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Subject: Stone Age Economic 101 - turning pips into resources rss

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Jason Cawley
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This is the first of a series of posts explaining the basic economics of Stone Age. New players may find it helpful, and more experienced players who think they figured it all out right away may discover points they missed. This first post covers the resource gathering areas, the next will cover the village, and the third will cover the VP actions, building huts and buying cards.

I choose that order because the fundamental accounting unit of Stone Age economics is the pip - a die roll value unit. Pips are worth slightly less than resources of the same numerical value, for reasons this post will explain. In turn resources are worth slightly less than victory points of the same numerical value, as the last will explain. The second post covers income vs weath and the role of time.

There are 5 gathering locations - technically the hunting location gets food which is not a resource in the strict sense, but we can treat it as one here, because its mechanics are similar. They have pip costs per item of 2 through 6, as everyone knows, and the easiest deduction of the budding Stone Age economist is that therefore food "is worth 2" and gold "is worth 6". The easiest, but slightly off, because it overlooks that economist's mainstay, transaction costs.

Players quickly notice that the dice hate them and they always roll one less than they needed to get that next resource. Some pips are wasted whenever this happens. But what is the right way to think about this "wasted pips" cost? The answer is, it is a *tax on resource gathering actions*. How much is the tax? The answer is, the location's divisor minus 1, divided by 2. That is 0.5 pips for food actions, 1 pip for wood actions, 1.5 pips for brick, 2 pips for stone, and 2.5 pips for gold. We can talk about methods for mitigating this cost later, and how to think about the accounting for those methods correctly. But the base fact must be seen first - each time you pick up the cup and put dice in it, you pay a tax of expected wasted pips, and the amount of that tax is the numbers given above.

Why those numbers? There is a modest amount of approximation in it, compared to detailed binomials varying by number of dice, but here is the right way to think about it, that gets all the essentials without those details. Think of the number rolled as evenly distributed in an indefinite range and ask what it "Mod"s to, given the location's cost. So 1/3rd of wood actions will Mod to 0, no lost pips, and 1/3rd will Mod to 1, 1 lost pip, and 1/3rd will Mod to 2, 2 lost pips. Total 3 lost over 3 possibles, 1 lost pip. Repeat the analysis for an arbitrary cost, and you get (N-1)/2 for lost pips.

Now notice, this tax is not on the individual resource gathering meeple, it is on the action, the overall die roll. You lose 2 pips on average rolling for stone whether you roll 2 dice or 6 dice. If you roll 2 dice for stone on each of 3 successive turns, you will lose 6 pips in expectation. Rolling all 6 of them once, you'd lose only 2. The difference is worth more than a full action - in fact you can roll 5 dice there once instead of 2 dice there 3 times and save a full action.

So, the first rule of resource gathering is that a finished resource is worth somewhat more than the pips it costs, because it is an "after tax" value. And the second rule of resource gathering is "divided we fall". Other things being equal, large gathering actions minimize the tax of wasted pips.

The next thing to discuss about resource gathering and its tax is the role of tools in limiting lost pips. Tools are more valuable than new players think they are, and the reason is simply that their accounting is more obscure. Most players think that a tool is worth one pip per turn, and some may think they are worth slightly less than this because they will occasionally not get them anything. But these are illusions. All pips are exposed to the lost pip tax, there is nothing specially bad about tools in that regard. In fact, the ability to pick whether to use tools on the first roll of the turn or a second makes them worth more, not less, than one pip per tool.

First notice that if you put all your meeples on one location, your tools just add to the roll at 1 pip each. Scale reduces the number of locations you pay tax for to 1, but you still pay the full tax. The tools do not meaningfully smooth your roll in this case, because there is no place to use the remainder. This is the wrong way to use tools, but it is also a minimum value they produce - one pip per tool per turn (as long as you do any resource gathering).

