Terraforming Mars: Production Valuations

Production Issues

Producing resources in Terraforming Mars occurs at the beginning of every generation after the first. Two complications arise when calculating Production in Terraforming Mars.

First, the longer a game of Terraforming Mars runs, the more of a resource will be generated through production. Since the average game was calculated, the best thing is to standardize on an 'average' game. So, 10 generations (turns) is the number to use in calculating production for comparison purposes. As more players enter the game, the number of turns will decrease, but 10 provides a common baseline for most 2-4 player games.

Second, total output will differ based on when the production begins. Started at the beginning of a game, Production will generate the greatest returns. If Production is started on the last turn, it provides no benefit (plant's excepted).

Minimum Production

For evaluative purposes, Awards and Milestones will be ignored. This makes the minimum Production for all resources 0mc, except plants. Plants may be spent to boost final scores at End Game (if they total 8). Thus, plants will have one extra generation of production if produced on the last turn of the game.

Maximum Production

For all resources, except plants and Electricity, the maximum production is 9 turns of production. Thus, generating 1mc per turn will yield 9mc in total. Remember, production on Turn 1 is impossible as no production will occur until the start of Turn 2.

Plants receive a maximum of 10 turns of production since they may be used the turn after the game ends in an end game condition style mechanism (described in Minimum Production above). During this last turn, a plant can only be spent for 1VP since there is no oxygen. Both of these have minor impact on plant calculations, but they are factored into the table below.

Electricity takes an extra turn before become usable heat.

Electricity Production has an additional built-in delay of 1 turn. This is because electrictity becomes Heat on the turn after it is generated. Thus, an Electricity production on Turn 1 will become Heat on Turn 3. This delay means electricity production has only 8 turns of useful maximum production.

Average Production

For most resources, average production occurs for roughly 4.5 turns (9/2). Plants will undergo 5 turns of production (10/2), while electricity will experience 4 turns of production before becoming heat.

Value of Production

The value of production is calculated for Maximum and Average production. Minimum production is always 0, so it isn't worth noting. Multiplying out the production, and assuming every resource is efficiently spent on generating VP (e.g. every amount generates a VP), the following values are calculated for each Resource Production:

	Actual		Normalized
Production	Max	Average	Max	Average	Return
Money	9	4.5	9	4.5	1
Electricity	11	5.5	13	6.5	1.181818
Heat	15.75	7.875	14.625	7.3125	0.928571
Iron	18	9	18	9	1
Plant	28.75	14.375	16.25	8.125	0.565217
Plant-oxy	28.75	15.8125	30.875	16.25	1.073913
Titanium	27	13.5	27	13.5	1

Actual and Normalized Resource production values

Summary

The Return of all Production values didn't change, except for Plants which generate oxygen. This dropped slightly from 1.13 to 1.07. This is due to the last turn of production being worth just slightly less. Still, it remains above 1, which indicates it is still a good option.

When looking at Totals output, Plant production is always the best purchase by a long shot, especially when Normalized to VP values. Titanium and Iron make a second and third "best" investment, but this is only if the Titanium and Iron can be converted directly into VP.

With Production values and resource values determined, it is now time to begin evaluating the "worth" of elements in the game.

Terraforming Mars: Valuing Resources

Resources

The goal of this post is to normalize the cost of all resources for comparison purposes.

Normalized & Actual Cost of Resources

Calculating the Actual value of a resource requires looking at that Resources Standard Project cost and dividing by its conversion rate (typically 8). Similarly, the Normalized cost is the VP cost (13) divided by the resources conversion rate.

Money (mc)

Money is the easiest to calculate, as it is the basis of all analysis, 1mc=1mc. This is both the Normalized and the Actual cost for money.

Steel & Titanium

Iron and Steel are worth 2mc and 3mc. This is because Iron and Steel may be traded 2 to 1 and Titanium 3 to 1 when play Buildings or Space tags, respectively. For this to work, we will assume every token of generated either resource is also spent.

 Normalized Heat & Energy

It takes 8 Heat to generate one Temp increase (1VP).Thus, Heat and Energy have the same "normalized" cost of 1.625mc.

Plants

8 Plants will generate 1 Greenery tile. This will provide either 1 or 2 VP depending on if Oxygen will increase or not. With Oxygen, the Normalized value of Plants becomes 3.25mc, and without Oxygen it is the same as Heat or Energy, 1.625mc.

