Digging For Gold

[khumak]

Originally posted by Mylon
That probability isn't very low at all. At 1/1250 chance of success, if you work a mine for 100 turns, there's a 7.69% chance of finding something. Do this for 20 tiles, and you have a 79.8% chance of finding a resounce in that time frame.

Hmm, if this is accurate then mines are ALWAYS superior to windmills eventually. I question whether this math really works out this way though because so far in all of my games I have NEVER had a new resource discovered in one of my mines.

Barring the new resource discovery windmills actually come about even to mines once you get all the techs for them assuming you value food more than production and commerce less.

[OzzyKP]

Thanks for the comment Soren. Saves me the trouble of rebuilding mines, heh.

But yea, this is an interesting aspect to be considered. Windmills vs. mines?

[Handel]

Originally posted by khumak


Hmm, if this is accurate then mines are ALWAYS superior to windmills eventually. I question whether this math really works out this way though because so far in all of my games I have NEVER had a new resource discovered in one of my mines.

The only advantage of the mills is it gives +1 food.

[peyoan]

Actually, it's very nice indeed.

My game i'm playing now, i have 7 cities, each with about 4 mines a piece. In one of the cities, i've had TWO silver resources appear, and an extra IRON appear near my Capital. This is over a period of about 200 turns.

Recap: 7 cities, about 25 mines in total.
3 Mines developed resources over the 200 turns.

I've actually seen this to a lesser degree in my other games, you'll usually always have a gems or a gold or a silver pop up, it seems the strategic resources are less likely to appear though.

[mountainlion2]

Solver, if I understand you correctly everytime you gain a new tech that uncovers a resource your chance of uncovering a resource with a mine improves? For example, if you have a RNG that spits out numbers between 0 and 9999 for each resource tech you have do you get another number in the range to better mprove your odds? Or do only get one number in that range and if the RNG spits out the correct number does the program move to a seperate table to again randomly pick what you discovered?

Originally posted by Mylon
That probability isn't very low at all. At 1/1250 chance of success, if you work a mine for 100 turns, there's a 7.69% chance of finding something. Do this for 20 tiles, and you have a 79.8% chance of finding a resounce in that time frame.

I think the stats is flawed here, but it's been a while since I took stats. I do not think the computer counts how many times it didn't find something in a given square, and ajusts its computation for the next turn to better improve the odds. Therefore the chances for finding something remain the same over that 100 turns. Your odds of finding something will not improve with time, they will remain the same at 0.08% each turn. The probability will always remains low, I believe the only way to increase the likelyhood of a resource to appear is to have more mines being worked each having a 0.08% chance of finding something.

[Artuero]

It's 0.08% per turn, per worked mine. I'm not sure why Mylon said the chance was 7.69% if you work a single tile for 100 turns; I thought it would be an 8% chance. Working 20 tiles for 100 turns the chance would be in excess of 100% (160%). I think that you can just multiply the number of chances you are getting against the probability of success to get the result, but perhaps I am overlooking something.

Mountainlion2, you are right, in any given turn the chance is 0.08% per worked mine. And if you went 100 turns without finding anything the chance of one coming up on the next turn is 0.08% per worked mine. But looking forward at how many resources you expect to find over the next 100 turns if working 20 mines it is 1.6.

[Falconer999]

Originally posted by mountainlion2

I think the stats is flawed here, but it's been a while since I took stats. I do not think the computer counts how many times it didn't find something in a given square, and ajusts its computation for the next turn to better improve the odds. Therefore the chances for finding something remain the same over that 100 turns. Your odds of finding something will not improve with time, they will remain the same at 0.08% each turn. The probability will always remains low, I believe the only way to increase the likelyhood of a resource to appear is to have more mines being worked each having a 0.08% chance of finding something.

That is correct. Think of it this way: If it's 1 in 1250 every turn, let's say the computer has to 'roll' the number 23 for you to get gold. The first turn, it rolls 32 - you don't get gold. I would think it doesn't scratch off the number 32 - it can still 'roll' 32 again the very next turn - your odds don't improve.

The same as playing Powerball - your odds don't improve the more you play, they're always the same.

[Jcg316]

Probabilities are not linear. As more sample sets are drawn while replacing all possibilites it does not increase linearly.

The simplest way to show this is that if you have a jar with nine green balls and one blue you have a 10% chance of drawing the blue ball.

If you are replacing the balls after each drawing you are not guaranteed to have drawn the blue ball after the tenth drawing. You very well could have picked a green ball ten or more times in a row.

Linearly you would have had a 100% chance, hence were that to be true it would have been impossible not to have drawn the blue ball.

If the balls were not replaced the odds changed to 1 in 9 if you did not draw the blue ball on the first sample and so forth. That way you would have had a 100% chance to get the one blue ball out of ten total balls if you had drawn all ten balls without replacing them, obviously.

Whether the numbers he mentioned are right I wouldn't know without checking but they certainly could be right, and they do look about right so I'd guess they are.

[Artuero]

It's better to look at this in terms of expected gain. With the 1 in 10 blue ball game, you have an expectation of picking out 1 blue ball in ten tries. Not a certainty- you could never draw the blue ball or you could draw 10 blue balls, but your expectation would be that you would gain 1 blue ball for every ten tries. Your expected gain is .01 blue ball per try.

Which is why you expect to get .0008 resources per turn per mine worked, .08 resources per mine worked for 100 turns, and 1.6 resources per 20 mines worked for 100 turns. What you actually get will be different because you cannot actually get .08, 1.6 or .0008 resources. But in evaluating whether to mine a hill versus put a windmill on it, you should include the .0008 "expected resource" per turn in addition to shields, commerce and food.

[Jcg316]

That has nothing to do with the probability. The probability of getting a discovered resource is not linear. If you work a mine for 100 turns as mentioned above the probability is not 2/25 or 8%. The math does not work that way, it very much does not match what you might think intuitively without the statistical grounding to understand binomial distribustions. yes it seems to make sense the other way, no that is not nearly accurate.

The 7.69% chance to find a resource from a mine after 100 turns is very much accurate. That is the expected results of drawing from a 100 set sample with a 1/1250 probability. That is a 7.69 percent chance to have found a resource, as more than one resource cannot be found in that one mine. If it were something that could have more than one success that 7.69% is the chance to have found at least one.

It's better to look at this in terms of expected gain. With the 1 in 10 blue ball game, you have an expectation of picking out 1 blue ball in ten tries. Not a certainty- you could never draw the blue ball or you could draw 10 blue balls, but your expectation would be that you would gain 1 blue ball for every ten tries. Your expected gain is .01 blue ball per try.

Which is why you expect to get .0008 resources per turn per mine worked, .08 resources per mine worked for 100 turns, and 1.6 resources per 20 mines worked for 100 turns. What you actually get will be different because you cannot actually get .08, 1.6 or .0008 resources. But in evaluating whether to mine a hill versus put a windmill on it, you should include the .0008 "expected resource" per turn in addition to shields, commerce and food.

This is not nearly accurate. It is a guess that seems to make sense without knowing the mechanics of how such a probability will operate.

[Artuero]

Aha, I stand corrected and see how to get the 7.69% probability in 100 worked turns of getting a single resource, and the 7.98% probability in 2000 worked turns (20 worked mines x 100 turns each). I feel like I accomplished something in understanding that.

Can you elaborate a little on what the expected value is? Seems to me like that is the important question in deciding whether to build a mine or a windmill on a given hill.