Now instead imagine that you have all your meeples except for 1 on a single resource location, and the last meeple is gathering food instead. Furthermore, imagine that you have a number of tools equal to or greater than 1 minus the cost of the space - 4 tools going for stone, for example. Then the tools pay more than a pip each. In fact, they completely eliminate the lost pip tax for the stone space, while leaving the lower 0.5 pip tax for the food space unchanged. But this is a net savings of 2 pips on top of the 4 the tools produce directly.

How is that, you ask? Well, anything you roll will now be rounded up to the next full stone resource. The remainder, exactly, without any lost pips, will be left as unused tools before you roll for food. You will be left with an even number of tools half the time, and an odd number half the time. When you roll for food, you will either roll even or roll odd, again half the time each. if they match - odd with odd, or even with even - you will have no wasted pips at all, for your entire resource gathering phase. If they don't, even with odd in either direction, you will have 1 wasted pip on the food action. You should roll the more expensive action first because you will end up paying the tax for the action you roll last. At that point, you are in the situation we mentioned first (everyone on one spot) and tools make no difference.

The impact of tools, correctly used, is to reduce the resource gathering tax. The correct use is to spread over 2 actions and resolve the more expensive resource first. If you have more than enough tools to smooth the first roll, you can safely go to three actions without incurring more tax. E.g. I have 5 tools, and put 2 meeples each on brick and wood, plus 1 meeple on food. I will never need more than 3 tools to smooth the brick roll to the next full brick, so I will always be left with at least 2 for the wood roll. Which is enough to always smooth it, too, and get the remainder on food. My total resource tax for the whole phase will be its absolute minimum, 0.5 pips for the turn.

When you have enough tools and use them correctly, and also use scale to minimize taxes paid that your tools can't handle, you drive the value of pips all the way up to the value of resources, minus only 0.5 pips per turn. When instead you skip getting tools and divide your meeples over multiple small gathering actions every turn to meet your just-in-time no-inventory juggling acts to complete all your plans this very turn, "The Taxman Cometh".

To see just how ruinous these taxes can be, consider a tool-less civilization that puts one meeple each on wood brick and food, in an early game juggling act. He thinks of his 3 meeples as producing an average of 10.5 pips (3.5 each), and thinks it is a matter of indifference where he puts them. Sure he might roll low and lose pips, but he doesn't see any way around that, and he might roll well. What's the big deal? Well, first off he has to feed those 2 people every turn, which costs 6 pips, leaving 4.5 net income. And he is signing up for taxes of 0.5 + 1 + 1.5 = 3, or 2/3rds of his whole surplus from those meeple. If he needs food and put all 3 of them on food, he would pull ahead by 4 pips, or by 3.5 if he really needs wood to buy that card and can afford it in food terms.

One meeple on wood is basically at break even in tax terms. You should never be putting less than 3 people on gold and better still 5, with 3-5 tools. Having tools frees you from lost pip taxes if you use your tools correctly, and at higher levels they also allow division of gathering actions to support juggling acts, without ruinous lost pip ("tax") consequences. Before you have high tools to gather multiple resources efficiently, stick to two actions, one of them always an inexpensive type (food or wood) to use your modest tools. And otherwise trust in scale, keeping the number of times per turn you pick up dice to a minimum.

The next article will use what we have learned here, including proper accounting for the value of tools in reducing gathering costs, to evaluate the village locations, farm tools and population.

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Randall Bart
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Interesting. Please see prior threads listed below. I was accused of sucking the life out of the game. meeple

Re: Farm vs Tool vs Hut
Valuing all 36 cards

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For some reason, this got me to thinking of similar real life examples.....


Paying $40/mo for 600 minute on a cell phone contract, but then using only 400 minutes per month... you're really paying $40 for 400 minutes then....

A roommate used to buy a gallon of milk and only finish about half of it before it expires....

All cases of "wastage"
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Jason Cawley
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Reading the previous threads, your pick order for the village spots - farm beats tool beats population - is normally correct, but there are minor errors in the reasoning and accounting.

The biggest is that you correct for the need to feed the new person (cost 9 pips total, check), but overlook the fact that farm and tool both pay you the turn you choose them, not the following turn. This makes the net cost of picking the farm slot only 1.5 pips invested, and for the tool slot only 2 pips invested for the first few tools (up to about 5 of them), and 2.5 pips invested thereafter.

