, with 0 being the expected result.
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vanvlak
 Post subject: Is my opponent just luckier than me?
PostPosted: Sat May 03, 2008 11:03 am 
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Ah, I see - I think!

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ragnarok
 Post subject: Is my opponent just luckier than me?
PostPosted: Sat May 03, 2008 10:16 pm 
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Another quick question.

were your dice correct for your army?

I had horrid luck with my merky yellow/black dice, even more so when I used them with my slaanesh.

however my luck improved when I swapped them for pink and black marble with white dots.

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Lord Inquisitor
 Post subject: Is my opponent just luckier than me?
PostPosted: Sun May 04, 2008 3:49 pm 
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It was a Slaanesh army and I was using my shiny new pink-and-black dice with white dots too. :( So there goes that theory.

Although I'd have a difficult time coming up with a scientific explanation as to why pink dice rolled better...
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ragnarok
 Post subject: Is my opponent just luckier than me?
PostPosted: Sun May 04, 2008 7:36 pm 
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(Lord Inquisitor @ May 04 2008,15:49)
QUOTE
It was a Slaanesh army and I was using my shiny new pink-and-black dice with white dots too. :( So there goes that theory.

Although I'd have a difficult time coming up with a scientific explanation as to why pink dice rolled better...

In that case my only suggestion is that slaanesh turned his/her back on you for having dealings with tzeentch.

You were playing with the princes of pleasure army and were trying to figure out luck, the domain of the trickster god.

Though how you can give that as a scientific explanation I will leave up to you.  :D

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illuvitar
 Post subject: Is my opponent just luckier than me?
PostPosted: Sun May 04, 2008 8:07 pm 
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do a new experiment and buy new dice, also have both players use the same dice, every roll. much more valid experiment eh ?

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Lord Inquisitor
 Post subject: Is my opponent just luckier than me?
PostPosted: Mon May 05, 2008 4:03 pm 
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(illuvitar @ May 04 2008,15:07)
QUOTE
do a new experiment and buy new dice, also have both players use the same dice, every roll. much more valid experiment eh ?

Well, I thought this was the most valid ... perhaps we get the same overall result if we use the same dice in a dice box with a shaker: but I wanted to know whether there was a difference under our normal playing conditions. Essentially, I wanted to know if it was my imagination and general pessimistic whinging that was making it look like he rolls better than me or if there was something to it!

I think I will run a follow-up experiment. I don't think I'll go as far as to buy new dice, but I'll ask if we can both use my dice (which are uniform) and see what happens. I can do that during one game (rather than eight!) using a multidimensional log-linear contingency table analysis (which is far less complicated than the name suggests!). That way we can see if it's the dice.


(ragnarok @ May 04 2008,14:36)
QUOTE
In that case my only suggestion is that slaanesh turned his/her back on you for having dealings with tzeentch.

You were playing with the princes of pleasure army and were trying to figure out luck, the domain of the trickster god.

Oh, well, that explains everything! (Maybe I should get me some Thousand Sons?)
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illuvitar
 Post subject: Is my opponent just luckier than me?
PostPosted: Tue May 06, 2008 6:04 pm 
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multidimensional log-linear contingency table analysis

if you dont think that sounds bad your too used to hearing it. :) the first part (multidimensional log-linear) should be enough to scare off most folks !

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Lord Inquisitor
 Post subject: Is my opponent just luckier than me?
PostPosted: Tue May 06, 2008 6:40 pm 
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No, I meant that the analysis itself isn't that bad - the name is scary!

It just goes to show that statisticians are like any scientist: whatever you're working on, you need to use a really complicated and important-sounding name. If necessary (or, indeed, if at all possible), you need to make up new jargon and make that as complicated and important-sounding too. Because if everyone could understand it, people might realise how easy it all is...
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illuvitar
 Post subject: Is my opponent just luckier than me?
PostPosted: Tue May 06, 2008 9:36 pm 
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ah... i see. the word multi dimensional always makes me think of tensors. and thus want to bury my head in the sand.
and although you say it's simple, one thing i learned in statistics class is.. leave it to the experts or they'll throw big ugly integrals at you :)
cool experiment, thanks for sharing.

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