Lucas Hedgren
United States Dublin Ohio

Hey all,
So, it sure seems that Stone Age is ripe for mathematical analysis. Here’s my take:
I want to compare the point return from gathering food vs. the point return from gathering up stuff and building buildings.
First, if I want to compare the starving vs. nonstarving strategy, I need to know what my return is in each situation. Let’s start with finding out how many points you can make with dudes, just gathering and building buildings. In order to find that out, I need to know how many pips get wasted on average when I gather goods.
I created a spreadsheet, where for each number of dudes (only up to 5, just because the answer was becoming apparent) what the average waste would be. For example, for 4 dudes, gathering bricks, I multiplied each of the dice outcomes by its probability of occurring, then by the waste for that number. Add those up, and you get a weighted average waste. For 4 dudes, at bricks, it was 1.503. In fact, for any number of dudes, for bricks, the number fluctuated very slightly around 1.5. For all the resources, the number of wasted pips does not change (much) based on the number of dudes you put there. The numbers were .5, 1,1.5,2,2.5 for Food, Wood, Brick, Stone, and Gold, respectively.
This passes the smell test, in that it just shows how much better it is to put your dudes together on one resource, rather than spread them out. Your waste is fixed for each different resource you gather on a turn.
Now, using those numbers, how many points can I make? Well, over the course of 6 turns, I spend 25 dudeturns gathering stuff, then 5 dudeturns building 5 buildings. Lets say I gather a little of each resource, in order to more easily fulfill building requirements. So, an average waste of (1+1.5+2+2.5)/4 times 5 turns of gathering, leaves a total waste of 8.75 pips. All other pips became stuff. So 25 dudes who gather create (25*3.5) = 87.5 pips minus 8.75 waste is 78.75 pips worth of stuff. Now, I spend 5 dudeturns building buildings, which is (5*3.5) = 17.5 pips.
So, I spent (17.5+ 87.5) = 105 pips to get 78.75 points. (78.75/105) = .75 exactly.
Whew. Now, there are a few qualifiers here. You have to gather goods 5 total times over the 6 turns, and build the exact 5 buildings that go with those resources. But, this is an estimate, and I’m assuming intelligent building selection, etc. I think it’s a fair estimate.
Now, how does that compare to gathering food? Well, for 5 dudes, you have 17.5 pips to gather food with. With a waste of .5, that makes 17/2 = 8.5 food. 8.5 food is 1.7 turns worth of food for 5 dudes. A turn of food is 10 points, so 1.7 turns is 17 points. Using my calculated number of .75 pips per point, those 17.5 pips used to gather food and create 17 points could have been spent on (17.5*.75) = 13.125 points. Yay for food!
But, not so fast! Lets increase the number of people.
Doing the same math as above, 6 people can make 17.083 points gathering food, but 15.75 points building buildings. Getting closer.
The breaking point is 7 dudes. 17.14 points gathering food, but 18.375 points building buildings. Yay starving!
Conclusion: If you ever have to create 7 food to not starve, don’t do it. (Including situations like 10 dudes and 3 agriculture, or 3 leftover food from the turn before.) Your people spent gathering those 7 food could be doing better things building buildings.
Comments will be cherished.

dale yu
United States Cincinnati Ohio
If you're not part of the soultion...
You're part of the precipitate!

