Two MGLs in a row: 255-1 odds

[Pook]

I had a freaky event- two military great leaders in a row.
Playing as the Byzantines, a non-miliaristic civ, I hadn't had a leader all game. One of my elite knights won a battle and produced a leader. I moved this leader to a nearby city and made an army. Very next combat was another elite knight and I got another great leader. The way I figure it, the odds of a MGL are 1 in 16 if you haven't built the Heroic Epic, so the odds of two in a row are 1 in 16x16 or 255-1 against.
The next time you're ready to whine about freaky random events , remember that freaky events can happen in your favor too.
Even a blind squirrel finds an acorn now and then.

 

[Padma]

You've got it, Pook!

That's the kind of thing that always bugs me about the "AI Cheats!" complaints. The PRNG works for you, too.

 

[Mr. Do]

I've had more than 255 citories with my elites and never had two in a row. The PRNG cheats me!!

 

[michael4000]

I had two in a row last weekend! I'm Rome at the moment, so the odds were only, um, 144-1.

 

[punkbass2000]

Being Rome makes no difference.

 

[michael4000]

Rome = militaristic. Doesn't that make the chance for a MGL 1/12 instead of 1/16? Or is that just promotions? Or am I completely in left field?

 

[Crimso]

JUST PROMOTIONS! I'm sorry, but everyday someone asks that question... but that sort of info should be in the Civlopedia.

 

[michael4000]

I am shamed and humiliated in my ignorance.

 

[Bagatur]

I had even more odd events last Saturday - with LAST three elites in army, I got two MGLs in a row, but i had Heroic Epic. But earlier, in same game, I had two MGLs, with my lonely two elites,also in a row, same like you, no Heroic Epic This made my cousin furious, bcs he just got his first MGL, and next turn I got two in a row!!! We always contend who is better "militarist"

 

[Crimso]

 

[punkbass2000]

Rome = militaristic. Doesn't that make the chance for a MGL 1/12 instead of 1/16?

You're thinking of the Heroic Epic with those probabilities

 

[DementedAvenger]

I've had more than 255 citories with my elites and never had two in a row. The PRNG cheats me!!

Counterintuitively, it isn't after 255 elite wins you should be upset about not getting back-to-back elite wins, it's 177 elite wins. Statistically, you have a 50% chance to get 2 leaders in a row after about 177 battles (I think). Half the time it takes less than 177 elite wins to get back-to-back leaders, and half the time it takes more. The chances of 255 elite wins w/o back-to-back leaders is about 37%, so you're only moderately unlucky.

 

[SirPleb]

I had a freaky event- two military great leaders in a row.
...
The way I figure it, the odds of a MGL are 1 in 16 if you haven't built the Heroic Epic, so the odds of two in a row are 1 in 16x16 or 255-1 against.

Probabilities are slippery things to put into English, you need to be careful.

The chance of getting two military leaders in a row is 1/16 or 1/256 depending on which of two different situations you are describing.

1) The first situation you describe, of getting two in a row. This implies that you already have one before the question of probability comes into question. Out of all the times you are in a position where you just got a great leader, the odds are that 1/16 of the time your next elite win will get another one resulting in two leaders in a row.
To look at this a slightly different way, 1/16 of the times you get a leader, the next elite win will get another leader giving you two in a row.

2) The situation represented by your calculation, of your next two elite wins both producing leaders. In this situation you are correct, the chance, in advance of knowing whether your next elite win produces a leader or not, of the next two elite wins both producing leaders is 1/256. To look at this another interesting way, the chance of getting three leaders in a row anytime you get a leader is also 1/256!

 

[michael4000]

Counterintuitively, it isn't after 255 elite wins you should be upset about not getting back-to-back elite wins, it's 177 elite wins.

SirPleb's point is very well taken.

After every MGL, you have a 1/16 chance that the next elite win will produce another great leader.

That means there is only a 93.75% chance that you won't have back-to-back leaders.

If I remember my college stats class rightly, since .9375^11 = .4917, you can start feeling upset about not getting back-to-back MGLs after only ELEVEN (MGL producing) elite wins!!

 

[stachnie]

Please look here: http://forums.civfanatics.com/showthread.php?t=101553

Me and some other player had 3 MGL's in a row. With Heroic Epic, it is 1/144.


Best regards,

Slawomir Stachniewicz.

 

[Elgalad]

I Loves my MGL's.

I usually get a few every time I play the Germans, since I like conducting wars of expansion at key points in the timeline. They can be a mixed blessing though.. The worst, absolute worst time to get one is when you've dwindled a stack of cavalry while conducting raids on the enemy's troop movements to the front (pikemen/medieval infantry/musketeers). I always seem to get one on the very Last attack I make with my cavalry stack, and now I've got this great prize stranded in the middle of the enemy's territory and protected by a few shot up nags.

Getting him to the safety of the nearest city can be a challenge all in itself sometimes.


-Elgalad

 

[Chieftess]

I had 4 in one turn at one time.... That's about as lucky as I ever got.

Although blitz does help...

 

[Bagatur]

I wrote it before, I had 14 in two turns, but it was with tanks, where blitz did the things. 6 in first turn, 1 in defence and 7 in next turn. Someone mentioned getting 11 MGLs in single turn.

Blitz is very strong, I consider Russians as very "gifted" civ, bcs cavalry blitz.

 

[punkbass2000]

I'm not sure about how many were in a row, but I got 8 SGL's out of about 20 techs researched last night.

 

[michael4000]

I wrote it before, I had 14 in two turns{QUOTE]

Wow! That must have helped!