Odds of winning various dice combinations in Risk

[VERBATIM666]

Odds of winning various dice combinations in Risk
Attacker: one die; Defender: one die:

Attacker wins 15 out of 36 (41.67 %)
Defender wins 21 out of 36 (58.33 %)


Attacker: two dice; Defender: one die:

Attacker wins 125 out of 216 (57.87 %)
Defender wins 91 out of 216 (42.13 %)


Attacker: three dice; Defender: one die:

Attacker wins 855 out of 1296 (65.97 %)
Defender wins 441 out of 1296 (34.03 %)


Attacker: one die; Defender: two dice:

Attacker wins 55 out of 216 (25.46 %)
Defender wins 161 out of 216 (74.54 %)


Attacker: two dice; Defender: two dice:

Attacker wins both: 295 out of 1296 (22.76 %)
Defender wins both: 581 out of 1296 (44.83 %)
Both win one: 420 out of 1296 (32.41 %)


Attacker: three dice; Defender: two dice:

Attacker wins both: 2890 out of 7776 (37.17 %)
Defender wins both: 2275 out of 7776 (29.26 %)
Both win one: 2611 out of 7776 (33.58 %)

Sample interpretation of the last data above (three vs. two). If an attacker starts with 1000 armies and a defender starts with 1000 armies and a 3 vs. 2 attack is ensued, the results should be (given fair dice): after 100 rolls, each side will have lost 1 army about 34 times. The defender will have lost 2 armies about 37 times, and the attacker will have lost 2 armies 29 times. Therefore, after 100 rolls, the attacker should have 908 armies left, and the defender should have 892 armies left.

Conclusion: heads up with three dice versus 2 dice, the attacker has an advantage in the long run. Similar interpretations can be made for the remainder of the data, which can be summarized as follows:

Attacker 1 versus defender 1: defender has the advantage, winning about 4 out of 7 battles
Attacker 2 versus defender 1: attacker has the advantage, winning about 4 out of 7 battles
Attacker 3 versus defender 1: attacker has the advantage, winning about 2 out of 3 battles
Attacker 1 versus defender 2: defender has the advantage, winning about 3 out of 4 battles
Attacker 2 versus defender 2: defender has the advantage, winning about 3 out of 5 battles
Attacker 3 versus defender 2: attacker has the advantage, but the advantage is much more narrow than any of the battles described above. The attacker's advantage is such that he will win about 7 out of 13 battles on average.

[dominationnation]

It may have been easier to just download the dice analyzer.

[Herakilla]

did you use actual results or calculate with probability cuz calculating it would b more accurate

[peanutsdad]

It may have been easier to just download the dice analyzer.

Wait, there's a dice analyzer?????

[dominationnation]

It may have been easier to just download the dice analyzer.

Wait, there's a dice analyzer?????

click on the third sub fourm. THeres all sorts of downloads.

[-ShadySoul-]

It may have been easier to just download the dice analyzer.

Wait, there's a dice analyzer?????

yep...check the plug in section D:

[CrabNebula]

did you use actual results or calculate with probability cuz calculating it would b more accurate

Checking the numbers you can see this is the actual probability. However, actual results may/may not differ since probability is the "chance of happening" and thus doesn't necessarily state that it will/will not happen. However, on a very large sample space, you will get the posted results.

[firstholliday]

I haven't installed the dice analyzer. Can some of you explain me the benefits?


1st

[jiminski]

I haven't installed the dice analyzer. Can some of you explain me the benefits?


1st

I am not sure that it really has any benefits to be honest mate ...

I find the data to be mildly 'interesting' (not cleavage interesting .. let's say as interesting as finding a heart-shaped potato-crisp in a packet.) as it roughly confirms probability.

But I find that the format which displays data of possible rolls to border on pointlessness. (no offense intended to the creator.. great work!)

The analyser does not project percentage of probable success, it gives a best case result... an ideal.. and a worst case for both attacker and defender...

perhaps i am not using it correctly and someone else can instruct in its better usage but i find it a clumsy tool (which was incidentally my nickname at school)

[rwingett]

Does the CC dice randomizer actually adhere to these probabilities? As an attacker it seems like I almost always suffer more casualties than the defense in 3 dice to 2 battles. Enough so that the game is becoming a major drag. I really don't think its just my stilted perception at work either.

