In our last post, we played a solo game of “At the Gates of Loyang” and did our best to balance regular customers and casual customers, use of helpers versus market stalls, and vegetable distribution in hopes of advancing to the end of the Path of Prosperity. We reached stone 15, which we thought was okay, until we noted that, according to the game’s (legendary) designer (Uwe Rosenberg), a “Good” player will reach stone 17. In other words, what we thought was a simple game did a pretty good job of putting us in our place, and it did so in less than an hour. Ouch!

However, we’re the rock stars of the upcoming resource revolution, so we should do better. And if we apply, and hone, our unique marketplace analysis skills, I bet we can. And while it’s hard to know just how well we can do in any given game, just like it’s hard to know how well we can do on any given buy, as we never know what cards we are going to be dealt until we get them (in the following turn), just like it’s hard to know what new opportunities are going to arise in the midst of a category sourcing project, we have the advantage that the game provides a fixed number of possibilities and an analysis thereof can shed light on the best general strategies to adopt and when to shift based upon the options presented to us.

So, in this post, we are going to do a basic analysis and then apply it in a subsequent game (in our next post). If we do better in the next game, we prove that up-front analysis works (both in games and in te real-world) and sharpen our analytical skills in the process (and in our profession, that certainly can’t hurt).

The game consists of 9 player fields, 6 common fields, 14 market stalls, 14 regular customers, 14 casual customers, and 13 non-lantern helpers. The breakdown is as follows:

Player Fields:

Vegetable	Wheat	Pumpkin	Turnip	Cabbage	Beans	Leeks
1×9 Plots	Y	Y	Y
2×6 Plots	Y	Y	Y
2×5 Plots	Y	Y	Y	Y
2×4 Plots	Y	Y	Y	Y	Y
2×3 Plots	Y	Y	Y	Y	Y	Y
Compatible Plots	9	9	9	6	4	2
Maximum Yield	45	45	45	24	14	06

Expansion Fields:

Vegetable	Wheat	Pumpkin	Turnip	Cabbage	Beans	Leeks
2×5 Plots	Y	Y	Y	Y
2×4 Plots	Y	Y	Y	Y	Y
2×3 Plots	Y	Y	Y	Y	Y	Y
Compatible Plots	6	6	6	6	4	2
Maximum Yield	24	24	24	24	14	06

Total Opportunities for Planting Between Player and Available Fields:

Vegetable	Wheat	Pumpkin	Turnip	Cabbage	Beans	Leeks
Compatible Plots	15	15	15	12	08	04
Maximum Yield	69	69	69	48	28	12

This analysis demonstrates that while one is always able to plant wheat, pumpkin and turnip, one is rarely able to plant beans and (especially) leeks. Furthermore, the maximum amount of leeks that one will be able to harvest is extremely limited, only 12 in the best case scenario (where a player acquires, and plants, both 3-plot public fields and both private fields before the end of round 6). Beans are also limited, as only 28 can be produced in the best case scenario (where a player acquires, and plants, both 3-plot public and private fields before the end of round 6 and both 4-plot public and private fields before the end of round 5), and that’s only if the player chooses not to plant any leeks. Cabbage, while not always able to be planted, can be planted in all but 2 private and 2 private fields, and can be readily available by round 4 even in the worst situation.

Casual (One-Time) Customers:

Vegetable	Wheat	Pumpkin	Turnip	Cabbage	Beans	Leeks	Cash
Customer				1	1	1	12
Customer			1	1		1	11
Customer		1			1	1	11
Customer	1			1		1	10
Customer		1	1			1	10
Customer		1		1	1		10
Customer	1	1				1	9
Customer		1	1	1			9
Customer	1		1		1		9
Customer	1			2			9
Customer		2			1		9
Customer	1		2				8
Customer	2				1		8
Customer	1	1	1				7
Wants	8	8	7	7	6	6

