Why do I keep getting a great artist in my NE city?

[ParadigmShifter]

I'd like to see your working out of 1/5.6

 

[Manfred Belheim]

Ten heads in a row has a probability of 1/1024

Ten tails in a row has a probability of 1/1024

Ten heads OR tails in a row therefore has a probability of 1/512 (as you said)

If you do only ten flips, then this is your chance of getting that run

If you do eleven flips, then you have two chances to get the run - the first ten flips, or the last ten flips. In this case the chance of getting a run is 2/512

If you do 12 flips then you get three chances - the first ten flips, the middle ten flips or the last ten flips. Chance this time is 3/512

Working up from this, if you do 100 flips you get a probability of 91/512

I'll let you do the last step yourself

Edit: This is actually all wrong the more I think about it, as the two chances to get a run of 10 with 11 flips, for example, have a large area of overlap in the middle and so aren't independent. In that case you actually need to work out the odds of getting a run of 9 and then the odds of getting one more head or tail in two more flips, and the odds of that work out at 1/341 not 1/256 as I said above.

However.... if you have 10 independent tries at getting a run of 10 then the odds of getting one then work out at 1/51.7. For a run of 100 though the odds must be better than this as there can be an overlap between tries (getting 3 in a row at the end of one run, then 7 in a row at the start of the next for example).

So I'll say the odds must be somewhere between 1/5.6 and 1/51.7 then

 

[Mec AntiKythera]

10 in a row wouldn't be very common in 100 trials. I can't be bothered to do the maths

PS, I think you are trying too hard to shift the paradigm here, if I may say so. Too many trees, too little forest. Like I said, the exact numbers aren't really fixed here. Try a string of 9 out of 500 flips. I got that in my first try. Now, if you were asked to imitate random coin flips would you go for 9 in a row? It just doesn't feel random, does it?

 

[Danelius90]

I remember once I had a desperate need to build a shrine, and I had so many Great People EXCEPT prophets. Had 60-80%+ sometimes.
Kept getting other types.. does happen.

 

[TheMulattoMaker]

Harvey Two-Face frowns upon this thread.

 

[ParadigmShifter]

Ten heads in a row has a probability of 1/1024

Ten tails in a row has a probability of 1/1024

Ten heads OR tails in a row therefore has a probability of 1/512 (as you said)

If you do only ten flips, then this is your chance of getting that run

If you do eleven flips, then you have two chances to get the run - the first ten flips, or the last ten flips. In this case the chance of getting a run is 2/512

If you do 12 flips then you get three chances - the first ten flips, the middle ten flips or the last ten flips. Chance this time is 3/512

Working up from this, if you do 100 flips you get a probability of 91/512

I'll let you do the last step yourself

Edit: This is actually all wrong the more I think about it, as the two chances to get a run of 10 with 11 flips, for example, have a large area of overlap in the middle and so aren't independent. In that case you actually need to work out the odds of getting a run of 9 and then the odds of getting one more head or tail in two more flips, and the odds of that work out at 1/341 not 1/256 as I said above.

However.... if you have 10 independent tries at getting a run of 10 then the odds of getting one then work out at 1/51.7. For a run of 100 though the odds must be better than this as there can be an overlap between tries (getting 3 in a row at the end of one run, then 7 in a row at the start of the next for example).

So I'll say the odds must be somewhere between 1/5.6 and 1/51.7 then

Asking people to show their working out always makes them think harder

Anyway, this is an interesting question that was raised and once again I direct you to my "let's discuss mathematics" thread in sci/tech if we want to discuss this further.

 

[Mec AntiKythera]

Keeping this on topic, my guess is you kept getting GAs because of dumb luck. Does anyone have any hard facts to the contrary?

 

[Bushface]

Remember that the RNG in Civ does, and always will, produce streaks, and humans remember best those which go against them, such as when you lose at 99% winning chance. You don't usually notice the streaks in your favour, because there will be very few times when you attack at 1% and win against the odds: although the AI sometimes does that, you normally would not notice because the combat odds are not shown when you're defending. Even I, micromanager that I am, don't check the combat log after every battle. As for what type of Great Person you get, unless absolutely all the GP points are of the same type the AI hands you one apparently at random: I have (very occasionally) been given one which didn't even appear in the probablity list. Getting the type you least want is yet another case of anti-human-player bias . . .

 

[ParadigmShifter]

I started a discussion about the coin toss thing in the maths thread

http://forums.civfanatics.com/showpost.php?p=10274317&postcount=666