[Herakilla]

Does the CC dice randomizer actually adhere to these probabilities? As an attacker it seems like I almost always suffer more casualties than the defense in 3 dice to 2 battles. Enough so that the game is becoming a major drag. I really don't think its just my stilted perception at work either.

thats thing... with probability you can never be sure

but the dice here ARE random

[Visaoni]

Does the CC dice randomizer actually adhere to these probabilities? As an attacker it seems like I almost always suffer more casualties than the defense in 3 dice to 2 battles. Enough so that the game is becoming a major drag. I really don't think its just my stilted perception at work either.

For the 'I don't know how manyith' time.. random.org. The dice come from there, check them for randomness if you want.

[VERBATIM666]

Now that I have somebodys attention.
The dice come from random org correct ?
Now is it one set of dice used by all players?
If so then there lies the reason behind the bad luck.

So now ask why I come to this conclusion.
or just post you reason.

[VERBATIM666]

Code to calculate Risk dice odds
/*
* odds.c -- calculate the odds of winning/losing various dice
* configurations in the game "Risk"
*/

#include

main()
{
int a1=0, a2=0, a3=0, d1=0, d2=0;
int atotal=0, dtotal=0;
int atotalhi=0, atotalmid=0;
int dtotalhi=0, dtotalmid=0;
int total=0;
int ahi=0, amid=0, dhi=0, dmid=0;
int hiwin=0, midwin=0;
int bothwin=0, bothlose=0, oneandone=0;
float atotalperc=0.0, dtotalperc=0.0, oneandonetotalperc=0;

/*
* One attacker die vs. one defender die (this one is easy: just whether
* or not the defender's die is equal to or higher than the attacker's)
*/

for(a1 = 1; a1 <= 6; a1++) {
for(d1 = 1; d1 <= 6; d1++) {
++total;
#ifdef DEBUG2
printf("a1 is %d, d1 is %d, total is %d\n",a1,d1,total);
#endif DEBUG2
if(a1 > d1) {
++atotal;
#ifdef DEBUG
printf("%d vs. %d: Attacker wins!\n",a1,d1);
#endif DEBUG
} else {
++dtotal;
#ifdef DEBUG
printf("%d vs. %d: Defender wins!\n",a1,d1);
#endif DEBUG
}
#ifdef DEBUG2
printf("atotal is %d, dtotal is %d\n",atotal,dtotal);
#endif DEBUG2
}
}
atotalperc = (float) atotal * 100 / total;
dtotalperc = (float) dtotal * 100 / total;
printf("\n");
printf("Attacker: one die; Defender: one die:\n");
printf("\n\t");
printf("Attacker wins %d out of %d (%.2f %%)\n",atotal,total,atotalperc);
printf("\t");
printf("Defender wins %d out of %d (%.2f %%)\n",dtotal,total,dtotalperc);
printf("\n");

/*
* reset all the variables
*/

a1=0; a2=0; a3=0; d1=0; d2=0; atotal=0; dtotal=0;
atotalhi=0; atotalmid=0; dtotalhi=0; dtotalmid=0;
total=0; ahi=0; amid=0; dhi=0; dmid=0; hiwin=0; midwin=0;
bothwin=0; bothlose=0; oneandone=0;
atotalperc=0.0; dtotalperc=0.0; oneandonetotalperc=0;

/*
* Two attacker dice vs. one defender die (this one is pretty easy also:
* if the defender's die is greater than or equal to both of the attacker's
* dice, then the defender wins)
*/

for(a1 = 1; a1 <= 6; a1++) {
for(a2 = 1; a2 <= 6; a2++) {
for(d1 = 1; d1 <= 6; d1++) {
++total;
#ifdef DEBUG2
printf("a1 is %d, a2 is %d, d1 is %d, total is %d\n",a1,a2,d1,total);
#endif DEBUG2
if(a1 > d1 || a2 > d1) {
++atotal;
#ifdef DEBUG
printf("%d - %d vs. %d: Attacker wins!\n",a1,a2,d1);
#endif DEBUG
} else {
++dtotal;
#ifdef DEBUG
printf("%d - %d vs. %d: Defender wins!\n",a1,a2,d1);
#endif DEBUG
}
#ifdef DEBUG2
printf("atotal is %d, dtotal is %d\n",atotal,dtotal);
#endif DEBUG2
}
}
}
atotalperc = (float) atotal * 100 / total;
dtotalperc = (float) dtotal * 100 / total;
printf("\n");
printf("Attacker: two dice; Defender: one die:\n");
printf("\n\t");
printf("Attacker wins %d out of %d (%.2f %%)\n",atotal,total,atotalperc);
printf("\t");
printf("Defender wins %d out of %d (%.2f %%)\n",dtotal,total,dtotalperc);
printf("\n");


