Dice analyzer 1.5.1a, 1.5.1b and 1.5.1c

cyberdaniel · Post by **cyberdaniel** » Wed Oct 18, 2006 9:06 am

Ok, if we really want a big analisys we should get all the dice registred from the users that have a lot of dice right now. AK_iceman was testing it on large battles and I know a few others that have a lot of dice registred right now. So could you post the current result you have and we'll add them up and we'll get something like 20000 dice. I think after that we'll see that in fact the dice are random and the only thing bothering us is the streaks.

subdork · Post by **subdork** » Wed Oct 18, 2006 4:32 pm

Bad Speler wrote:2000 isnt that many rolls to base a conclusion on. Here's a larger sample:

These are closer to actual odds, but are still off a bit, and are actually biased towards me, the attacker.

Mathematically, we would like to see if there is less than a 5% chance of achieving results that are at least as "bad" as these randomly. We use the Chi-squared test with 5 degrees of freedom (6 possible values of a die... subtract 1). So that p-value (critical value) is 11.07. If we get a Chi that is greater than 11.07, then we conclude that there is only a 5% chance of having rolls that are this far off from the norm.

Null hypothesis: The dice are fair
Alternative hypothesis: The dice aren't fair

Using the chi-squared test on the attacker rolls, one obtains a value of 8.99. We fail to reject the Null hypothesis. (We cannot say the dice are unfair)

Using the chi-squared test on the defender rolls, one obtains a value of 7.02. We fail again to reject the Null hypothesis (We cannot say that the dice are unfair).

horizon · Post by **horizon** » Thu Oct 19, 2006 3:13 pm

Mathematically, we would like to see if there is less than a 5% chance of achieving results that are at least as "bad" as these randomly.

Interesting ... what is the justification for 5%?

subdork · Post by **subdork** » Thu Oct 19, 2006 4:58 pm

horizon wrote:
Mathematically, we would like to see if there is less than a 5% chance of achieving results that are at least as "bad" as these randomly.

Interesting ... what is the justification for 5%?

It is mostly custom. It comes from doing Normal analysis (z-tests), where the 5% chance indicates that something is more than 2 standard deviations away. Also, using 5% and 1% are actually endorsed by the U.S. Supreme Court

horizon · Post by **horizon** » Fri Oct 20, 2006 2:17 pm

Thanks for the responce, subdork. OK, went out on the web and boned up on chi-squared test. Very informative, but leads me to another question.

Correct me if I am wrong - When using the chi-squared test to evaluate fair dice, we are saying that the observed variances can be attributed to "random fluctuations" when the chi-squared total is less than 11.07.

What if a signifcantly large number of the sample sets all have the same pattern of variance, for example the only significant portion of the chi-squared total comes from the same die face in each sample set. While these samples would be deemed fair according to the chi-squared test, surely they are not a statistically probable sample set and therefore can be classified as "un-random" using some other statistical analysis.

Thanks.

Nappy Bone Apart · Post by **Nappy Bone Apart** » Fri Oct 20, 2006 5:16 pm

That would be simple pattern recognition. If the same thing if off the same, or very similar, amounts, in more than one case, then it is likely to be non-random. I haven't seen any evidence to suggest that yet, tho.

cyberdaniel · Post by **cyberdaniel** » Fri Oct 20, 2006 5:18 pm

Ok, the new version (1.3) is out. If you want to download it follow the link on the first post. I hope you find it better and more accesible.

More info about the update is also on the first post.

subdork · Post by **subdork** » Fri Oct 20, 2006 7:59 pm

horizon wrote:Thanks for the responce, subdork. OK, went out on the web and boned up on chi-squared test. Very informative, but leads me to another question.

Correct me if I am wrong - When using the chi-squared test to evaluate fair dice, we are saying that the observed variances can be attributed to "random fluctuations" when the chi-squared total is less than 11.07.

What if a signifcantly large number of the sample sets all have the same pattern of variance, for example the only significant portion of the chi-squared total comes from the same die face in each sample set. While these samples would be deemed fair according to the chi-squared test, surely they are not a statistically probable sample set and therefore can be classified as "un-random" using some other statistical analysis.

Thanks.

Some of the problems with this as mentioned above is that the chi-squared test doesn't measure how far off a single proportion is... for example it doesn't measure how far the number of sixes is from the norm, it measure the entire distribution at once. If the 6s were off in one test and the 2s were off in another, the chi-squared test could give you the same result, but it would not be further evidence that the distribution is flawed. It would be a better idea to pool the data and do the test over.

However! one could theoretically do the test several times, then average the values to test whether we're getting results that indicate the individuals in our collection have different luck. This could be to see if the program favors people with certain characteristics. Not a very likely problem here, but in certain instances where you might expect a bias it would be a valid analysis.
Note however, I don't think this method would prove anything about "streakyness" since I imagine that there are usually several people taking turns about the same time.

