Wednesday, June 30, 2010

Stone Age Strategy Compilation

This is my 1st in depth strategy posting for a game but my win ratio in Stone Age has been pretty solid so hopefully I can add at least one branch to all of your strategy trees.

I'm going to divide this Stone Age strategy guide into two sections.

1st, and I know this has been talked about ad-nauseum, my take on
The Relative Strengths of Meeples vs. Fields vs. Tools.

2nd. Huts vs. Cards

Before I go into depth about the 1st, let me clearly and concisely give you my take on the 2nd.

Cards are almost ALWAYS better than huts until the end of the game. Here's why. You must evaluate every card on a cost basis of giving up 3 VP (1 wood hut value) per row. The most expensive card will cost you 12 VP worth of hut VP. Now barring extreme aberrations in your board, every single card (maybe with the exception of the 1 free food raft symbol if you have no other symbols) is going to earn you more than 3 VP. You should have more than 3 fields, 3 tools, and 3 huts by games end, and you start the game with 5 meeples, so any 1X multiplier should score you more than 3 points. Many 2X multipliers will likely provide you with double-digits points come scoring time, plus whatever other benefit they provide making most clearly worth even a 4 wood purchase.

The math is simple for everything except the shop cards. Decide how many resources and or points you will receive from a card, subtract 3/6/9/12 depending on the row the card is in. If you net up more than a few points, grab the card over a hut. I think getting first dibs at a shop roll varies in strength. At the beginning of the game, it can be huge, since you might get a field or tool to use throughout the rest of the game. Near the end, a resource you can sell to a hut might actually get you more points than a tool or field, so the overall value is far lower. At the beginning of the game, I will add an arbitrary 4 points to the relative value of the shop card combined with it's normal value when deciding on whether to purchase it. I subtract a point in value every several turns until it becomes negligible.

At the end of the game, you must concentrate on getting points fast and furious and finishing with no excess resources in your possession. Remember, you are only getting 1 point for those resources as opposed to face value 3/4/5/6 so look for a 1-7 hut or large 4-5 item huts to funnel your remaining resources into. Huts become more important than all other priorities if you have excess resources lying around. Yes that 8th symbol you've been searching for all game could get you 15 more points, but guess what, a 1-7 hut could get you 42 if you turn in all gold.

Okay, not so concise, but you get the picture. Cards early, huts late. One small exception - Grab a 1-7 hut and toss a single wood on it if it shows up early. It pisses off your opponents amassing gold and it gets you a cheap hut for those couple hut multipliers you'll inadvertently end up with at the end of the game. .

Alright, now that we got through the easy part lets confront the more debated issue, the relative strengths of fields, tools, and people.
In an earlier thread the math of Meeples, Fields and Tools was talked about by Jonathan.

He gave a relatively sound analysis.

A farm produces 1 food per turn, and each food costs 2 pips. So a Farm produces 2 pips/turn, assuming you can use the food.

A single tool produces at least one pip per turn. First, it is evident that when you have lots of tools, the incremental tools are worth exactly one pip. Once you’ve used tools to “round up”, when you use 5 more to buy another stone, those 5 were clearly worth 1 pip each.

What about one tool? If you roll in a single location, that tool has an expected value of 1 pip. Say you roll for gold with 1 die. On a roll of a ‘5’, that pip earned you a value of 6 when the gold is sold for a hut. On any other roll, the pip earned nothing. So the expected value of the tool is: 6 * 5/6 = 1. The same holds true in any other location.

However, suppose you roll in two locations with 1 tool. The tool becomes more valuable. Suppose we first roll for gold, and then for wood.

In the first roll, on it’s own, the tool is worth 1 pip. But there is a 5/6 chance that we’ll still have the tool left over. So now we go to the forest, where the tool is still worth 1 pip. The total value of the tool is 1 5/6.

[6 * (1/6)] + [5/6 * 3 *(1/3) ]

So a single tool is worth at least one, and up to 1 5/6 if you roll in two places. It can be worth more if you roll in 3+ places, but I agree that this should be done infrequently.

A meeple produces on average 3 ½ pips per turn. The meeple eats 2 pips per turn, for a net value of 1 ½ pips. However, he cost two meeples to make, so each meeple invested netted you ¾ pips per turn.

Farm: 2 pips per turn (per meeple invested)

Tool: 1 to 1 5/6 pips per turn (per meeple invested)

Meeple: ¾ pips per turn (per meeple invested)
Now here are my gripes to Jonathan and everyone else out there who love to undervalue the importance of meeples.

