100 dices
 

I'm pretty proud that I found a solution (well, not really the "solution", but the exact values and how to calculate them) for this by myself, so I wondered if you can do so, too:

(As suggested by my superior)
Throw a dice 100 times (or 100 dices at once, if you're a dice-collector). Count the number of scores of each dice, a(1) being the number of 1's, a(2) the number of 2's and so on. Then, consider the maximum and the minimum value of the 6 values a(n), for mathematical correctness denoted a(n[SUB]max[/SUB]) and a(n[SUB]min[/SUB]).
What is the probability that a(n[SUB]max[/SUB]) is equal to or greater than two times the value of a(n[SUB]min[/SUB])?

[QUOTE=mart_r;248024]Throw a dice 100 times (or 100 dices at once, if you're a dice-collector).[/QUOTE]

Sorry, I can't stop myself: Singular "die", plural "dice".

[QUOTE=mart_r;248024]What is the probability that a(n[SUB]max[/SUB]) is equal to or greater than two times the value of a(n[SUB]min[/SUB])?[/QUOTE]

I'm not sure. Oddly, I was dealing with a similar problem a few hours ago, but I just (wrongly!) treated the events as independent, since in my problem that was a reasonable approximation (it isn't here).

[QUOTE=mart_r;248024]I'm pretty proud that I found a solution (well, not really the "solution", but the exact values and how to calculate them) for this by myself, so I wondered if you can do so, too:

(As suggested by my superior)
Throw a dice 100 times (or 100 dices at once, if you're a dice-collector). Count the number of scores of each dice, a(1) being the number of 1's, a(2) the number of 2's and so on. Then, consider the maximum and the minimum value of the 6 values a(n), for mathematical correctness denoted a(n[SUB]max[/SUB]) and a(n[SUB]min[/SUB]).
What is the probability that a(n[SUB]max[/SUB]) is equal to or greater than two times the value of a(n[SUB]min[/SUB])?[/QUOTE]

[B]About[/B] 41% ....sorry I used brute force averaging cause my stats knowledge is inadequate to let me compute it.

[QUOTE=CRGreathouse;248038]Sorry, I can't stop myself: Singular "die", plural "dice".[/QUOTE]Mouse - mice

louse - lice

douse - dice

and everyone knows that the plural of spouse is spice.


Paul

[QUOTE=xilman;248049]everyone knows that the plural of spouse is spice.[/QUOTE]
Goose -> geese
Moose -> meese ?

house -> hice ?

Aw maaan.... can't I at least edit the title??

100 dices
 

"Dices" is a perfectly good word. Unfortunately, it is usually used as a verb.

So cut the guy some slack.

[QUOTE=Wacky;248074]"Dices" is a perfectly good word. Unfortunately, it is usually used as a verb.

So cut the guy some slack.[/QUOTE]

Don't you mean slice the guy some slick ?
That synonymous idiomatic form is clearly preferable.

[QUOTE=davar55;248089]Don't you mean slice the guy some slick ?
That synonymous idiomatic form is clearly preferable.[/QUOTE]

S-L-I-C-E, slice me nice...

Okay, the value, to 15 digits, is [SPOILER]40.9348246595353%[/SPOILER].

Maybe today or tomorrow I try to convert my VB program into Pari-style so I can give the number as a multiple of 6[SUP]-100[/SUP].

So, the exact number is
[SPOILER]267434832997843047170816167609147911673149856178056366366182308284997409845376
out of
653318623500070906096690267158057820537143710472954871543071966369497141477376
[/SPOILER]
And here's my poorly written Pari-Code:
[CODE]dice(w)={
x=vector(524288);v=vector(5);e=vector(170);z=0;m1=0;m2=0;if(w<100,l=" ",l="");n=concat(Str(w)," dice.txt");
for(u=1,170,for(t=1,28,e[u]=concat(e[u],0)));
forstep(p1=w,floor((w+5)/6),-1,
a=w-p1;if(a>p1,a=p1);
forstep(p2=a,floor((w-p1+4)/5),-1,
b=w-p1-p2;if(b>p2,b=p2);
forstep(p3=b,floor((w-p1-p2+3)/4),-1,
c=w-p1-p2-p3;if(c>p3,c=p3);
forstep(p4=c,floor((w-p1-p2-p3+2)/3),-1,
d=w-p1-p2-p3-p4;if(d>p4,d=p4);
forstep(p5=d,floor((w-p1-p2-p3-p4+1)/2),-1,
p6=w-p1-p2-p3-p4-p5;
z=z+1;
for(u=1,5,v[u]=1);u=1;
x[z]=p1;
x[z]=concat(x[z],p2);if(p1>p2,u=u+1,v[u]=v[u]+1);
x[z]=concat(x[z],p3);if(p2>p3,u=u+1,v[u]=v[u]+1);
x[z]=concat(x[z],p4);if(p3>p4,u=u+1,v[u]=v[u]+1);
x[z]=concat(x[z],p5);if(p4>p5,u=u+1,v[u]=v[u]+1);
x[z]=concat(x[z],p6);if(p5>p6,u=u+1,v[u]=v[u]+1);
x[z]=concat(x[z],p1-p6);
t=720;for(u=1,5,t=t/v[u]!);x[z]=concat(x[z],t);
)
)
)
);print("Phase 1: "floor((w-p1)*100/(w-floor((w+5)/6))+0.5)"%")
);
write(n,"Number of dice: "w,,Strchr(13),Strchr(10),"Number of different distributions: "z,Strchr(13));
for(y=1,z,
i=w!/x[y][1]!/x[y][2]!/x[y][3]!/x[y][4]!/x[y][5]!/x[y][6]!;
e[x[y][1]][1+x[y][6]]=e[x[y][1]][1+x[y][6]]+i*x[y][8];
if(y%1000==0,print("Phase 2: "floor(100*y/z+0.5)"%"));
);
for(y1=floor((w+5)/6),w,
for(y2=0,floor(w/6),
if(e[y1][1+y2]>0,write(n,y1"+ "y2"- "e[y1][1+y2],Strchr(13));if(w<51,print(y1" "y2" "e[y1][1+y2],Strchr(13))));
if(y2*2>y1,m1=m1+e[y1][1+y2],m2=m2+e[y1][1+y2])
)
);
print("Results see "n);
write(n,Strchr(13),"max<2min: "m1,Strchr(13),Strchr(10),"max>=2min: "m2,Strchr(13),Strchr(10),"6^"w" = "l,6^w)
}[/CODE]

Pari note:
instead of
write(n,Strchr(13),"max<2min: ")
you can write
write(n"\nmax<2min: ")