Dude...
If nothing else, I'm going to forever remember the term "dudeturn".
Otherwise, it is an interesting mathematical process here... Though, in my games, there aren't many times that I "need" to make 7 food... By the time I'm that far along in the dudecount, I'm already making at least something on the Agriculture track...
Though this analysis makes me wonder if I shouldn't just skip the agricultural track altogether and see what happens
Dale
boomtron wrote: Hey all,
So, it sure seems that Stone Age is ripe for mathematical analysis. Here’s my take:
I want to compare the point return from gathering food vs. the point return from gathering up stuff and building buildings.
First, if I want to compare the starving vs. nonstarving strategy, I need to know what my return is in each situation. Let’s start with finding out how many points you can make with dudes, just gathering and building buildings. In order to find that out, I need to know how many pips get wasted on average when I gather goods.
I created a spreadsheet, where for each number of dudes (only up to 5, just because the answer was becoming apparent) what the average waste would be. For example, for 4 dudes, gathering bricks, I multiplied each of the dice outcomes by its probability of occurring, then by the waste for that number. Add those up, and you get a weighted average waste. For 4 dudes, at bricks, it was 1.503. In fact, for any number of dudes, for bricks, the number fluctuated very slightly around 1.5. For all the resources, the number of wasted pips does not change (much) based on the number of dudes you put there. The numbers were .5, 1,1.5,2,2.5 for Food, Wood, Brick, Stone, and Gold, respectively.
This passes the smell test, in that it just shows how much better it is to put your dudes together on one resource, rather than spread them out. Your waste is fixed for each different resource you gather on a turn.
Now, using those numbers, how many points can I make? Well, over the course of 6 turns, I spend 25 dudeturns gathering stuff, then 5 dudeturns building 5 buildings. Lets say I gather a little of each resource, in order to more easily fulfill building requirements. So, an average waste of (1+1.5+2+2.5)/4 times 5 turns of gathering, leaves a total waste of 8.75 pips. All other pips became stuff. So 25 dudes who gather create (25*3.5) = 87.5 pips minus 8.75 waste is 78.75 pips worth of stuff. Now, I spend 5 dudeturns building buildings, which is (5*3.5) = 17.5 pips.
So, I spent (17.5+ 87.5) = 105 pips to get 78.75 points. (78.75/105) = .75 exactly.
Whew. Now, there are a few qualifiers here. You have to gather goods 5 total times over the 6 turns, and build the exact 5 buildings that go with those resources. But, this is an estimate, and I’m assuming intelligent building selection, etc. I think it’s a fair estimate.
Now, how does that compare to gathering food? Well, for 5 dudes, you have 17.5 pips to gather food with. With a waste of .5, that makes 17/2 = 8.5 food. 8.5 food is 1.7 turns worth of food for 5 dudes. A turn of food is 10 points, so 1.7 turns is 17 points. Using my calculated number of .75 pips per point, those 17.5 pips used to gather food and create 17 points could have been spent on (17.5*.75) = 13.125 points. Yay for food!
But, not so fast! Lets increase the number of people.
Doing the same math as above, 6 people can make 17.083 points gathering food, but 15.75 points building buildings. Getting closer.
The breaking point is 7 dudes. 17.14 points gathering food, but 18.375 points building buildings. Yay starving!
Conclusion: If you ever have to create 7 food to not starve, don’t do it. (Including situations like 10 dudes and 3 agriculture, or 3 leftover food from the turn before.) Your people spent gathering those 7 food could be doing better things building buildings.
Comments will be cherished.

Lucas Hedgren
United States Dublin Ohio

yudp wrote: Dude...
If nothing else, I'm going to forever remember the term "dudeturn".
Otherwise, it is an interesting mathematical process here... Though, in my games, there aren't many times that I "need" to make 7 food... By the time I'm that far along in the dudecount, I'm already making at least something on the Agriculture track...
Though this analysis makes me wonder if I shouldn't just skip the agricultural track altogether and see what happens
Dale
Exactly! If you never need 7 food, then feeding people is the right thing to do.
Next thing to do is to analyze the village actions. I think cards are going to be much harder though......

Greg Payne
United Kingdom Bristol

I thinkk this also shows that if you only need 1 or 2 food, you may be better of putting that last man on a cheap resource with your others than by sending it off for food by itself. Although tools do factor into the decision. Would be interesting to see what differece they make...

Matthew M
United States New Haven Connecticut
8/8 FREE, PROTECTED
513ers Assemble!

Pfah...calculating card values is (mostly) easy. Calculating the value of a farm  now THAT will get fuzzy.
MMM

