I also have a membership at AAMC and the complaints about Dicey's randomness surfaced recently again.
The latest hypothesis was that in a roll of 10 dice, a number would repeat itself 4 times "far too often". Jens did the probability calculations and determined that in 100 rolls of 10 dice, you should expect to see 33 sets of the 100 containing at least one foursome. (Actually, 29 sets with 1 foursome and 2 sets with 2 foursomes).
I ran three sets of 1,000 subsets each of 10 rolls and Dicey was just fine. I was asked to run some tests on the IAAPA roller, and it is fine too.
I ran 11 rolls of 99 dice on the single roller to give over 1,000 numbers total. The full data set is copied at the end of this email.
If you look at the total data set below, I retreived 1,000 sets of 10 numbers by taking the first 10, then shifting 1 digit to the right, and using the next ten, and so on.
6116312612
1163126124
and so on...
The results I crunched show that the IAAPA roller had about 34.6% of the groups of 10 with 4 numbers matching, which is close enough to 33 to keep me happy.
The average number rolled was 3.48, as opposed to the expected 3.5 (no great surprise here either).
For the first 1,000 rolls the actual distribution was:
1's = 177; 2's = 181; 3's= 149; 4's=153; 5's=154; 6's=186
1,000 rolls total.
Regards,
BW
Here's the data set.
611631261246314431332524134116264622361266162522113654455555
532146424111211166342432666226561466525422412221635446532461
322451611541243334225116561134214131212253126143316313634562
243645661126242523636626314332136214422615643226133413461534
343523363413531521432642215212461136333625225152144561525123
634226442645151423435112126523456531611446126443324115555622
151451142453434224155165256461261556565412244562666352642561
266112154135333114615532352336346364516311635222653536153544
243225331631263133443636151341524153466131561354151666126463
164426321254525556236425341465163314416262662351221441424226
226566152322311562515456325615214146126354226431165256125361
244535152446252664151254445564465661215633554453566333652233
536615522264154221211136414226216164655643123265526664332355
162625465365511612551166512466166321452243366366416153642626
631312644553143441412132133664611252243426315254532124155461
564441432664516323222634161625633365452352241246254231335545
162564233535512344656124622446151462661334126446144425513564
246453445361516444323544541643336633631225511462645411456413
4344125164
The latest hypothesis was that in a roll of 10 dice, a number would repeat itself 4 times "far too often". Jens did the probability calculations and determined that in 100 rolls of 10 dice, you should expect to see 33 sets of the 100 containing at least one foursome. (Actually, 29 sets with 1 foursome and 2 sets with 2 foursomes).
I ran three sets of 1,000 subsets each of 10 rolls and Dicey was just fine. I was asked to run some tests on the IAAPA roller, and it is fine too.
I ran 11 rolls of 99 dice on the single roller to give over 1,000 numbers total. The full data set is copied at the end of this email.
If you look at the total data set below, I retreived 1,000 sets of 10 numbers by taking the first 10, then shifting 1 digit to the right, and using the next ten, and so on.
6116312612
1163126124
and so on...
The results I crunched show that the IAAPA roller had about 34.6% of the groups of 10 with 4 numbers matching, which is close enough to 33 to keep me happy.
The average number rolled was 3.48, as opposed to the expected 3.5 (no great surprise here either).
For the first 1,000 rolls the actual distribution was:
1's = 177; 2's = 181; 3's= 149; 4's=153; 5's=154; 6's=186
1,000 rolls total.
Regards,
BW
Here's the data set.
611631261246314431332524134116264622361266162522113654455555
532146424111211166342432666226561466525422412221635446532461
322451611541243334225116561134214131212253126143316313634562
243645661126242523636626314332136214422615643226133413461534
343523363413531521432642215212461136333625225152144561525123
634226442645151423435112126523456531611446126443324115555622
151451142453434224155165256461261556565412244562666352642561
266112154135333114615532352336346364516311635222653536153544
243225331631263133443636151341524153466131561354151666126463
164426321254525556236425341465163314416262662351221441424226
226566152322311562515456325615214146126354226431165256125361
244535152446252664151254445564465661215633554453566333652233
536615522264154221211136414226216164655643123265526664332355
162625465365511612551166512466166321452243366366416153642626
631312644553143441412132133664611252243426315254532124155461
564441432664516323222634161625633365452352241246254231335545
162564233535512344656124622446151462661334126446144425513564
246453445361516444323544541643336633631225511462645411456413
4344125164