I taught an introductory level stats course, and one of the assignments was to flip a coin 100 times and record the results. Then I would make it a point to call out anybody that didn't have any long streaks as being liars who fudged their data

Anyway, I hate statistics as it's really an area where people can cheat and lie simply by not reporting all their findings... In the world of beauty like that of numbers, I don't like to see such base things .... I doubt anybody has continued to read this far... so I'll stop

cyberdaniel · Post by **cyberdaniel** » Fri Oct 20, 2006 9:33 pm

Nope, I'm still reading.

By the way, if anyone downloaded the 1.3 version of the script before this post please check if the included page is http://*conquerclub.com* (or if it's active on http://www.conquerclub.com). I forgot to change it before posting (I was testing it). If you're going to download it now, it's ok, I've modified it.

Thank you,
cyberdaniel

lackattack · Post by **lackattack** » Sat Oct 21, 2006 9:12 am

That's so cool how you added an item to the menu

Nice script, cyberdaniel

Tr0y · Post by **Tr0y** » Sat Oct 21, 2006 1:03 pm

^ yea I like that too.

I think I might do something like that for my gm script's options.

cyberdaniel · Post by **cyberdaniel** » Sat Oct 21, 2006 7:31 pm

Thanks, I hoped you liked it. It integrates a lot better in the web-site and there aren't any extra buttons or tables in the game page.

gavin_sidhu · Post by **gavin_sidhu** » Sat Oct 21, 2006 9:00 pm

Beautiful script cyberdaniel

Idea: Maybe you should have a dice analyser for individual games inside the game, so you can see if you have been lucky of unlucky that game.

Another Idea: Instead of having the ideal and actual stats next to each other, y dont u just have actual and in brackets the amount you are off. Eg.

Before:
(39.12% / 31.61% / 29.27%) (37.17% / 33.58% / 29.26%)

After: 3
9.12 (+1.95) / 31.61 (-1.97) / 29.27 (+0.01)

Anyone know how come when you right click open in new tab a page the same as the one you are on opens up and not the analyzer?

cyberdaniel · Post by **cyberdaniel** » Sun Oct 22, 2006 10:46 am

Idea: Maybe you should have a dice analyser for individual games inside the game, so you can see if you have been lucky of unlucky that game.

I'm already working on the individual game stats

Instead of having the ideal and actual stats next to each other, y dont u just have actual and in brackets the amount you are off.

Good one, I'll make the modifications and post it, but I'll keep them separate, maybe someone likes this one better.

Anyone know how come when you right click open in new tab a page the same as the one you are on opens up and not the analyzer?

It's because the <a> link which is pointing to the same page you're on. There is another onclick listener that opens the dice analyzer window. I can get rid of the <a> link but I need the onclick listener (you won't be able to right click and open in new tab).

cyberdaniel · Post by **cyberdaniel** » Sun Oct 22, 2006 1:31 pm

Ok, I've modified it and came up with 3 models. If you follow the link on the first page (http://cyberdaniel.50webs.com) you should see the 3 models (refresh the page if you can't see them). You can install any of the 3 direcly from the links provided.

gavin_sidhu · Post by **gavin_sidhu** » Mon Oct 23, 2006 4:21 am

v.nice, ive got b, it is great. If uve got nothing better to do u should put + signs in the brackets for positive numbers, would make it a little easier to undrestand. Not urgent however.

A tougher but nice addition would be for the percantage data for the overall stats, with a calculated ideal and percentage showing how much you are off. Im guessing you would calculate the ideal using a weighted average system or something.

Another useful but not necessary updeate would be to make copying and pasting of data more easier (so that only the column you want to highlight gets selected not the whole row).

These results have made me quesy:
39.43% (2.26%) 31.44% (-2.14%) 29.12% (-0.14%)
66.01% (0.04%) 33.99% (-0.04%)
33.33% (10.57%) 9.52% (-22.89%) 57.14% (12.31%)
77.27% (19.40%) 22.73% (-19.40%)
38.46% (13.00%) 61.54% (-13.00%)
43.75% (2.08%) 56.25% (-2.08%)

I am currently doing very well, which mean a massive streak of bad luck is about to come my way

.

Phobia · Post by **Phobia** » Thu Nov 02, 2006 1:26 pm

Attacker dice distribution Defender dice distribution
1s █████████████████████████ 59 / 335 (17.61%) █████████████████████████ 23 / 174 (13.22%)

2s █████████████████████████ 72 / 335 (21.49%) █████████████████████████ 35 / 174 (20.11%)

3s █████████████████████████ 63 / 335 (18.81%) █████████████████████████ 28 / 174 (16.09%)

4s █████████████████████████ 55 / 335 (16.42%) █████████████████████████ 32 / 174 (18.39%)

5s █████████████████████████ 26 / 335 (7.76%) █████████████████████████ 24 / 174 (13.79%)

6s █████████████████████████ 60 / 335 (17.91%) █████████████████████████ 32 / 174 (18.39%)

1st column is attacker, second column is defender

i know not many throws atm but it does seem very uneven even for 300 throws. ill come back here when its 1000 throws. nearly 40% 1 & 2's for attacker? im having real bad luck

Stopper · Post by **Stopper** » Thu Nov 02, 2006 3:19 pm

I have the dice analyzer installed, and have had for some time, but I'd like to zero the figures again, because I'm not sure they're accurate after a site upgrade some time back.