/*
* reset all the variables
*/

a1=0; a2=0; a3=0; d1=0; d2=0; atotal=0; dtotal=0;
atotalhi=0; atotalmid=0; dtotalhi=0; dtotalmid=0;
total=0; ahi=0; amid=0; dhi=0; dmid=0; hiwin=0; midwin=0;
bothwin=0; bothlose=0; oneandone=0;
atotalperc=0.0; dtotalperc=0.0; oneandonetotalperc=0;

/*
* Three attacker dice vs. one defender die (still pretty simple: if the
* defender's die is greater than or equal to all three of the attacker's
* dice, then the defender wins)
*/

for(a1 = 1; a1 <= 6; a1++) {
for(a2 = 1; a2 <= 6; a2++) {
for(a3 = 1; a3 <= 6; a3++) {
for(d1 = 1; d1 <= 6; d1++) {
++total;
#ifdef DEBUG2
printf("a1 is %d, a2 is %d, d1 is %d, total is %d\n",a1,a2,d1,total);
#endif DEBUG2
if(a1 > d1 || a2 > d1 || a3 > d1) {
++atotal;
#ifdef DEBUG
printf("%d - %d - %d vs. %d: Attacker wins!\n",a1,a2,a3,d1);
#endif DEBUG
} else {
++dtotal;
#ifdef DEBUG
printf("%d - %d - %d vs. %d: Defender wins!\n",a1,a2,a3,d1);
#endif DEBUG
}
#ifdef DEBUG2
printf("atotal is %d, dtotal is %d\n",atotal,dtotal);
#endif DEBUG2
}
}
}
}
atotalperc = (float) atotal * 100 / total;
dtotalperc = (float) dtotal * 100 / total;
printf("\n");
printf("Attacker: three dice; Defender: one die:\n");
printf("\n\t");
printf("Attacker wins %d out of %d (%.2f %%)\n",atotal,total,atotalperc);
printf("\t");
printf("Defender wins %d out of %d (%.2f %%)\n",dtotal,total,dtotalperc);
printf("\n");

/*
* reset all the variables
*/

a1=0; a2=0; a3=0; d1=0; d2=0; atotal=0; dtotal=0;
atotalhi=0; atotalmid=0; dtotalhi=0; dtotalmid=0;
total=0; ahi=0; amid=0; dhi=0; dmid=0; hiwin=0; midwin=0;
bothwin=0; bothlose=0; oneandone=0;
atotalperc=0.0; dtotalperc=0.0; oneandonetotalperc=0;

/*
* One attacker die vs. two defender dice (this one is also pretty simple:
* the attacker's die must be greater than both the defender's dice)
*/

for(a1 = 1; a1 <= 6; a1++) {
for(d1 = 1; d1 <= 6; d1++) {
for(d2 = 1; d2 <= 6; d2++) {
++total;
#ifdef DEBUG2
printf("a1 is %d, d1 is %d, d2 is %d, total is %d\n",a1,d1,d2,total);
#endif DEBUG2
if(a1 > d1 && a1 > d2) {
++atotal;
#ifdef DEBUG
printf("%d vs. %d - %d: Attacker wins!\n",a1,d1,d2);
#endif DEBUG
} else {
++dtotal;
#ifdef DEBUG
printf("%d vs. %d - %d: Defender wins!\n",a1,d1,d2);
#endif DEBUG
}
#ifdef DEBUG2
printf("atotal is %d, dtotal is %d\n",atotal,dtotal);
#endif DEBUG2
}
}
}
atotalperc = (float) atotal * 100 / total;
dtotalperc = (float) dtotal * 100 / total;
printf("\n");
printf("Attacker: one die; Defender: two dice:\n");
printf("\n\t");
printf("Attacker wins %d out of %d (%.2f %%)\n",atotal,total,atotalperc);
printf("\t");
printf("Defender wins %d out of %d (%.2f %%)\n",dtotal,total,dtotalperc);
printf("\n");

/*
* reset all the variables
*/

a1=0; a2=0; a3=0; d1=0; d2=0; atotal=0; dtotal=0;
atotalhi=0; atotalmid=0; dtotalhi=0; dtotalmid=0;
total=0; ahi=0; amid=0; dhi=0; dmid=0; hiwin=0; midwin=0;
bothwin=0; bothlose=0; oneandone=0;
atotalperc=0.0; dtotalperc=0.0; oneandonetotalperc=0;