Even though the object of the game is to primarily satisfy regular customers (as illustrated by the fact that there is a penalty for having more casual customers than regular customers in any round you service a casual customer), appropriately timed service to casual customers can be quite lucrative (even though they will require a third vegetable). Analyzing the distribution of casual customers, we note that even though the ability to produce different vegetables varies considerably, with some vegetables (like leeks) considerably rarer than others (like wheat), casual customers, on average, vary little in their demand for different vegetables as the demand difference between wheat and leeks is only two (2). This tells us two things:

1. No matter what vegetables we produce, for any three vegetables we produce, there will be at least one casual customer who wants two of them.
2. We probably shouldn’t orient our vegetable production strategy around casual customer demands.

Regular Customers:

Vegetable	Wheat	Pumpkin	Turnip	Cabbage	Beans	Leeks	Cash
Customer					1	1	7/8/9/10
Customer				1		1	7/8/9/10
Customer				1	1		6/7/8/9
Customer		1				1	6/7/7/8
Customer			1		1		6/7/7/8
Customer			1	1			5/6/7/8
Customer	1					1	5/6/7/8
Customer		1			1		5/6/7/8
Customer		1		1			5/6/6/7
Customer			2				5/6/6/7
Customer	1			1			4/5/6/7
Customer		1	1				4/5/6/7
Customer	2						4/5/5/6
Customer	1	1					4/5/5/6
Wants	5*4	5*4	5*4	5*4	4*4	4*4

This tells us that, like casual customers, regular customers, on average, vary little in their demand — the total demand difference between wheat and leeks is only four (4). However, of the 36 possible pairings (where we allow a customer to want a vegetable twice), there are only 14 pairings in the game, and the only vegetables wanted twice are wheat and turnip. Thus, your vegetable production should in part be driven by the demands of the regular customers who appear.

Marketplaces

Vegetable	Wheat	Pumpkin	Turnip	Cabbage	Beans	Leeks
Trade Units			1	1	2
Trade Units		1	1		1
Trade Units		1		1	1
Trade Units	1			1	1
Trade Units			1		2	2
Trade Units		1			2	2
Trade Units	1				1	2
Trade Units		1		1		2
Trade Units			1	2		2
Trade Units	1	1				1
Trade Units	1			1		1
Trade Units	1		1			1
Trade Units	1		1		1
Trade Units		1	1	1
Available Units	6	6	7	7	8	8
Average    Cost	1.00	1.00	1.00	1.15	1.38	1.63

While the distribution of vegetables for trade is rather equal, we have the situation where there are actually more of the rarer vegetables for trade than the more common one, but for a price. On average, the cost for leeks is 1.63 of your vegetables for 1 leek. (However, as you can only trade full units, this means more often than not, if you need a leek, and you cannot buy one, you’ll be trading 2:1 for it.)

So, at a first glance, this says you probably want to focus on acquiring the customers who desire the more easily produced vegetables, as the chances of meeting their needs is much higher. However, this is only one part of the picture. The other part is the selling price — customers may be willing to pay more Cash for the vegetables that are harder to produce, Cash that you need to progress down the path of prosperity.

If we analyze the demands of the casual customers, by generating an optimization model on a series of linear equations on the six vegetables available (Wheat, Pumpkin, Turnip, Cabbage, Beans, Leeks) by adding a Gratuity variable, and minimize over the sum of the gratuity variables, we find that the following are the average prices paid for each vegetable by Casual Customers:

Vegetable	Wheat	Pumpkin	Turnip	Cabbage	Beans	Leeks
Average Price	2	2	3	3	4	5

In fact, only 4 customers pay more than these prices. The customers who want Bean, Cabbage, and Pumpkin; Cabbage, Turnip, and Pumpkin; 2 Cabbage and 1 Wheat; and Bean and 2 Cabbage are willing to pay 1 more Cash for these sets of vegetables than the other 10 casual customers.