I tried uninstalling and reinstalling this dice analyzer, but the old figures are still there. Does anyone know what I can do to zero them?

cyberdaniel · Post by **cyberdaniel** » Thu Nov 02, 2006 5:01 pm

i know not many throws atm but it does seem very uneven even for 300 throws. ill come back here when its 1000 throws. nearly 40% 1 & 2's for attacker? im having real bad luck

Interesting distribution, but they will start to even out when you get to 1000 dice.

I have the dice analyzer installed, and have had for some time, but I'd like to zero the figures again, because I'm not sure they're accurate after a site upgrade some time back.

I tried uninstalling and reinstalling this dice analyzer, but the old figures are still there. Does anyone know what I can do to zero them?

Just clear your cookies and it should get back to 0.

Stopper · Post by **Stopper** » Thu Nov 02, 2006 7:25 pm

Cheers for that, but erm, I must admit, I've been trying to clear my cookies, and I've successfully managed to clear all my logins for my credit/debit cards, and Amazon too (which now appears to be offering 50% off erotic books to me for some reason), but not for Conquer Club, which stubbornly loads up my login name and password... and still those damned Analyzer numbers are still there.

Is there a filename on windows I could search for, and delete, by any chance...? Sorry if I seem a bit computer-illiterate, I even tried looking at the script, but couldn't work anything out... Everything seems to have moved on a bit from BASIC.

zip_disk · Post by **zip_disk** » Thu Nov 02, 2006 8:20 pm

This is the specific cookie (the one with all the numbers in the content) you should want to delete but deleting them all would probably be easiest.

You can ignore the fact that the buttons look different then yours since I'm using a theme.

cyberdaniel · Post by **cyberdaniel** » Thu Nov 02, 2006 9:22 pm

Yep, follow zip_disk's instruction. You might want to save that line of numbers for future reference. I even have a separate html page that creates the graphs from that line of numbers.

Novokaine · Post by **Novokaine** » Fri Nov 03, 2006 12:50 pm

gavin_sidhu wrote:I am currently doing very well, which mean a massive streak of bad luck is about to come my way .

No it doesn't - anyone who knows something about statistics -or, well, logic- will tell you that previous throws can't possibly have an influence on following throws.

Stopper · Post by **Stopper** » Fri Nov 03, 2006 12:59 pm

Cheers, I got the cookies cleared...It never occurred to me to clear them from within Firefox...

Phobia · Post by **Phobia** » Fri Nov 17, 2006 5:29 pm

1st column attacker, second column defender
still very uneven for 4's & 5's for attacker, guess ill have to keep going -

█████████████████████████ 205 / 1129 (18.16%) █████████████████████████ 96 / 567 (16.93%)
2s █████████████████████████ 203 / 1129 (17.98%) █████████████████████████ 93 / 567 (16.4%)
3s █████████████████████████ 191 / 1129 (16.92%) █████████████████████████ 100 / 567 (17.64%)
4s █████████████████████████ 166 / 1129 (14.7%) █████████████████████████ 94 / 567 (16.58%)
5s █████████████████████████ 166 / 1129 (14.7%) █████████████████████████ 87 / 567 (15.34%)
6s █████████████████████████ 198 / 1129 (17.54%) █████████████████████████ 97 / 567 (17.11%)

Battle Outcomes Actual Stats Ideal Stats
3v2 █████████████████████████ 60 / 51 / 54 (36.36% / 30.91% / 32.73%) (37.17% / 33.58% / 29.26%)
3v1 █████████████████████████ 121 / 67 (64.36% / 35.64%) (65.97% / 34.03%)
2v2 █████████████████████████ 0 / 4 / 4 (0% / 50% / 50%) (22.76% / 32.41% / 44.83%)
2v1 █████████████████████████ 15 / 6 (71.43% / 28.57%) (57.87% / 42.13%)
1v2 █████████████████████████ 0 / 0 (NaN% / NaN%) (25.46% / 74.54%)
1v1 █████████████████████████ 8 / 4 (66.67% / 33.33%) (41.67% / 58.33%)

Overall stats
Attacker threw 1129 dice.
Defender threw 567 dice.
Wins / Ties / Loses █████████████████████████ 204 / 55 / 135
█████ Attacker wins
█████ Attacker wins 1, defender wins 1
█████ Defender wins