Economic Scholia

[Dominae]

I've had several games where I worked Flood Plains almost from turn 1 for the duration, and never lost a pop (Emperor difficulty). If the chances really are around 5%, there's something like a one in a million chance of this happening. I don't know the exact number, but the chances of using Flood Plains really are low enough for it to be a safe (and very profitable) gamble. In Blackjack, why hold at 20 when the dealer could get 21, at the loss of a lot of money? Because the chances are relatively low the dealer will hit the mark.


Dominae

[Shiber]

Well, if the chance is really 5% then the chances of working a flood plains tile for 10 turns without getting any disease is ~59.87%. The chances for not getting disease for 20 turns are not as good: ~35.85%. 30 turns: ~21.46%.
I wouldn't recommend making this gamble because apparently, the odds favor the house.

[DeepO]

Nah, anecdotical evidence suggests it more in the region of 1%, not 5%. It is rare to see it happening in games, and if floodplains are irrigated, they will be picked by the governor (which is most of the times on for me, certainly now the food overproduction has been solved).

DeepO

[nbarclay]

Originally posted by Shiber
Well, if the chance is really 5% then the chances of working a flood plains tile for 10 turns without getting any disease is ~59.87%. The chances for not getting disease for 20 turns are not as good: ~35.85%. 30 turns: ~21.46%.
I wouldn't recommend making this gamble because apparently, the odds favor the house.

That's just it, though. Experience doesn't bear out the 5% figure. Think back to your games and think whether you've averaged disease every twenty turns using one FP tile or every ten turns using two.

Nathan

[Shiber]

Yes, you must be right.
It could be 1%. Check out these numbers (chances of not getting disease with one disease tile worked):
After 10 turns: ~90.44%
After 20 turns: ~81.79%
After 69 turns: ~49.98%
After 100 turns: ~36.60%
Conclusion: with one disease tile worked, disease will strike your city every 69 turns in average.
Now with three tiles:
After 10 turns: ~73.97%
After 20 turns: ~54.72%
After 23 turns: ~49.98%
Conclusion: with three disease tiles worked, disease will strike your city every 23 turns in average. Makes more sense.

[nbarclay]

Originally posted by Shiber
Yes, you must be right.
It could be 1%. Check out these numbers (chances of not getting disease with one disease tile worked):
After 10 turns: ~90.44%
After 20 turns: ~81.79%
After 69 turns: ~49.98%
After 100 turns: ~36.60%
Conclusion: with one disease tile worked, disease will strike your city every 69 turns in average.
Now with three tiles:
After 10 turns: ~73.97%
After 20 turns: ~54.72%
After 23 turns: ~49.98%
Conclusion: with three disease tiles worked, disease will strike your city every 23 turns in average. Makes more sense.

No, at 1%, the average would be one disease every 100 turns. The "69 turns" figure is for a 50-50 chance of having disease one or more times, and the reason it's 69 rather than 50 is that cases where there is more than one disease early are only counted once by the methodology you used (since you're looking for probability of no disease).

Nathan

[DeepO]

Originally posted by nbarclay
No, at 1%, the average would be one disease every 100 turns. The "69 turns" figure is for a 50-50 chance of having disease one or more times, and the reason it's 69 rather than 50 is that cases where there is more than one disease early are only counted once by the methodology you used (since you're looking for probability of no disease).

Nathan

Yup, that is correct. counting it like 'no disease will occur' doesn't give the correct results here. It's another valid stat if you were calculating the odds of having to work a tile, remaining disease free though.

DeepO

[Shiber]

You're right, I overlooked that.
Do you know the correct method of calculating this?

[DeepO]

Standard binomial calculation: if you got a chance p, it will on average take 1/p throws (or turns in our case) for the first event to happen.

Your thing boils down to: with a chance p of something to happen, there will be a (1-p)^n chance of that event NOT to happen in n throws.

DeepO

[nbarclay]

If we want the probability that we can get away with using flood plains, it's the probability of going n turns without disease that counts. So Shiber's calculations were basically on the right track toward figuring out where the odds of winning the bet for the early game would be above 50-50 - if the 1% figure the calculations were based on was right. But is the 1% figure right?

Nathan

[Dominae]

Assuming the 1% figure is right, here are the probabilities we don't get disease after using the Flood Plains for the indicated number of turns:

1 turn: 0.99% (obviously)
2 turns: 0.9801%
3 turns: 0.970299
4 turns: 0.96357808
5 turns: 0.95397219

As you can see, the "speed" at which the probabilities that we do get disease are decreasing. Thus, you would need quite a few more than 50 turns to get a 50% chance of getting at least one lost pop from a diseased tile. It really doesn't happend very often.

By the way, I used the Geometric probability distribution and a trusty calculator to figure this out.


Dominae

[Shiber]

What happens when your city has 1 pop and you get disease? Does your food storage box go empty instead because you can't lose your single pop? Or perhaps the game is programmed simply not to allow disease to strike a town with 1 pop.
If the latter is correct then we should be able to work disease tiles in towns that have 1 pop without fearing disease.
There's no way we can be sure, but we can be convinced to a certain degree. We can make a lot of experiments and see if this theory is correct. However, this will take a while.
I'll be very busy tomorrow but I can put this to the test the next day. I'll report back if I find anything.

[DeepO]

Originally posted by nbarclay
If we want the probability that we can get away with using flood plains, it's the probability of going n turns without disease that counts. So Shiber's calculations were basically on the right track toward figuring out where the odds of winning the bet for the early game would be above 50-50 - if the 1% figure the calculations were based on was right.

Well, yes, but you can't visualise this. With 1% chance, it will take on average 100 turns before you lose a pop to disease...

As to Geometric distribution: you could look at it that way, as we are indeed measuring how long it will take before the first success. But it boils down to the same problem: the average of a geometric distribution is 1/p, so still on average there would be 100 turns before the first pop is lost. Your numbers are only relevant if you know in front you're going to have 30 turns of possible disease, and want to calculate the chances of remaining disease-free. Again, also correct, but hard to work with, while the average is in this case more intuitive.

Maybe we could stop with this statistical debate, and just focus on how risky it really is... 1% seems about right, so working a fp for a few turns isn't the biggest risk... certainly when you won't get punished when the city is size 1 (I have never seen disease on a 1-pop city).

DeepO

BTW: Dominae: did I read it correctly that you used a handcalculator to do the math? Many people keep doing it, while they are sitting in front of the biggest calculator they have ever owned... but you are right, a PC is used for playing games, right

[Dominae]

Originally posted by DeepO
Your numbers are only relevant if you know in front you're going to have 30 turns of possible disease, and want to calculate the chances of remaining disease-free.

I thought this was what someone was asking for. I consider the numbers above to more "intuitive", in the sense that, given ten turns to that we need to use Flood Plains (to get a Settler out earlier, or somesuch), we have around 91% chance of not getting disease. Those are pretty good odds and I'll gamble on them anyday if it means faster expansion.

As for the calculator, I don't know how to do stats on my computer (I guess I could write a program), and figuring it out would take longer than it took me to the the math manually. One of those laziness things, you know.


Dominae

[DeepO]

Originally posted by Dominae
As for the calculator, I don't know how to do stats on my computer (I guess I could write a program), and figuring it out would take longer than it took me to the the math manually. One of those laziness things, you know.

Oh, I'm just joking here, of course... I still consider one of the best things for this kind of calculation Excell, so it's not really needed to write programs or so. But many people have a handcalculator on their desk next to their pc, while the same thing exists in the start menu. Somehow, people are not used to thinking of a PC as a big calculator

DeepO