If we now analyze the demands of the regular customers, by generating an optimization model on a series of linear equations on the six vegetables available (Wheat, Pumpkin, Turnip, Cabbage, Beans, Leeks) by adding a Gratuity variable, and minimize over the sum of the gratuity variables, we find that the following are the average prices paid for each vegetable by regular customers over 4 deliveries:

Vegetable	Wheat	Pumpkin	Turnip	Cabbage	Beans	Leeks
Average Price	2.5	2.5	3.0	3.5	4.0	4.5

In fact, only four customers don’t pay these prices. Two customers, who want Cabbage and Leeks and Pumpkin and Cabbage, respectively, pay more (an extra 2 Cash), and one customer, who wants Cabbage and Wheat and Wheat and Leeks, respectively, pay less (by 2 Cash).

In other words, when all is said and done, we find that the average price for each vegetable when casual and regular customers are analyzed is the following:

Vegetable	Wheat	Pumpkin	Turnip	Cabbage	Beans	Leeks
Average Price	2.36	2.36	3.00	3.37	4.00	4.64

Each vegetable, with the exception of wheat and pumpkins, while harder to plant and harvest, is worth more, and leeks are worth almost double what wheat and pumpkins are worth. This says that if the opportunity arises to grow leeks and service customers who want leeks, this is the best course of action, but, if the opportunity is not available, given that almost every field can grow turnip, turnip is preferable to wheat and pumpkin, and if your choice is between wheat and pumpkin, you might as well grow wheat as it’s cheaper to buy. Also, there isn’t that much of a premium for cabbage over turnip, but beans are definitely worth pursuing as well. However, if one needs to do a lot of trading to meet demand, it’s best to grow and trade wheat, and even pumpkin, for leeks, beans, and even cabbage.

The Regular Helpers available are:

• Book-keeper Restock the shop as you see fit. Also, for a chosen vegetable, receive 1 Cash for each field planted with the vegetable.
• Haggler Once only, buy 2 vegetables of the same kind from the shop for the price of 1.
• Harvest Helper Harvest 2 vegetables from each field (except home field) that contains 4 or more vegetables OR each field planted this round holds one additional vegetable.
• Maid you may exchange all vegetables 1:1 at market stalls in one round
• Market Crier Refill all market stalls with vegetables or sell one to three vegetables from the market stalls to the shop at shop prices.
• Merchant You may buy, for 1 Cash from the shop, 1 of any vegetable that must be delivered at least twice to regular customers this round.
• Messenger-Boy Deliver twice to any regular customer in this action phase.
• Official The buy a “Two-Pack” action is free.
• Plough-Man Return all vegetables from one (non-Home) field that contains at least two vegetables to the supply. Then, re-sow the field OR immediately harvest from all fields that contain exactly one vegetable.
• Saleswoman Make all customers satisfied OR all casual customers delivered to this round pay the +2 Cash bonus.
• Shopper Buy 1 vegetable from the Supply for 2 Cash less than it would in the shop.
• Squire During the Card Phase, take 1 Card from your hand and up to 3 from the Courtyard.
• Tenant Farmer Pay 3 Cash to choose the next field from your private fields OR place one empty field under your private supply and select one other field from it.

Some of these helpers can be very useful, but only at the appropriate time. For example, the plough-man can be very useful if you have a number of fields that contain exactly one vegetable – as this can allow for more deliveries, especially in round 9 (or very early when advancing up the path of prosperity multiple spaces is cheaper). However, some of these helpers are more helpful when used in pairs. For example, using the haggler and the merchant allows a player to buy two vegetables that need to be delivered for 1 Cash. The Tenant Farmer followed by the Haggler can allow a player to sow two fields with the same vegetable for the price of 1. Knowing the abilities and interaction abilities allows one to compare the value of a potential helper to a Stall to casual customer to a regular customer to an extra field.

In our next post, we’ll go solo again and see how we do when we put our newfound insights to use.