Upgrade Disable Compromise

[techgump]

He does not explain where he comes up with the variable of 47%.

Darkas Words:

Chance of winning a 8v8 attacking with no bonus is 47.1%, therefore the reroll gives you for ONE battle 72% chance of winning, not bad.

Formula supplied by him (which appears correct to me):

(1-p)*(1-p)

And the Math using his mysterious 47% win with 8x8, means 53% probability of loss:
(1-.53)*(1-.53) = 22%
Hence your win is not 72% chance, as he states, but rather 22%.
EDIT: And if this is reversed (which I did not read it this way), it means the defender has a 78% of winning.
Either way, I do not see how this is adding up to 72%. And if this variable is wrong, what else is in regards to coming up with the 47%. Hence, the math I would like to see, rather than just being shut down with my references and request for applied numbers.

So where I am going wrong. Because based on what I see, this is not "adding" up, let alone where the 47% came from. I merely want to understand.

[techgump]

Are you talking about the reroll thing, or the plain probability of winning a fight?

Well, before we go using 47%, sure I'd like to know what you did to calculate it! Seeing how that becomes the foundation for everything beyond that.

[Darkas]

My calculator tells me that (1-.47)*(1-.47) = 28% (therefore the 1-0.28=0.72 is right).

Here is why I do it:

It's very easy to actually compute it:

The chance of winning a battle is 1 - the chance of losing it.

You have to lose both fight to lose the combat, in other word the defender have to win both fights.

If your chance of winning is p, the defender's are 1-p. So for him to win both is (1-p)*(1-p)=(1-p)^2

Therefore the chance that you win is 1-(1-p)^2, times 100% if you want percent units.

In our case p=0.47

If you're arguing about the 47.1%, which is really not obvious at all (:P) reading your messages, yes, I never proved it. I totally agree with you on this point.

I just gave you how I did it:

I basically computed all permutation of 1 to 8 dices.
Then, I sum up all the combinations of battle results for each type of combat.
Dividing all the possible outcome by the total of outcome gives you the probability of winning.
I also added the possibility to see how bonuses and maluses change that.
It's determinist and exact results (in the given precision, which is derived from BigDecimal scale, up to infinity), it's not simulation-based (what I previously did, far easier but less precise and far less efficient)).

And I won't be able to prove you that the program I wrote is correct, you'll have just a hint on how I did calculate it, that the methodology is right (the realization could be wrong) and that the results make sense.

I also manually computed some of the probability, like 2v8, and they matched my program's result, so I guess it should probably be right.

[techgump]

This is what I am doing with my calcualtor:
You state that the formula is 1 minus the probably of loss... not win.
Hence, if the win % is 47%, then the loss probability is 53%. Hence, based on everything I understand, your formula should not be
(1-.47)*(1-.47) = 28%

but rather mine of:
(1-.53)*(1-.53) = 22%

So, am I right, or wrong.

[Darkas]

Yeah, sorry, what I wrote is a little bit confusing maybe:

General rule: The chance of winning a battle is 1 - the chance of losing it.

You have to lose both fight to lose the combat, in other word the defender have to win both fights.

If your chance of winning is p, the defender's are 1-p. So for him to win both is (1-p)*(1-p)=(1-p)^2

We're calculating the defender's chance of winning, and for him the probability to win a fight is 1-p.

--> Defender chance of winning = (1-p)^2

--> Your chance of winning = 1 - Defender's ones = 1 - (1-p)^2

Where p is the chance of the offender to win, 47.1% by my magical results :).

So (1-.47)^2 = 0.28
1 - 0.28 = 0.72

[techgump]

Ok, so can we start form ground 0, because it still seems to me the numbers are not correct. Something is getting mis-matched.

Even assuming your 47% is an accurate number, what is 47% a number for? The chances of winning as an attacker, or the chance of winning as a defender? As you stated earlier:

Chance of winning a 8v8 attacking with no bonus is 47.1%

EDIT: Ok, you answered that as I typed the question... the offender.

[Darkas]

Yeah, let's start over !

Chance of winning a 8v8 attacking with no bonus is 47.1%

--> It's chance for offender. It's below 50% because in case of equality the defender wins.

[MisterWinter]

Well, before we go using 47%, sure I'd like to know what you did to calculate it! Seeing how that becomes the foundation for everything beyond that.

Basically you have two options,
1) Use a probability textbook a computer and a brain. (Obviously you are already using one of them, that's a good start)
2) Trust.
That's because it's pretty impossible to explain math to someone without being aware of his math knowledge.


But if you want other opinions I can give you two of them. On the question "how do you calculate this 47%?",

the mathematician will answer: "ho, we could probably approximate the result with a stochastic model, but if you want an exact result you will need to compute all the probabilities",

the computer scientist will say: "hmm, let's brute force all probabilities and compute the exact result".

[Lopdo]

the computer scientist will say: "hmm, let's brute force all probabilities and compute the exact result".

wannabee programmer would say that, computer scientist would do same thing as mathematician

[techgump]

Ok, I still look at this and say:

You are calculating the attacker/offender at 47% in one sentence, and then making a statement about the defenders win percentage in the next at 72%. It is surely easily to stick to one side or the other. Whatever the results, 100%-X% is the output for the opposing side.

That said, I still look at this and say, from EITHER side (offending or attacking) that: (1-p)*(1-p)=(1-p)^2
P being, as you stated, the probability of loss.

Hence if and attacker/offender has a 47% win percentage, then no doubt he has a 53% loss percentage. Hence:
(1-.53)*(1-.53) = 22%

And if the attacker/offender has 47% win percentage, than the defender must have a 53% win percentage. Which means his formula for win is:
(1-.47)*(1-.47) = 28%

And in doing such, I have to ask how does this compute? Why should it matter what side you are looking at it from? To me, something looks drastically wrong. How can an attacker have a 22% win, and defender 28% win; the other 50% lost in space.

And frankly, I was more-so interested in how you came up with this 47% if you do not know what Lopdo used for an alog on dice roll (but maybe you do). Hence I was asking for the math. Seems to me this is a crucial part of understanding the output.