ksnake wrote:
For what it is worth, the odds of rolling 1,1,2,1,1,2,1 (or worse) are 1/58320 ...
Hi ksnake. I'm afraid the odds are a bit higher than the ones you just computed.
(A) The odds of rolling
1,1,(1 or 2),1,1,(1 or 2),1, in this exact order,
are 1/(6*6*3*6*6*3*6)=1:69,984
(B) The odds of rolling either
(B1) seven 1's, or
(B2) six 1's and one 2, or
(B3) five 1's and two 2's
(that is, the above combination or worse, but the 2's may be put anywhere)
are (1+7+6*7)/(6^7) = 1:6,600
But these are the odds for rolling these sequences of 7 numbers in exactly 7 rolls!
The odds of (B) happening anywhere in a sequence of 8 rolls is 2*(1+7+6*7)/(6^7)=1:2,800
The odds of (B) happening anywhere in a sequence of 9 rolls is 3*(1+7+6*7)/(6^7)=1:1,867
The odds of (B) happening anywhere in a sequence of 20 rolls
is 14*(1+7+6*7)/(6^7)=1:400
Then again, I see you played 1318 games. Let's say that there were about 6 players in each game, and that each player rolled exactly 7 times a die in each game. Then I expect you to have observed, very roughly, 6*1318*(1+7+6*7)/(6^7)=1 or 2 occurrences of sequence (B) rolled by some single player in a given game in your past career.
Since, however, about 10 thousand Blue Max games have been played (so far) I would expect sequence (B) to have happened about 6*10000*(1+7+6*7)/(6^7)=11 times in the course of all the past Blue Max games. Of these, a couple were probably even longer sequences, with a couple of additional 2's either before or after sequence (B).
Since you were in more that 10% of all the blue max games (WOW!) I'm not surprised that you reported such an event. In fact, I would be surprised if nothing like that had ever happened!
In a punchline: thank you webmasters for designing such a wonderful random numbers generator as rand() 
I don't think I have messed up the maths very much. Maybe 7 rolls per player is a lot (I don't know), but remember that if a player rolls 9 dice then the odds rise a lot (think of Bristols, for example). Everyone is welcome to contribute to these calculations...
neko 
--- Message edited by flying_neko |
Donate
Leagues
Gonzaga
Blue Max
Cartagena
Wooden Ships...
King Me!
VampiRing