1st - It doesn't always just come down to pips, there is also an added flexibility that having more meeples gives you. You're going to need a certain amount of wood this turn to buy your card which will give you a gold which you want to use to build a hut. Can you do all that will 5 meeples a crap-load of fields and some tools? Maybe, maybe not. Also, (and I don't recommend doing this too often) having an extra meeple around to screw someone out of a hut or card they really want even if you can't afford is another benefit a tool and field cannot offer.

2nd. - Meeples are most assuredly not worth 3/4 pips per turn. On the 1st turn, they return -2 pips for your 2 meeple investment (not so good I grant you) as you need to feed your child and he/she does nothing for you. On subsequent turns they are worth 1 1/2 pip per turn. To find their true full game value, multiply out the # of turns left in the game by 1.5 and subtract 2. It will probably come out to something like 1.47.

3rd. - IMO, tools are not quite as valuable as stated above. The 1st 3 tools are, but after that they begin to have diminishing returns. You often waste a 2/3/or even 4 tool, when all you need is to add 1 to your roll. Here's another example, let's give you 4 arbitrary things. 3 meeples and 1 tool versus 1 meeple and 3 tools. And lets say to help prove my point further that you want to go for gold. Odds are you will only get 1 gold both ways 3 x 3.5 + 1 = 11.5 versus 3.5 +3 = 6.5, but one way you have an infinitely greater chance to get 2 or even 3 gold whereas you're maxed out at 1, and even that's only if you roll a 3 or greater.

I personally will almost always, barring the multipliers in my hand take people over tools even if I am lacking in fields. I will have the newly born children feed themselves and then some for a couple turns. Also remember that hunting is the only way to guarantee 2 (1) tools don't go to waste.

In conclusion, Stop ragging on the meeps, peeps! They're actually quite useful.

Hope someone out there found this long-winded Stone Age rant useful. Kids use it lay the smack down on your parents. Parents make sure your kids can never embarrass you again.
I haven’t been contributing much to BGG the last couple of months, but I have an excuse – I have been sucked into the BSW Stone Age vortex. I’ve now played over 180 games online, plus another dozen or so in person.

The reason I’m so hooked is that I still feel like I don’t play nearly as well as I can – and will. It’s a steep steep learning curve for a game that is both quick (often 45 minutes) and, to me, very relaxing. So my thoughts may well change 100 plays from now.

Till then, please let me know what you think!

I've also written three shorter strategy posts this week. There is some overlap in concepts between the different posts (sorry):

- Starvation ain't all it's cracked up to be?

- Are sets too weak? And if so, is it a game flaw?

- Opportunity cost, not just pips per meeple

These are my observations:

1. There is no dominant strategy. One thing I love about this game is the certainty with which inexperienced players publicly proclaim that they have found a clear, consistent dominant strategy. It ain’t so. Not cards, not huts and hut multipliers, not even starvation. My experience, anyway, of playing against many of the top players is that they use a variety of strategies for different situations. Why?

2. All strategies are highly dependent upon the strategies of other players – more so than many other games. Stone is really like an economic market: if others overvalue farms, go for meeples (perhaps with starvation); if others overvalue multipliers (meeple/tool/hut/farm) and undervalue sets, go for sets, etc. One of the first rules of wise business acquisition is “Never want anything too little or too much.” If you are hell bent on getting meeple multipliers, you may end up paying too much for them, for example.

3. Flexibility, especially early. I go into this more later. Essentially, Stone Age, even more than Puerto Rico or Caylus, rewards doing what other people are not doing. You have about 4-6 turns to get a sense of what people are valuing. Later in the game, focus on implementing it. Unlike Puerto Rico, however, there is a highly variable cost to taking a desired action – particularly in the cards. So focus must be tempered with discipline in what cards to take (see below).

4. Pips/meeple is a handy tool, but don’t forget opportunity cost. The calculation you see in many strategy posts here is, in general terms: EV (expected value) per die roll (3.5) of a meeple on resource minus the cost of feeding a meeple (2/turn) minus wasted pips on resource rolls minus the cost to convert resources into VPs.

So, for example, a hut requiring two wood and a gold is worth 12 points. That’s 12 pips of resources requiring, on average about 4 workers (with a pretty minimal 2 pips of wastage) plus one meeple to “claim” those VPs plus 10 food for those five workers (10 pips). So 12 pips resources + 2 pips wastage (this is too low, actually) + 10 pips food +3.5 pips for that last worker on the hut = 27.5 pips to get 12 points. Note that spending 4 wood (also 12 pips of resources) on a card that, top and bottom, gives you 12 points, would also be 27.5 pips to get 12 points.