The second minor error in the accounting is that your slope for gains from the tools you are using the approximation that a tool produces only 1 pip per turn, while the reality is the first few produce as much as 1.5 pips per turn, by reducing the resource-gathering "tax" of lost pips.

Last on that subject, one of the replying posters mentions the lower cost of starvation versus fully paying to feed everyone in population intense strategies. This is indeed a fair point, and not by the way one that I regard as "broken" in the game. The cost of supporting population can either be 2 pips per turn per pop to feed, or 10 VPs per turn regardless of population to starve. VPs are always worth more than pips; how much more varies, but 1.2 is a reasonable lower bound. At max pop a starver may save 8 pips a turn or average +2.3 per meeple. He still paid 9 pips to get that increase, where the farm gives +2 for 1.5 paid and still smokes it.

The reality is the max pop plus starvation strategy does not turn on the efficiency of starving, but on getting maximum value from the population bonus cards, especially the 2x pop cards. If the pop max starver never sees those and his opponents take them instead, he will not benefit from having taken the population action more often than his opponents. When that approach wins, it wins on getting those cards, not on the extra pip income from the people.

The card thread on the other hand has many valuable insights. It too has some minor errors in the accounting, the biggest being its tendency to rank the ending bonus items in too similar a fashion. See, farms, tool, and huts all start at 0. But people start at 5. This is a huge built in bonus in ending value for the pop bonus cards over the other bonus cards. Huts can expect to end at 5 to 8 depending on game length, but the others will only climb to even 5 if they are a focus of that player. They aren't going to hit 9, whereas people can easily hit 10 if a player focuses on people.

If no one at the table goes for high numbers of people (rare, since if the hut is open somebody should pick that approach), where the double people cards end up (including whether they appear) will still be important in the final score. And anyone who does get one of them instantly gets an extra incentive to ramp people, unless it comes out quite late.

A last point concerns the choice of going for technologies or not. There are a number of technology cards that are otherwise quite unattractive, giving only a few food e.g. If no one else is trying to collect techs, these should be available at the lowest price slot, if they appear. When you go tech you have to average what you pay for the tech cards over all of them, and balance it with the benefit from all you manage to collect. The average value of each is simply the number you manage to get. Even so you make a VP vs pip profit only buying at the lowest slot, and break even at the 2 resource slot. You shouldn't be chasing techs at the most expensive slots, and if others are, then the technology gathering strategy is too crowded already and you should avoid it.

Personally I find the hut bonus cards the second most important behind people. The big reason is that 3x bonus card being possible, and the fact that even without a hut building focus you will tend to end with 5 huts or so in a typical game. With a hut focus you can easily make that 7-8, the only bonus category climbing to the level of people in the people focused strategy. A extra 1-2 on the bonus multiplier (from 2s rather than 1s or the 3 over a 2, from cards) can easily make up for the difference.

I think people have the impression of people focus plus starvation as a dominant strategy, and the population action being particularly good, mostly from games played with many newer players who do not properly value the best bonus cards, and let the same player accumulate those. Even if they see their high value for themselves, they will only later come to see the importance of competing for them to deny them to a leader in that category. The marginal value of picking a pop bonus card as the first action of the turn when you only have 6 people, say, but an opponent has 8-9 on his way to 10, can be positive, even if another spot would earn you more pips to game end. I think newer players miss such plays and mechanically go to the village spots first, not noticing how fast their value is declining as the end approaches, and the like.

When opponents properly value the pop bonus cards, I don't think pop and starve is a dominating strategy. I've readily won with 5 people and 7 tools against players with 10 people and 1 tool, for example. They didn't notice or manage their collect lost pip expense very well, and I and others at the table didn't give them pop bonus cards for free. If a pop bonus card came out, they only got it if they were the chief that turn, otherwise somebody would snap it up first. Similarly, when an opponent invests in a manner that will only pay off if the game goes 12 more turns, experienced players will drill huts to run out the clock before then, while newer players won't notice or think of that, and will just let the opponent's longer term strategy play out as he hoped.

