FIBS Board backgammon forum

Ummm......that would be a big YES!  

socksey



If high heels were so wonderful, men would still be wearing them. - Sue Grafton

Hi all,

This is an interesting topic. I wanted to check randomness of dice but not so deeply as Turner did. I wanted only to see if the probabilities are the same between all the rolls.

I used the fibs command dicetest and I got the frequency of all the Ω set of rolls.

*** Rolled 14268220 times with 2 dice
1-1 395576 1-2 396390 1-3 395832 1-4 397299 1-5 397240 1-6 396932
2-1 397146 2-2 395874 2-3 396027 2-4 396438 2-5 395265 2-6 396834
3-1 396427 3-2 396050 3-3 396131 3-4 395451 3-5 396527 3-6 395925
4-1 396060 4-2 396742 4-3 397411 4-4 396301 4-5 396704 4-6 394445
5-1 396278 5-2 396445 5-3 397166 5-4 396466 5-5 395360 5-6 396824
6-1 397473 6-2 395630 6-3 396712 6-4 397091 6-5 396219 6-6 395529


Normality assumption doesn't hold so we can use asymptotic theory. I use a simple chi square test that is based on the distance between the expected probability of each roll and the actual probability. This statistic was very close to zero and this distance is very small so we accept that there is an equal probability between all the rolls near 1/36.

Finally in this sample of near 15000000 rolls, gives us a mean of: 14268220/36=396339.444 letââ,¬â,,¢s say 396340 rolls and a variance of near 474674.
The double mean was 2374771/6=395795 less than the real sample mean.
So in this sample the doubles were less than we expect. (Note that 2374771/14268220=0.1664<1/6)

It's almost sure than the dice is random here if you consider only the equal probabilities of each roll.

I want to take into account the "toggle win" and "toggle lose" modes the dice apparently take when i climb 100 pts and suddenly drop 100 rating pts.  LOL

Don't say it, diane!  LOL

socksey



"You can never show a kindess too soon, for we never know how soon will be too late"  -  T.M.

QuoteDon't say it, diane!  LOL

erm - really - ya got me - WHAT??

Y "play better", of course.  Isn't that what you always say when I attempt to whine?  

socksey



"We cannot, in a moment, get rid of habits of a lifetime." Mahatma Gandhi

QuoteIsn't that what you always say when I attempt to whine?

Not that I recall    What I think is always to myself    

Adam O'Sad may well have found that doubles occur less frequently than expected in his survey. If he included first rolls, which by definition have to be non doubles, this may account for his results.
Nice to see Van Dyke respond with such courtesy and wit. Clearly his 40 years of playing experience have taught him a lot, if his rating of 1356 is anything to go by. I do hope that he will give us the benefit of his great understanding in the future.

QuoteNice to see Van Dyke respond with such courtesy and wit. Clearly his 40 years of playing experience have taught him a lot, if his rating of 1356 is anything to go by. I do hope that he will give us the benefit of his great understanding in the future.

Oh my, dorbel.  I think we all shared this sentiment but were hesitant to express.  I, for one, had a nice giggle reading it.

mookie

QuoteNot that I recall  What I think is always to myself 

Oh, sorry, diane.  I was sure you meant me.  Maybe you meant someone else, or maybe you always talk to yourself in shouts?  Or maybe it was my own guilty conscience I heard in shouts with your name on them?  heheheheeee

socksey  



Laugh and the world laughs with you. Cry and you cry with your girlfriends. - Laurie Kuslansky

QuoteAdam O'Sad may well have found that doubles occur less frequently than expected in his survey. If he included first rolls, which by definition have to be non doubles, this may account for his results.

Hi Dorbel, thx u for my nickname modification and of course for the info. I didn't know that. In Cyprus we play something similar that it is called "tavli". The main difference is that it's a cubeless BG. I thought that the only difference was this one. Well there is another one. Start of the game each player rolls 1 dice then highest takes both dices and he rolls. This is the first roll which can be a double.

Unfortunately, as i didn't know that, the chi-square results were not true. I should replace the expected probability for doubles with a new estimated probability lower than 1/36 then. Maybe Dorbel knows how to estimate that probability and correct the test....