This seems to be primary tool folks are using to compare strategies. What I haven’t read much about is importance of making your first, and to a degree, your second, placement really count. That is, the EV of your first placement is likely to be much higher than your second, and so on…. But how to use it to your advantage? Well, if you try a strategy that others are not, or that people systematically undervalue (such as collecting sets of symbols), it is generally easier to use your second (or even third) placement to take the action you want. Conversely, if you use a strategy that is popular in general (and especially in your particular game), then not only will it require your first placement most of the time, but often that will not even be enough (b/c 75% of the time someone else will go first, in a 4p game).

5. Pay specific attention to whether you are in the early, middle, or late game. This is what I’m struggling with a lot at the moment. Timing is everything. You don’t want to end the game with a lot of wood (or gold!) you didn’t use. But you also don’t want to spend all your resources and food two turns from the end game (unless there is a really compelling reason to do so!). This could be a whole article in itself, but I define the early game as going until there are 4-5 huts available in a stack, and the end game as when there are just 2 huts available in a stack. This of course ignores the speed of card depletion, which is a bigger issue in a 4p game than a 3p game, but you can extrapolate that fairly easily.

The early game is for building your economic engine, and developing your game strategy (symbol sets? Huts galore? Starvation and huts? Etc.). I try to amass a fairly even distribution of resources, such as: 3 gold, 3 stone, 5 brick, 7 wood. Gold and stone can be slightly more efficient (especially with a lot of tools), but brick has less wastage so it’s the perfect hut material and can be used in a pinch to buy cards at minimal pain. Having 7 wood guarantees that if the 2 cards you desperately want come out in the 3 and 4 slots you can take them both without worrying about paying for them. Of course, in most games you just can’t get even distribution, but getting it gives you maximum flexibility, which in turn lessens your opportunity cost. How? Well, when you find the VP actions you want (huts, cards), it’s much easier if you don’t also have to worry about being locked out of the resource you need to execute those actions (this is especially harsh with huts).

The countervailing factor to resource balance is opportunity. If a 2x tool multiplier comes up in the 1 slot (or in the 2 slot on the second action), it’s usually good even if you currently have no tools. You can always get tools later. As I explain later, the problem with the pip evaluation method is that VP opportunities are highly finite. It’s very hard to pass up any cheap 2x mulitiplier in the early game – you can always adapt your strategy to it later. It’s far messier to amass 6 tools and pray that a 2x tool card comes out in the late game – especially because by then there’s a good chance you’ll get blocked.

Farms: Equally important is either having enough farms (perhaps with some food gained through cards) or abandoning food altogether, before you enter the middle game. Otherwise you will be spending half you people trying to feed your tribe the rest of the game. Don’t underestimate the awesome power of the early farm. It’s one meeple you will never ever have to feed again.

Tools: Slightly less important is tool distribution. I’m not crystal clear on the math here (others have documented it), but it seems that to maximize tool efficiency you should have at least 3 – which guarantees that at least one will always be used on wood, for example. So if you don’t get tools by the middle game, you may wish to abandon them altogether and perhaps just get more meeples – unless you can get a tool with a late placement (rare).

One fairly obvious point that I didn’t grasp for the longest time: the fewer tools you have (often in the early game), the better it is to pile your guys on cheaper stuff – because there is overall less risk of wasted pips. So the less tools I have the more I dump a lot of guys in wood or food (and later, especially in a starvation strategy, on gold and stone). On the other hand, the more tools I have (say, at least 5 or 6), the more sense it makes to diversify, even putting just one guy on a few different resources – because then there’s less chance of wasting tools (another way of wasting pips).

The middle game This is the best place to spend your resources, especially for huts, because you can often take a hut very late in the turn. This is also the place to really crank whatever strategy you’ve got. Usually it’s a pair, like meeples & huts or tools & set collection. Having a primary and secondary is almost always necessary, with the secondary strategy being developed mainly in late turn and/or cheap moves. The key here is to buy huts/cards late in a turn if you can, b/c you can’t do it the last 2 (and sometimes 3) turns of the game.