I hope this helps. Thanks for the pointers to the previous analytic posts.
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Ian Dembsky
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Awesome posts.

Just wondering though- Do you really think that someone who maximizes population only wins by getting the pop multiplier cards? That seems to overlook buying huts and hut multipliers. 10 guys and a couple of tools can get a lot of resources, and a lot of hut points from that. At a Stone Age tournament final table I won using that strategy with only one population card, but much more so by getting lots of resources and buying lots of huts. without the population card I still would have won (not without the triple hut card though).
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Randall Bart
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JasonC wrote:
The biggest is that you correct for the need to feed the new person (cost 9 pips total, check), but overlook the fact that farm and tool both pay you the turn you choose them, not the following turn. This makes the net cost of picking the farm slot only 1.5 pips invested, and for the tool slot only 2 pips invested for the first few tools (up to about 5 of them), and 2.5 pips invested thereafter.
surprisewow You are right. blush I thought that issue had been raised and corrected, but the other version of the graph has the same error.



Quote:
The second minor error in the accounting is that your slope for gains from the tools you are using the approximation that a tool produces only 1 pip per turn, while the reality is the first few produce as much as 1.5 pips per turn, by reducing the resource-gathering "tax" of lost pips.
I point that out in the FvTvH thread and in the earlier starting player thread from which the graph and my analysis derived.

Quote:
Last on that subject, one of the replying posters mentions the lower cost of starvation versus fully paying to feed everyone in population intense strategies.

My analysis completely ignored the hunger strategy.

Quote:
But people start at 5.
Yeah, double meeple cards start at 10 points. They are huge.
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Jason Cawley
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Thanks. I think that normally yes, that is the mechanism whereby pop can pay, and that when it isn't present, pop is paying much less than you suppose. No doubt in your game, getting the 3xhut card was a big boost to your score, but you could have gotten that card and built huts without the last several people. Whether your big crew actually netted you points turns on how long the game went after you got them, and on starvation issues.

I will illustrate this with a hypothetical contrast. I have to make up some of the timing variables and some of the alternative actions available. You can try fiddling with those afterward to see how much it changes the analysis, but one fully worked example will show what is going on.

So we assume a player can take one of two forks in the strategy road, and we suppose this fork happens 8-9 turns before the end of the game. In fork one, population, the player takes the following village actions over the 4 turns, ending 4-5 turns before the end - population, none (turn order), population, population. The other fork in the road takes tool, nothing, farm, nothing - from the village spots, mind. I'll start by assuming both players feed their people, and that they started with 7 people, 2 tools, and 3 farms before the fork (having raised income early as turn order allowed). We assume no tool or farm bonus cards and 1xpop at the end. I'll number the turns from 1 to 4, then there are 4-5 turns of steady state for the people to pay off. What does the accounting look like?

The pop player has 1 less meeple on other tasks on turn 1 (hut takes 2, tools takes 1), gets one less tool, and feeds one extra person. That is a net pip income of -7 compared to the other strategy.

On turn 2, neither player can take a village spot (turn order). The tool player gets one extra tool including its tax-reducing smoothing effect, and feeds one less person. This matches the income from the extra person for the other strategy. No change for this turn, but the population player is still 7 pips behind.

On turn 3, the pop player sends 2 to the hut again, but he has one more to send, while the other strategy puts one on farm. They each have 6 out gathering. The other guy also has +1 tool and +2 farm income, and at the end of the turn the population guy has -4 extra food cost. Net change that turn, another -7. The population player is 14 pips behind.

On turn 4, the pop player again takes population, while the other skips the village entirely even though the hut is open when it comes to his turn. He isn't ramping income any more, just using what he already has.
Both players have 7 people out collecting - the non-pop guy because that is his whole team, the pop guy because 2 of his larger team are in the village not in the fields. Pips collected are the same, except the non pop guy has an extra tool and a farm, together worth 3.5 pips, and the pop guy ends with 3 more mouths to feed for 6 higher food expense.
For the turn, therefore, the pop player falls another 9.5 pips behind. His total lag is now 23.5 pips.