/*
* Two attacker dice vs. two defender dice (now things get a bit more
* complicated since we must compare the attacker's hi die to the
* defender's hi die, and the attacker's low die to the defender's
* low die)
*/

for(a1 = 1; a1 <= 6; a1++) {
for(a2 = 1; a2 <= 6; a2++) {
for(d1 = 1; d1 <= 6; d1++) {
for(d2 = 1; d2 <= 6; d2++) {
++total;
/*
* Figure out which attacker die is highest
*/
if(a1 >= a2) {
ahi = a1;
amid = a2;
} else {
ahi = a2;
amid = a1;
}
/*
* Figure out which defender die is highest
*/
if(d1 >= d2) {
dhi = d1;
dmid = d2;
} else {
dhi = d2;
dmid = d1;
}
#ifdef DEBUG2
printf("a1 is %d, a2 is %d, d1 is %d, d2 is %d, total is %d\n",a1,a2,d1,d2,total);
printf("Attacker: %d - %d: high is %d, low is %d\n",a1,a2,ahi,amid);
printf("Defender: %d - %d: high is %d, low is %d\n",d1,d2,dhi,dmid);
#endif DEBUG2
/*
* Now, compare attacker hi to defender hi and attacker low
* to defender low
*/
if(ahi > dhi) {
hiwin = 1;
++atotalhi;
} else {
hiwin = 0;
++dtotalhi;
}
if(amid > dmid) {
midwin = 1;
++atotalmid;
} else {
midwin = 0;
++atotalmid;
}
if(hiwin && midwin) {
++bothwin;
#ifdef DEBUG
printf("%d - %d vs. %d - %d: Attacker wins both!\n",a1,a2,d1,d2);
#endif DEBUG
} else if((hiwin == 0) && (midwin == 0)) {
++bothlose;
#ifdef DEBUG
printf("%d - %d vs. %d - %d: Defender wins both!\n",a1,a2,d1,d2);
#endif DEBUG
} else {
++oneandone;
#ifdef DEBUG
printf("%d - %d vs. %d - %d: ONE AND ONE!\n",a1,a2,d1,d2);
#endif DEBUG
}
#ifdef DEBUG2
printf("atotal is %d, dtotal is %d\n",atotal,dtotal);
#endif DEBUG2
}
}
}
}
atotalperc = (float) bothwin * 100 / total;
dtotalperc = (float) bothlose * 100 / total;
oneandonetotalperc = (float) oneandone * 100 / total;
printf("\n");
printf("Attacker: two dice; Defender: two dice:\n");
printf("\n\t");
printf("Attacker wins both: %d out of %d (%.2f %%)\n",bothwin,total,atotalperc);
printf("\t");
printf("Defender wins both: %d out of %d (%.2f %%)\n",bothlose,total,dtotalperc);
printf("\t");
printf("Both win one: %d out of %d (%.2f %%)\n",oneandone,total,oneandonetotalperc);
printf("\n");

/*
* reset all the variables
*/

a1=0; a2=0; a3=0; d1=0; d2=0; atotal=0; dtotal=0;
atotalhi=0; atotalmid=0; dtotalhi=0; dtotalmid=0;
total=0; ahi=0; amid=0; dhi=0; dmid=0; hiwin=0; midwin=0;
bothwin=0; bothlose=0; oneandone=0;
atotalperc=0.0; dtotalperc=0.0; oneandonetotalperc=0;

/*
* Three attacker dice vs. two defender dice (the most complex configuration:
* we need to figure the attacker's highest die and second-highest die,
* then compare them respectively to the defenders hi and low)
*/