The end game: Ideally, you will have at least one of everything and 4 or 5 wood by the last 2 turns. Better yet to have 2 of everything. More than that is a bit risky, because you may not be able to churn all your gold and stone into huts the last two turns. But holding onto resource diversity is most important heading into the end game because otherwise you can – and will – often be blocked from the resources you need to buy huts and (efficient) cards. The last 2 turns players usually choose huts/cards FIRST, then the resources they need, and finally the town spaces. The problem comes when you want a hut, but all the available huts require stone, and you don’t have any. THEN you have to hope that you can take stone on your second placement (usually losing a key chance at a card or other hut). If, on the other hand, you planned ahead, you can use your key second and third placements to take a good card and/or a town spot to crank on the multipliers you’ve been getting (that tool or farm on the last turn could be worth 6 or more points in multipliers even if it never gets used).

One of my favorite cards is the leaf that gives you two of any resource. I love it not so much because it can make two gold, but because it can make 2 of anything, any time you want. So effectively, as long as you have it, you can rarely get blocked. (Of course, as I have learned, you can keep it too long!)

6. Avoid minimal efficiency gains that sacrifice all-important flexibility. You know who gets really good bargains at public auctions? People who save money for when they can get a great deal. In Stone Age, you got to save your resources for the next great deal. For example, spending a ton of resources in early or middle game on a 1-7 hut is, I admit, really efficient. But it may take 2-3 turns (or more) to pump your resources up again. What if a great card that plays right into your primary strategy comes up and you have no wood. You play on the card, then all the wood slots get taken, and suddenly you’re spending 3 brick – and perhaps incurring other opportunity costs.

First flexibility, then efficiency, then focus. Take what is given to you cheap and late in a turn.

My personal preference is to build at least 3 farms and one meeple fairly early if possible, then add tools and more meeples. I tend to ignore huts early (except the 1-7) and try to build them mostly in the middle game. I don’t think it’s critical to have a lot of people (unless you’re doing a starve strategy), but it’s tough without at least 6, mainly because there are times when you have a lot of good things to do and simply run out of meeples, even if you just put one on each resource. I think I tend to over-farm – perhaps it’s best to chose a 6th meeple, for example, before a 4th farm. Tonight I ended up with 9 farms and 7 meeples – and lost 203-192 in a 3-player game.

I’m still really struggling with timing, and have games where I’m stuck with resources I didn’t spend. Obviously, the optimal efficiency is to end the game with zero food and zero resources, but this is tough to do. And above all, have fun! I tend to play fast, and guesstimate a lot, because doing the math during a game just slows it down for everyone. You can always think through your mistakes later.

First of all, let me say that Stone Age has quickly risen to become my favorite board game at this point in my life. After say, twenty or so games, I have included some strategy to think about…

1.SIT TO THE RIGHT OF THE PERSON WITH THE LEAST STONE AGE EXPERIENCE – kind of funny, but they will tend to make poor choices and give the better choices to you. Okay, joking aside, let’s move on to strategy that has a little more integrity…

2.IT MATTERS WHEN YOU TAKE YOUR HUTS – This is especially true in a two-player game. At the end of the game, huts become more of a commodity, but, lets say you want to buy a hut, say early-midgame. The best time to buy it would be on the turn preceding the turn that you are first in the placement order. This is only true because there are some game changing huts, especially the 1-7 huts of any commodity. This ensures that if they show up, that they are yours.

3.IS THERE A MATHEMATICAL EQUATION THAT ENSURES YOU WISDOM IN YOUR MEEPLE CHOICE? I believe that there is, and I hope to expound upon this in a later article. But, for simplicity sake, consider what the [1x Meeple / 1 Stone] card is worth in the 2-spot on the board.

To answer that you have to consider how many Meeples you would have at the end of the game. E.g. If you expect 8 meeples at the end, the card is worth roughly (and for simplicity sake)

1x Meeples = 8 points
1 stone = 5 pips
minus 6 pips = the cost of 2 wood to buy the card

For me, pips and points are synonymous is determining the value of a card. So the value of that card is 8+5-6 = 7. Notice I didn’t consider many other things, like the cost to feed that man, in determining this value. I also hope to explain why in later articles, but to me it’s negligible, and adds confusion.

There is some difficulty in determining, say, what a random bonus on a card is worth, because frankly, I believe this bonus is worth far less later in the game, than in the beginning, and may even hurt you later in the game. Also, there are plenty of things on the board that are worth less later on in the game. I hope to write about this at a future date, as I hope to answer statistically what I mean. In the meantime, I hope these couple of tips kept you interested. Any feedback would be appreciated.

Credit: KingBubba, dzevin