Temple of the Dice Gods

[edsdad]

I usually clinch my butt,hold my breath,stare at the screen till my eyes bleed and roll the bones.But that sacrifice thing thingy sounds soooooooooo much better.

 

[stone123]

1 out of 7,747 times, impressive.

U sure that`s correct?

It is 3 rolls/spins of the dice for the attacker and 1 roll/spin for the defender

That is losing with the odds of 3 to 1 an astonishing 7 times........ a loss of 2 to 1, 1 time ......and a Draw at 1 v 1.......or another way of putting it, a loss of 24 rolls in a row.

I am sure there are lots of different ways to calculate it but that the simplest i could do.

I suspect the odds of loosing like this are in the millions

 

[Tyro]

My back of a fag packet calculation has it as defender has a 8.4% chance of victory, 3 v 1. This is compounded i.e. 0.084 to the power of 7, multiply this by 0.246 for 2 v 1 and then finally by 0.583 for the 1 v 1.
Give or take a few figures (rounding errors will be quite significant) I get a final odds of 2.0 x 10^-10
Measure it in 1 in a hundreds of millions. Why don't you buy a lottery ticket? It has more chance of winning

 

[stone123]

My back of a fag packet calculation has it as defender has a 8.4% chance of victory, 3 v 1. This is compounded i.e. 0.084 to the power of 7, multiply this by 0.246 for 2 v 1 and then finally by 0.583 for the 1 v 1.
Give or take a few figures (rounding errors will be quite significant) I get a final odds of 2.0 x 10^-10
Measure it in 1 in a hundreds of millions. Why don't you buy a lottery ticket? It has more chance of winning

WOW, That`s impressive calculations Tyro. And this is why i complain about the dice programme. We are seeing near impossible odds way too often

 

[Dalinar]

Yes, I'm pretty sure of the calculation - the big difference comes from the fact Tyro is using a much smaller (and incorrect) number. Killing one of the attacker's troops during a 3v1 roll happens 34.03% of the time, not 8.4%

http://en.wikipedia.org/wiki/Risk_(game)

(.3403^7) * .4213 * .5833 = .0001298...
1/.0001298 = 7699.86...
I must have rounded differently the first time.

That's the only way to calculate this particular probability - you can't consider 3v1 as 3 rolls, the odds and probability math don't work like that because the outcomes of the 3 v 1 are interdependent.

 

[Tyro]

Interesting, Dalinar. I looked at the wiki page and some of the numbers just don't feel right. The probability of a defender winning against 4 dice is, I feel, too high at 0.3407. I can't be bothered to do the maths, but my source http://recreationalmath.com/Risk/ shows the figure I used. Which feels too low
Amazing what a difference it makes, eh?
If I have the time I'll run the numbers and post.

 

[stone123]

When you say you can`t consider 3v1 as 3 rolls why not? Does that mean the actual programme is wrong?

I have no idea how to begin to calculate the above but to me it does not feel right. If i physically roll a die just under 8 thousand times then i can expect at some point a loss of 24 to nil. I'm just not buying that.

If two or more people can come up with, and agree, the same calculations and same answer then i guess i will be somewhat satisfied.

I am in no way saying you are wrong, just to me it does not feel right at all

 

[Tyro]

Here is the maths:
You need to add each line to get the final result:
defender rolls 6, 0.16667 x 1 (always wins) = 0.166667
5, 0.16667 x (5/6 ^3)
4, 0.16667 x (4/6^3)
3, 0.16667 x (3/6^3)
2, 0.16667 x (2/6^3)
1, 0.16667 x (1/6^3)

I've crunched the numbers, 34% is about right, I should know better than to doubt wikipedia

 

[Cagey]

I don't think the Dice Gods would like you trying to quantify their fiendish ways...

 

[Dalinar]

When you say you can`t consider 3v1 as 3 rolls why not? Does that mean the actual programme is wrong?

I have no idea how to begin to calculate the above but to me it does not feel right. If i physically roll a die just under 8 thousand times then i can expect at some point a loss of 24 to nil. I'm just not buying that.

If two or more people can come up with, and agree, the same calculations and same answer then i guess i will be somewhat satisfied.

I am in no way saying you are wrong, just to me it does not feel right at all

You can't consider it 3 rolls because the rolls in a 3v1 are related. Rolling 1 die versus a defenders 1 die three times (where the attacker only loses 1 if they lose all three rolls) would mean the defender wins only 20% (.5833^3) of the time. The actual win rate for the defender 3v1 is 34.03% as I said above.

