Probability of generating a GL

[Shiber]

To finally set things straight, here is a simple formula to calculate the chances of generating a GL (where n is the number of successful attacks by elite units and m is the number of successful defenses by elite units):
(1 - (15/16)^n * (31/32)^m) * 100 = chances of generating at least one GL in percents.
E.g. the chances for generating at least one GL in case our elite units successfully attack five times and successfully defend twice is ~32.036%.
Have a math day.

[Donal Graeme]

"What do all those funny symbols mean mommy..."



Good work Shiber, that stuff can be very important later on.

[=OttomusCeasar=]

NOOOOOOO!

Apolytonia's new Political Party is "The Mathematicians"

Quick burn them at the stake now!

[BigFurryMonster]

So you're saying that, when defending, an Elite unit has only 1/2 the chance of generating a Leader than when attacking? Where did you learn that?

For the rest of the formula - I agree. It's probably influenced by the Militaristic trait and the presence of a Heroic Epic in your empire.

[UnOrthOdOx]

Militaristic, no. That only speeds how fast you get Elites. Heroic Epic base rate is 1/12.

Defenders DO only get 1/2...can't remeber where I read that, though.

[GePap]

Honestly, GL's are a little inbuilt goody to keep the player excited about using elites in battle... as I say, we should not pin our hopes of eventual victory on getting lots of GL's. We should pin our hopes on wise strategy and solid gameplay, and then be open and grateful when the CPU bestows us with a nice little lottery win.

[DAVOUT]

Originally posted by UnOrthOdOx

Defenders DO only get 1/2...can't remeber where I read that, though.

FIRAXIS (Soren)

[DAVOUT]

Originally posted by GePap
... as I say, we should not pin our hopes of eventual victory on getting lots of GL's. We should pin our hopes on wise strategy and solid gameplay, and then be open and grateful when the CPU bestows us with a nice little lottery win.

I agree with you, but this does not preclude an immediate use of the GL, considering that whatever we do with it its extra benefit. What is wrong IMHO, is a tactic aiming to reach victory through a systematic gain of GL.

[kring]

The problem is that probabilities aren't guarantees. Each chance is still independent of all other chances. The problem with stats and probabilities is that IRL they don't occur the way or time you want them to quite often.

Also, considering we just got a leader that could skew your probability, and would need to be taken into account. You would need to factor that into the equation.

And if we don't do something with our GL before battle, the odds of getting another one are 0%.


quote:
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Mike B., does it look like the odds 1/12 and 1/16 are applied under the correct conditions (before/after Heroic Epic) for generating a leader?
----

Odds with Heroic Epic = 1/12
Odds without Heroic Epic = 1/16
The odds are halved for defenders (1/24 and 1/32).

Mike

Found here: http://forums.civfanatics.com/showth...0&pagenumber=2; It is in this thread somewhere since there was a number of questions related to GL's in that thread.

I agree that it is a lottery drawing for GL. How many times have you gotten a GL on your 16th attack? I don't think we can expect one to happen just because probabilities dictate it could. I have seen one game where they happened back to back, with the first being used before the next Elite attacked; but I have seen hundreds of games where I got less than the 1/16 or 1/32 statistic. On average, it has been around those numbers, but I have games with none and games with plenty to balance that average out.

I don't think we are wise to count on getting one as part of strategy. If you want to figure what to do with them if it happens, that's one thing. But, to factor a guaranteed one into the equation is another.

[BigFurryMonster]

Hey, they're still only statistics! No guarantees, whatsoever.

But I think we should aim to win as many battles as possible with Elites. We could use Veterans to soften up the enemy first.

"43.7% of Statistics are complete nonsense" - anonymous.

[Shiber]

"A new statistical study found that 3 out of 4 people are 75% of the population."

I will now relate to some interesting points raised in this thread:
* Yes, these are only statistics. We're talking chances here, probabilities, odds and other synonyms for stuff that's eventually based on luck. We can't get anything sure from my formula but we can assess our chances, which is just as much info as we have when we're planning military strikes.
* AFAIK the statistical data my formula is based on is correct. Should someone prove it wrong and post the correct data I can fix the formula within a moment.
* The recent generation of a GL does not skew any probabilities and should not be factored into my formula. When you roll a die and 6 comes out, it does not alter the chances of whether 6 would or would not come out again in the next roll(s).
In other words, these events are independant of each other, and therefore you could get 5 GLs in a row or not get a GL after 100 battles.

I think that's all.
Have a really, really, really math, I mean nice day.

[vulture]

Originally posted by kring
The problem is that probabilities aren't guarantees. Each chance is still independent of all other chances. The problem with stats and probabilities is that IRL they don't occur the way or time you want them to quite often.

Also, considering we just got a leader that could skew your probability, and would need to be taken into account. You would need to factor that into the equation.

Nope - the fact that we just had a great leader has exactly no effect on the probability of producing another one in the near future (unless we don't use the current one, in which case, as you say, we can't get another one - obsolete now since Ramses has been used).

I don't think we are wise to count on getting one as part of strategy. If you want to figure what to do with them if it happens, that's one thing. But, to factor a guaranteed one into the equation is another.

They are never guaranteed. OTOH it is useful to figure out the chances that another one will be generated in another 5 turns of war with Persia since it allows us to weigh up the costs/benefits of waiting to use a leader.

Shiber is spot on with his calculation. I'd just add that with the possibility of generating more than 1 leader in 5 (succesful) attacks and 2 defenses by elite units, the average number of leaders produced is 0.375, although unless the game is halted immediately upon the production of a GL to decide what to do with him, we are losing some of that chance by waiting until the end of the set of turns being played.

[DAVOUT]

Dices have no memory.