What are the steady state incomes thereafter? The non pop guy has an income 3.5 higher from his 2 village actions, and no increase in his food costs. The pop guy has an income 10.5 higher now that his extra people are finally all in the fields - but he also faces 6 higher food costs. If he feeds the crew, therefore, he gains on the other strategy only at a rate of 10.5 - 3.5 - 6 = 1 per turn. He does however also get 3 extra VPs at game end from 1xpeople bonus. But it would still take him 20 turns to claw back to even.

But that assumes the big pop guy feeds his people. When you have so many and haven't taken a lot of farming, it makes sense to starve them instead, particularly if you can get hut spaces. Suppose the pop player begins starving, deliberately, on the 4th turn, the one where he hit 10 people. Compared to the accounting above, this saves him 20 pips worth of food that turn at a cost of 10 VPs. VPs are worth more than pips, but not twice as much. Call it 12 pips worth, to account for lost pips in resource gathering, meeples standing on huts to build them, cards that have to be paid for slightly above their ending VP value, and the like. But there is another correction to make, because now the starving player's 3 farms bring him nothing instead of 6 pips per turn - a starver must turn in all food. He nets a closing rate pickup of only 2 extra pips.

Maybe it should be 4 extra, starting with a lower farm total and having planned to go "big pop" all along. He still needs 4 turns and his 3 bonus VPs at the end just to hit break-even, and pulls ahead only a tiny amount if the game goes a turn longer.

Here is what doesn't happen - the 10 meeple person doesn't just get 10.5 extra income without cost. He had to pay upfront in lost actions, he shuts off his farm income at some point if he starves, he nets little per extra person if he doesn't starve. And he probably gives up other valuable, income raising village actions his turn order would make available, to grab the population hut before others take it.

If the game goes long enough afterward, or if he has gathered 3-4 times population in card bonuses, then sure it can pay off. On the other hand, if he finds the hut spaces he needed on those last 4-5 turns too crowded to get more than 1 per turn, and sometimes by turn order gets stuck with 14 point 3-resource huts instead of the big ones, then his larger field crew has few ways to turn their labor into VPs. Maybe he has to gather foods some of the time to avoid the 10 VP starvation hit some turns when a second hut isn't available. Etc.

I hope this helps think about what lots more people actually cost you, and actually get you. They cost you more and get you less than you might at first suppose. The biggest question determining whether they will pay off is simply how much longer the game goes on. Getting pop early, especially when 3rd in turn order with the other village locations already taken, will almost always have time to pay off and makes sense. But ramping pop to full in the second half of the game is a much more dubious investment, and only makes sense if other elements of your strategy and what the board and other players make available, fits that strategy.

Especially those pop bonus cards...

Fine question BTW.
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JasonC wrote:
Suppose the pop player begins starving, deliberately, on the 4th turn, the one where he hit 10 people. Compared to the accounting above, this saves him 20 pips worth of food that turn at a cost of 10 VPs. VPs are worth more than pips, but not twice as much. Call it 12 pips worth, to account for lost pips in resource gathering, meeples standing on huts to build them, cards that have to be paid for slightly above their ending VP value, and the like.

I think this argumentation is a bit lopsided. If you value 10 VP at 12 pips due to resource gathering tax (among other things), you have to consider that you don't save 20 pips worth of food, you save 10 food. You would need more than 20 pips for acquiring them due to this tax. (So this is an argument in favor of the starvation strategy.)
But there is another factor to consider which makes the starvation strategy less attractive: The tax is lowest for food and if you have enough tools, you practically always get to only pay this lowest possible tax (as there is no limit for hunters). However, if you don't collect food at all and use your people to collect (the other) resources, you'll have to pay at least double the tax for wood (1 instead of 0.5) or more (if you don't get to collect wood on a turn due to the limit).
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