Testing Dices

[Evillevi]

Testing . Feel free to post and roll 13 dice to expand the pool
[dice]1308[/dice]

 

[Evillevi]

2nd test
[dice]1309[/dice]

 

[Evillevi]

Boop
[dice]1310[/dice]

 

[Evillevi]

4th test
[dice]1311[/dice]

 

[Evillevi]

5th test
[dice]1312[/dice]

 

[Evillevi]

6th test
[dice]1313[/dice]

 

[Evillevi]

7th test
[dice]1314[/dice]

 

[Evillevi]

8th test
[dice]1315[/dice]

 

[Evillevi]

9th test
[dice]1316[/dice]

 

[Evillevi]

10th test
[dice]1317[/dice]

 

[Evillevi]

1-10 >> 15
11-20 >>14
21-30 >> 15
31-40 >> 9
41-50 >>18
51-60 >> 10
61-70 >> 8
71-80 >> 13
81-90 >> 9
91-100 >> 19


Average = 49.6


End result of 130 data points with the QQ roller for those interested. My hypothesis seems likely though not conclusively so


Essentially there's a high tendency for the dice to roll at the low end of the range and when it rolls high there's a tendency to roll really high

 

[wayne82444]

That first roll was 15 die, so you actually tested 132 times. I'd imagine you found the average based on 130, so that one isn't right.
[dice]1319[/dice]

 

[Evillevi]

That first roll was 15 die, so you actually tested 132 times. I'd imagine you found the average based on 130, so that one isn't right.
[dice]1319[/dice]

Click to shrink...

I got rid of two dice from the first 15

 

[kinglugia]

Someone is bored I see...
[dice]1320[/dice]

 

[Evillevi]

Someone is bored I see...
[dice]1320[/dice]

Click to shrink...

Not that difficult.

Also there's a somewhat higher than normal possibility that the RNG for the QQ dice is borked.

 

[pepperjack]

I'm new to this sort of thing, but I looked up what a chi-square test was and tried to apply that here.

i	Oi​	Ei​	Oi​ −Ei​	(Oi​ −Ei​ )2​	(Oi​ −Ei​ )2​/Ei​
1-10	15	13	2	4	0.31
11-20	14	13	1	1	0.08
21-30	15	13	2	4	0.31
31-40	9	13	-4	16	1.23
41-50	18	13	5	25	1.92
51-60	10	13	-3	9	0.62
61-70	8	13	-5	25	1.92
71-80	13	13			0.00
81-90	9	13	-4	16	1.23
91-100	19	13	6	36	2.77
				Sum	10.46

Given nine degrees of freedom, the critical value to establish even 70% confidence that the dice roller has bias would be 10.66; that is, by this standard, a fair die would fail more than 30% of the time. The critical value for 95% confidence would be 16.92.

I'm going to maintain that these are not statistically significant results.

 

[Evillevi]

I'm new to this sort of thing, but I looked up what a chi-square test was and tried to apply that here.

i	Oi​	Ei​	Oi​ −Ei​	(Oi​ −Ei​ )2​	(Oi​ −Ei​ )2​/Ei​
1-10	15	13	2	4	0.31
11-20	14	13	1	1	0.08
21-30	15	13	2	4	0.31
31-40	9	13	-4	16	1.23
41-50	18	13	5	25	1.92
51-60	10	13	-3	9	0.62
61-70	8	13	-5	25	1.92
71-80	13	13			0.00
81-90	9	13	-4	16	1.23
91-100	19	13	6	36	2.77
				Sum	10.46

Given nine degrees of freedom, the critical value to establish even 70% confidence that the dice roller has bias would be 10.66; that is, by this standard, a fair die would fail more than 30% of the time. The critical value for 95% confidence would be 16.92.

I'm going to maintain that these are not statistically significant results.

Click to shrink...

Thanks for the link. It's been a looooong while since I did stats.

 

[Evillevi]

Given nine degrees of freedom, the critical value to establish even 70% confidence that the dice roller has bias would be 10.66; that is, by this standard, a fair die would fail more than 30% of the time. The critical value for 95% confidence would be 16.92.

I'm going to maintain that these are not statistically significant results.

Click to shrink...

Also it's been a long while but a question, if the hypothetical actual distribution of the QQ roller (in %) is say 12/10/.../10/8 for each group of ten would the Chi square test even notice the difference from the theoratical distribution of 10% for each group

 

[pepperjack]

Also it's been a long while but a question, if the hypothetical actual distribution of the QQ roller (in %) is say 12/10/.../10/8 for each group of ten would the Chi square test even notice the difference from the theoratical distribution of 10% for each group

Click to shrink...

The way you've got it set up, you're basically only testing the fidelity of the ten's place; every roll could end with 5 and the test wouldn't notice.

One alternative would be to set up a chart with a hundred rows (one for each actual roll). One hundred and thirty rolls probably isn't a large enough number to give good data for that, though.

 

[pepperjack]

Also it's been a long while but a question, if the hypothetical actual distribution of the QQ roller (in %) is say 12/10/.../10/8 for each group of ten would the Chi square test even notice the difference from the theoratical distribution of 10% for each group

Click to shrink...

Actually, I think I misunderstood your question. In my post above, I thought you were asking about percentage distribution within each group of ten. Reading you post again, I think you're asking about distribution across the groups. Like, you're asking if

1-10 (12% of rolls)
11-12 (10% of rolls)
...
81-90 (10% of rolls)
91-100 (8% of rolls)

would be noticed by the test.

If that's what you're asking, the answer is "it depends on how many rolls you make." For a lower number of rolls, this distribution might not register as biased. For a very high number of rolls, it definitely would register as biased. That's the magic of the exponent in the fifth column of the table.


Edit: That's a feature, of course, not a bug. If you roll a d6 twenty times and get five sixes, you might just have been lucky. If you roll the same d6 two thousand times and get five hundred sixes, something is probably up.

Edit 2: Example math

Only two rows matter on this table since the rest are rolling as expected.

One hundred rolls of 1d100

i	Oi​	Ei​	Oi​ −Ei​	(Oi​ −Ei​ )2​	(Oi​ −Ei​ )2​/Ei​
1-10	12	10	2	4	0.40
91-100	8	10	-2	4	0.40
				Sum	0.80

Ten thousand rolls of 1d100

i	Oi​	Ei​	Oi​ −Ei​	(Oi​ −Ei​ )2​	(Oi​ −Ei​ )2​/Ei​
1-10	1200	1000	200	40,000	40
91-100	800	1000	-200	40,000	40
				Sum	80

For a test of only a hundred rolls, this distribution is barely a blip; the critical value for even five percent confidence is 3.32 for nine degrees of freedom. However, for a test of ten thousand rolls, this distribution is proof positive that the die is biased: the critical value for 99.9% confidence is only 27.88.


Edit 3:

If you get the 12%/10%/.../10%/8% distribution over a test of 2,000 rolls, the sum is 16, which is pretty close to the critical value for confidence of 95%, but not quite there (it would need to exceed 16.92 to get a p-value of 0.05). So, you'd need more than 2,000 rolls for this distribution to be statistically significant, but not many more.

 

[Evillevi]

Interesting. Thanks for explaining it to me