What Major Improvements do you see as most useful in Agricola, and why?
For a grain-based strategy the Clay Oven is key. It's incredibly efficient (1 grain-> 5 food), and crucially, requires only one stone, so you can get it early (guaranteed before the second harvest). In most of my Agricola games, one player will take the fireplace/animal eating option, and the other will go for a grain/baking option.
My other key improvement is the Well. The in-game effect (5 food) is marginal, but the 4 points at the end make a huge difference, and are great value (often equivalent to renovating your entire house, for example).
Here are my rankings of the Major Improvements:
- Fireplace (2 clay): Hands down, the best Major Improvement. The person who gets this has an easy food engine. In most cases it will take 2 actions for someone else to get into the action giving you time to collect your sheep. You also are first in line to get a cheap cooking hearth.
- Well: 4 resources for 4 victory points, and it comes with food! This should be taken every game
- Cooking Hearth: The default food engine of the game. No matter what you have, you can probably produce food with a Cooking Hearth. You should try to get one of these unless your minor improvements grant you a decent food engine.
- Clay Oven: Overrated by many, still 5 food for one grain is hard to ignore! Takes a lot of actions to get up and running, but will then produce a lot of food. In 2-3 player games coming up with stone can be an issue. With 4-5, the one sow/bake action can be problematic to obtain when you need it.
- Fireplace (3 clay): Less important than the 2 clay version. Paying extra to be the second person in a food engine isn't great. Better to get the extra clay and go straight to a Cooking Hearth in most cases.
- Stone Oven: The victory points are the main thing here. Taken late in many games for the VP and the free bake action
- Basketmaker's Workshop: Collecting all the reed can deny other players house expansion, buying this gives you something to do with all the reed.
- Pottery: With the right minors you can make something of this, otherwise it is just 2 VPs
- Joinery: It isn't too many games that you have much extra wood.
Do you play with the Farmers of the Moor expansion? I've been finding, with that in the mix, that the Forester's Lodge is pretty amazing, definitely a valid alternative to grabbing an early Fireplace. Played early it's a win-win Improvement: either it puts your Wood production into overdrive, or you get a ton of VPs for conserving Forest tiles on your board till the end of the game.
The Peat-Charcoal Kiln might be similarly good in a game where Stone is available from Turn 1, but unfortunately I mostly play 2 player, so I don't see enough of those!
In the standard game I agree with Pat that the 2-clay Fireplace is the best, but only if you can grab it straightaway and then be the first to grab and slaughter 4-5 sheep! It's not like it's much good later on, if you weren't the "early bird". Aside from that, see my comment on his answer. Don't underestimate the potential power of the Basketmaker's Workshop!
Baking with ovens is more of a bonus than an early goal to shoot for and rely on. Livestock and even food from occupations/minors is a better deal than baking. Especially in 4 or 5 player games it's WAY too easy to be blocked out of huge baking action when you need it.
Pat's list has the right idea, although Pottery is by far the best of the "workshop" improvements. Clay is the most abundant resource in 90% of games. You can never have enough wood between building rooms, fences, and improvements. Reed is also scarce to the point that it's the primary bottleneck for development. Why would you eat it? Clay is almost as abundant as wood and is mostly only used for a cooking improvement and renovation; there's plenty of it and it's not too difficult to get food out of the Pottery every harvest and the full +3 bonus points.