Victor Galimbertti
Brazil Sao Paulo SP

Hi all,
First I would loke to say that finding the breaking point for starvation vs. gathering food is most useful due to the that being the basic strategic discussion of the game so far. But getting beyond that is a little too much for a dice game.
Take for instance Settlers of Catan (maybe the most popular game involving dice to date). Its obvious that in SoC having a "6" is better than having a "5" and so forth. No deep analysis is nedeed to find that out.
You can say that it is better to have 2 "9"s instead of 1 9 and 1 "10". Statistic proves that. But maybe you want to have more number options, in that case 1 "9" and 1 "10" is better. And then there is the fact that the "10" is less a target for the robber than the "9" and so on.
So my point is: With the amount of other factors involved in Stone Age such as...
 Civ cards rewards  can be food, or farms, or raw materials  Civ cards points  that are not close to being as easily calculated as huts points  Spaces available for workers  the wood field is not always available  The tools that you have  and so on...
... calculating statistics beyond the initial thread (starvation vs. gathering food) is quite pointless.
Please dont take me wrong, I also love to do math with game numbers, but the point of this game is to be FUN, not statisticaly perfect, or balanced.
Cheers,
Victor

Matthew M
United States New Haven Connecticut
8/8 FREE, PROTECTED
513ers Assemble!

I disagree...seeing through the math of the game is fun, and can drastically change some of the assumptions people go into the game with. Take a card that gives 2xVP for the number of people in your tribe. Previously, if I only had 5 or 6 people in my tribe I'd never look at it. But with an understanding of the math it is easier to see what the pipstopoints ratio of taking the card would be and can make it a viable choice, increasing my total choices on a given turn.
More meaningful decisions in a game like this = more fun, IMO.
What I'm most impressed with in the math of Stone Age is how well hidden it is such that someone can play intuitively letting the theme be the guide and still be competitive. It's brilliant!
MMM



Actually, if you did a statistical calculation, you will note that the game is quite statistically balanced. Not only balanced, but it also uses statistics and combines it with the "Caylus mechanism" in a very interesting way. Altogether which leads to a greater appreciation of the game, at least for me.
Whether I agree with the OP's calculation is another story. For one thing, I am afraid that using different number of dudes for gathering may change the relative expected waste for each resource. Using 2 dudes the waste may be greater in stone than in gold. Or maybe not, haven't done the math.

Thomas Taylor
United States Castro Valley California

I agree with Dale, the thing I came away with most was the term "Dudeturn". Awesome.

Lucas Hedgren
United States Dublin Ohio

drunkenKOALA wrote: Whether I agree with the OP's calculation is another story. For one thing, I am afraid that using different number of dudes for gathering may change the relative expected waste for each resource. Using 2 dudes the waste may be greater in stone than in gold. Or maybe not, haven't done the math.
Here you go ronaldinho. This is the math for 2 dudes at each resource. It ends up remarkably similar regardless of number of dudes. (WpD is Waste per Dude.)

Warren Cheung
Canada Vancouver BC

I'm still finding my valuations for everything evolving  pretty much the reason why I can't seem to stop playing the game Part of the fun in the analyses is that the game seems to be able to withstand it  sometimes, "doing the math" makes something the obvious best choice. In this case, "doing the math" seems to be revealing a lot of hidden depth, and making my "obvious" choices no longer as easy.
Octavian wrote: Take a card that gives 2xVP for the number of people in your tribe. Previously, if I only had 5 or 6 people in my tribe I'd never look at it. But with an understanding of the math it is easier to see what the pipstopoints ratio of taking the card would be and can make it a viable choice, increasing my total choices on a given turn. MMM
That's an interesting train of thought. The 2xVP for number of people is usually the only bonus card I'll always be happy to get, since you start with 5 meeples. That makes it worth at least 10VP, and if you can pay in wood, you spend wood that would net you 312VP in a building. Taking it at the 4 resource slot is only a little tough, but if you pay with 4 wood and get an extra meeple from the loveshack, you "break even". And that's without even counting the bonus at the top of the card...

Nikolai Cernavin
Germany Wonsheim RheinlandPfalz

boomtron wrote: drunkenKOALA wrote: Whether I agree with the OP's calculation is another story. For one thing, I am afraid that using different number of dudes for gathering may change the relative expected waste for each resource. Using 2 dudes the waste may be greater in stone than in gold. Or maybe not, haven't done the math.
Here you go ronaldinho. This is the math for 2 dudes at each resource. It ends up remarkably similar regardless of number of dudes. (WpD is Waste per Dude.)
The difference of 1 point per meeple is pretty high IMO. This is why it doesn´t make much sense to go for stone or gold with just 2 meeples if you don´t have tools. The difference of course becomes much smaller with more meeples. At 5 meeples it´s just 0.4 between food and gold.


