Registered: Sep, 2010
Re: Back Gammon , not realy dice by chanc....!
Feb 23, 2014 6:21 AM
My Last Post on Math & Probability :
Despite you have asked me to continue the discussion elsewhere, hence i am not going to continue i am asking you Not to delete this my last post about "Math and Probability".
SO, please publish this post.
_1_ Independence issue :
You say the dice is independence, so if there were a 6 in first and second roll , then in the third its probability is still 1/6 to have another 1/6.
It is true that " Conditional Probability " applies just for
" Dependent " variables, and that Dice is " independent ". So not exactly you can use conditional probability,
_1_A : think having three 6 in row is 1/27 (each 6 of two dice) and you have already rolled 1st, and you got a 6 so what is the probability of having another 6's ? You may say 1/9, Ok ,
then you make it done, it is all 6's.
So, now, what it was the probability of getting 6's ??? Still 1/27.
So you got a 1.27 chance.
and when this is repeated many times you may conclude maybe something is wrong with the dice !!!!
_1_B : its true with the real dice. Here there is not any real dice, it is just an algorithm which choose between supposedly random set of numbers, and redistribute them to assure they are random.
For Example : like if it gives first [ 1 3 2 4 1 6 5 2 3 4 6 5 ].
Then after the algorithm we have [ 3 1 2 6 5 4 2 4 5 6 1 3 ].
SO , if you got a double 3 in a row , just not like real dice, that it affects the all set.
_1_C : Poisson probability :
< http://en.wikipedia.org/wiki/Poisson_distribution >.
It says like an event happens 3 times per minute, what would be the probability of all three same event happens in 30 seconds ?
like if you expect 3 rolls of 6 / in 1 min what would it
be to have them all in 20 sec ???
_2_ Distribution & sample size issue :
@ Developer :
_2_A : Sample size of " 100 " was an example, for its simplicity and easy talking of the number "100" .
But still you can calculate its odds.
_2_B : Every year Lots of papers published on social sciences & medicine have the sample sizes between 100 and 1000 cases.
And that size can gives P value of 0.05 which means, by the 95% possibly you hypothesis is true.
and by the sample size of 1534 and margin of error of 2.5%, you can conclude with 95% confidence that your hypothesis is true for 1000000 people....
take a look at these sites :
< http://www.sciencebuddies.org/science-fair-projects/project_ide as/Soc_participants.shtml >
the sample sizes of millions are fine for testing airspace, odd mathematics, physics where there should be " PRECISE " calculations.
_2_C By 2x i meant : 2 sigma, Or better to say placing an even over 2 sigma of normal distribution.
_2_D you said :
" The rolls don't have to be evenly distributed over 20-30 rolls. Real dice rolls won't be either."
AND also one does not expect dice to aggregate, this way.
when numbers are randomly chosen from bigger group of numbers and then you continue to do so you may have " FUNDER EFFECT ".
In this case some dice may get enriched by special numbers.
Like number " 3 " in a set of 4 roll , and then " 1" or maybe 2 in another set.
Please take a look at this :
< http://en.wikipedia.org/wiki/Founder_effect >.
_2_E : Lets give an explanation here :
We have some factors :
Number of " types " or " kinds " and their probability.
Size of the set.
Size of the sample.
Like with dice; Sets of 5 rolls of double dice, ( 1-3,2-4 etc ) and sample size 1000 rolls and 200 set.
Well, based on distribution the way things may appear " Random " may differ , It can happen if the Variability of dice in sets gets lower than normal and still in the whole sample it seems normal.
Just like the difference of a " Harsh NOISE " and " FINE NOISE ".
In Large scale both seem to be randomized but they are not equal to each other.
_3_If my argument are not right then why don't you provide players with SGF records ???
With best regards I hope you fine a better way do dice the games.
Thank you for your patience and understanding.