First, the defender wins ties, so that automatically means they win 1/6 of the 3v1 rolls. If the rolls were individual, they'd have to roll a 6 three times - a lot less likely.
Second, consider the case where the defender rolls 1. 5/6 of the time the attacker wins on the first die and the next two rolled are irrelevant.
Every roll 3v1 is like that - one happens on one die affects the relevance of the other dice.

The intuition that's a bit hard is that the rolls are a related group, what happens on one die affects the relevance of the other dice, so they need to be considered as a group. You're right that rolling 24-nil is a much much smaller than 1 in 8000 event, but you can't think of the 3v1 as 3 rolls.

lol, Cagey may be right though, the dice gods seem to be frowning on me the last few games.

 

[rob6483]

The dice gods were extremely favorable to me yesterday. My army of 2 defenders successfully defeated an entire attacking army of 10 without a loss. I had little but 1's behind that army on Duck and Cover, so I should have been wiped out. Instead, things completely flipped and I won.

 

[SimonDeDanser]

Intuitive odds .......There is always such a big gap between people's guesstimates when it comes to odds i notice, and i could not believe odds are about 1 to 8000 in this case. So I could not help myself to put the numbers into a spreadsheet and refresh my high school mathematics in the process a little. surprisingly to myself the odds for a defender to win a '10 attackers to 1 defender position' is about one out of 76 according to my calculations. now i am doubting my math-skills... or my intuition If you are in this situation once every game, it would mean that after 760 games you have statisticly have had this bad luck 9 times already . Losing what odds would you consider bad luck?

My calculations:

 

[stone123]

Intuitive odds .......There is always such a big gap between people's guesstimates when it comes to odds i notice, and i could not believe odds are about 1 to 8000 in this case. So I could not help myself to put the numbers into a spreadsheet and refresh my high school mathematics in the process a little. surprisingly to myself the odds for a defender to win a '10 attackers to 1 defender position' is about one out of 76 according to my calculations. now i am doubting my math-skills... or my intuition If you are in this situation once every game, it would mean that after 760 games you have statisticly have had this bad luck 9 times already . Losing what odds would you consider bad luck?



My calculations:

Can you put that in layman's terms for me please.

So do you agree or disagree with the previous calculations? What is your opinion? Is the die programme correct or is it impossible to calculate?

 

[SimonDeDanser]

My conclusion is:
1) I Made a dumb calculating mistake and will have to go back to school.
2) Came on second glance to the same conclusion as Dalinar.
3) When the Defender has more dice it becomes exponentially more difficult to calculate probability.
And so have no opinion on the die programme yet. :fisheye:

 

[Bluebonnet]

Calculating the probability of dice rolls is fairly straightforward. But then comparing the probability to a specific instance to majcom dice rolls and state if majcom dice are correct or not is a incorrect conclusion. All you can state is the likelihood of that occurring. No matter how unlikely something is to occurr, it can occur.

What you need to do is record every single roll (no skipping the recording) for say somewhere between 10,000 or even 100,000 rolls. The run some statistical analysis. Determine if there are statically irregular rolls.

To put into english. The chance of being hit by lightning in the US is 1 in 700,000. Say 20 people got hit by lightning last year. You can't determine if the 20 is within reason or not unless you know the population of the United States. If the population is 100,000, then it is not within reason. If the population of the united states is 14,000,000 then it is within reason.

You need to know the population within your analysis.

 

[Cagey]

If I've got 3 cards and no set then I've got a 66.6(recurring)% chance of my next card giving me a set, right - 2 out of the 3 possible colours will give me a set - however this doesn't take into account the chances of my first 3 cards being a set before I turn over my 4th, which I reckon is 33.3(recurring)%. So. Clearly the chances of having a set with 4 cards is 66.6(recurring)%+33.3(recurring)% or 99.9(recurring)%.

 

[Wort]

Right then, it sounds like this is the place to go.

I need to correct my attacking dice so does anyone have a surefire way to stop my mass losses?! I am happy to offer up some nice beer, or hell I can even knock off one of our chickens.

To give you an idea of the scale of what I need to turnaround. I recently seem to be losing 2 attackers to 1 defender.

HELP!!!!

:cheers:

 

[Cardinalsrule]

Wort,
You need to face in the direction of the Pacific coast of North America, kneel and prostrate yourself to the great god ajdedo, and implore his royal maliciousness to please turn off the "dicerape" function on your profile. Or you could try to bribe him with beer. :beer:

 

[Wort]

I do have lots of beer Ajdedo...

:beers:

 

[Bluebonnet]

Don't forget the minor deities who serve The Great New Sheriff.

Carinalsrule, Masterjskye, Chilly, KungFuDuet, PackerHawkeye and the others I can't name off the top of my head.