for(a1 = 1; a1 <= 6; a1++) {
for(a2 = 1; a2 <= 6; a2++) {
for(a3 = 1; a3 <= 6; a3++) {
for(d1 = 1; d1 <= 6; d1++) {
for(d2 = 1; d2 <= 6; d2++) {
++total;
if(a1 >= a2 && a1 >= a3) {
ahi = a1;
if (a2 >= a3)
amid = a2;
else
amid = a3;
} else if(a2 >= a1 && a2 >= a3) {
ahi = a2;
if (a1 >= a3)
amid = a1;
else
amid = a3;
} else if(a3 >= a1 && a3 >= a2) {
ahi = a3;
if (a1 >= a2)
amid = a1;
else
amid = a2;
}
if(d1 >= d2) {
dhi = d1;
dmid = d2;
} else {
dhi = d2;
dmid = d1;
}
#ifdef DEBUG2
printf("a1 is %d, a2 is %d, a3 is %d, d1 is %d, d2 is %d, total is %d\n",a1,a2,a3,d1,d2,total);
printf("Attacker: %d - %d - %d: high is %d, mid is %d\n",a1,a2,a3,ahi,amid);
printf("Defender: %d - %d: high is %d, low is %d\n",d1,d2,dhi,dmid);
#endif DEBUG2
if(ahi > dhi) {
hiwin = 1;
++atotalhi;
} else {
hiwin = 0;
++dtotalhi;
}
if(amid > dmid) {
midwin = 1;
++atotalmid;
} else {
midwin = 0;
++atotalmid;
}
if(hiwin && midwin) {
++bothwin;
#ifdef DEBUG
printf("%d - %d - %d vs. %d - %d: Attacker wins both!\n",a1,a2,a3,d1,d2);
#endif DEBUG
} else if((hiwin == 0) && (midwin == 0)) {
++bothlose;
#ifdef DEBUG
printf("%d - %d - %d vs. %d - %d: Defender wins both!\n",a1,a2,a3,d1,d2);
#endif DEBUG
} else {
++oneandone;
#ifdef DEBUG
printf("%d - %d - %d vs. %d - %d: ONE AND ONE!\n",a1,a2,a3,d1,d2);
#endif DEBUG
}
#ifdef DEBUG2
printf("atotal is %d, dtotal is %d\n",atotal,dtotal);
#endif DEBUG2
}
}
}
}
}
atotalperc = (float) bothwin * 100 / total;
dtotalperc = (float) bothlose * 100 / total;
oneandonetotalperc = (float) oneandone * 100 / total;
printf("\n");
printf("Attacker: three dice; Defender: two dice:\n");
printf("\n\t");
printf("Attacker wins both: %d out of %d (%.2f %%)\n",bothwin,total,atotalperc);
printf("\t");
printf("Defender wins both: %d out of %d (%.2f %%)\n",bothlose,total,dtotalperc);
printf("\t");
printf("Both win one: %d out of %d (%.2f %%)\n",oneandone,total,oneandonetotalperc);
printf("\n");
}

[-ShadySoul-]

who cares alright?
we are not even playing risk here...its CC


P.S. i think you got no life man

[VERBATIM666]

Some people do,but not you.

Why bother to post if you only have negative crap to spew.

Oh I forgot your mouth and your ass discharge the the same stuff.

Why don't you get a life, I would say CC is more like risk than you think or did lack just think this up by himself?

I found out why the dice are messed up , and wanted to confirm it by asking a few question's and see what response to them I got.

I really don't care one way or the other if they work or not, but from a lot of the posts I have read seems that some do care.

And by the way for a guy that joined in October you talk alot but seem to be not winning many games or don't you know how to play?

[-ShadySoul-]

Some people do,but not you.

Why bother to post if you only have negative crap to spew.

Oh I forgot your mouth and your ass discharge the the same stuff.

Why don't you get a life, I would say CC is more like risk than you think or did lack just think this up by himself?

I found out why the dice are messed up , and wanted to confirm it by asking a few question's and see what response to them I got.

I really don't care one way or the other if they work or not, but from a lot of the posts I have read seems that some do care.

And by the way for a guy that joined in October you talk alot but seem to be not winning many games or don't you know how to play?

Aight, i might be new at this, but at least im smart enough to know when i got burned. So, all i can say, is im sorry i dissed your thread. I am not even sure why i did it, it just seemed like a right thing to say at the time. And about my wining record, i ahve only been playing for a week, and i got my premium the same day, so you can imagine how a noob reacts when he gets a chance to play unlimited games. I signed up to like 20 games at the same time, and without thinking straight , just lost all of them. So, again, sorry for the little display of my annoying side, and keep up the good work with your dice mission

[VERBATIM666]

Sorry about that but All I want to find out where dice come from and is it from 1 set or multi sets of them.
Will explain theory in a bit but would like to have more input on my question.
One part was answered the random.org part now need to know how many sets and are they exclusive to CC.
As for loosing games It's all part of the learning process, not like playing a board game where moves are right away.
With the 24 hour time limit people get impatient and need to make a move quick, hence the 20 games at the same time.
I figured if I could shed some light on it then we would have less post's on the dice.

[-ShadySoul-]

I figured if I could shed some light on it then we would have less post's on the dice.

even though your thread is doing a lot of good for those who care to read it, those who dont ( which is the majority of CC population ) will just ignore whatever you are trying to explain and will keep on pushing their shit. So, you are pretty much doing this for yourself and those few that care. But, and i hope, i might be wrong.