Cards (Patents)

It costs 3mc to keep a card in a player's hand. Therefore, if a card is generated it "saves" the player spending 3mc to keep the card. A card's value will differ depending on the card, but all cards can be sold for 1mc. Thus, the card's least value can be calculated as 1mc. If, after calculating a card's effectiveness, it is less than the value of selling a card, it would be best to sell the card.

Summary

In this post the value of individual resources were determined. From this, the calculated values for each resource are as follows:

Resources	Actual Cost	Normalized	Effectiveness
Plant w/oxy	2.875	3.250	1.130
Plant-no oxy	2.875	1.625	0.565
Heat	1.750	1.625	0.929
Electricity	1.375	1.625	1.182
Card (traded)	3.000	1.000	0.333
Iron	2.000	2.000	1.000
Titanium	3.000	3.000	1.000
Money	1.000	1.000	1.000

The most surprising result of this analysis is the most effective move possible is to gain Energy, although no cards offer this. This is because of the reduced cost in comparison to Heat. Next post will concern with calculating Production values of various resources.

Terraforming Mars: What a Game Looks Like

Charting a Game

(Pre-Note: Information I have is limited to 3 & 4 Player games. I am looking for data on 5-Player games, and if your interested in helping me collect data, please contact me at: cfolmar@gmail.com. I'd like to create a library of Game Plays and share the results after a period of time. If enough interest, I'll create a sheet to download and record game plays with instructions).

Having determined the magical 13MC/VP, it's time to look at what a game actually 'looks' like. This is important to determine how long a game of Terraforming Mars lasts. It also shows an interesting trend.

Any individual play will differ based on a number of factors: corporation chosen, card draw, player experience, set chosen, etc. The focus of these individual factors is for later blog posts. For this analysis, however, we will look at the total VP given out to all players each turn. We will also only look at the Terraform Rating gained from working towards one of the main End Game conditions. So, for example, if during Turn 1 Player A increased Oxygen 1 Step and Player B increased the Temp 1 Step, then Turn 1 earned a 2 VP total (just to different players).

This may seem a strange and arbitrary way of looking like at a game, but the insights are amazing.

3-Player Game

We start with a four 3-player games (graph below). The important thing to see is how the games ended from Generation 10 to 12. More can be seen, but we will dissect it more later in the post.

3-Player Games

4-Player Game

 Next we look at 4 player games. Here the games end from Generation 9 to Generation 12. Still, despite the somewhat shorter games, for which there is a reason we will go into later, we can see the beginning of a definite patter. To make it more obvious we will take the average of the 3 and 4 player games and compare them.

Comparison: 3v4 Player Game

The games above may seem to have no pattern, but when we average the games together, and compare these averages, we see a definite pattern. I've included an average of the 3-player and 4-player games as a reference in the graph below.

 Here we can see the general outline of a game take shape. The game starts with an initial rush of Terraform Rating increases, immediately followed by a slight dip in turn 2. We can begin our analysis here on a relatively turn by turn basis.

Turn 1 - Initial Grabs: Turn 1 sees a player's jockeying to get some early initial TR. This can provide a boost to income in later turns, and (as we'll see), an boost early is significant. I suspect much of these initial boosts are also related to the Heat bonuses on the Temperature chart at the 3 position.

Turn 2, 3, 4-Economy Setup: These turns see players grab a few additional TR, but money is in
shorter supply as they are now dependent on 'self generated' income and not on the initial income. This is also where most players begin focusing on building their economy. This may be either to supplement their gains from Turn 1 (focusing on Heat production), or building resource  mining operations.

Turn 5, 6, 7 (& 8)-Milestone Grabs: Here we see real activity occurring. In particular there are three points of interest.

First, the economies built from turns 1-4 have come to fruition. Players actively begin grabbing TR at a rapid rate. These are not haphazard, however, and lead to the second indicators.





The Second point is the "Turn 5/6 Plateau" in 4-player games or, in 3-player games, the "Turn 5/7 dips". I suspect this is caused as players begin to snatch up the Milestones. In both types of games this would be a reduction in total income of 24MC. However, in the 3-player games the removal of the MC effect is more pronounced.

Lastly, there is the Peak. In 4 player games this peak is more pronounced and definitely occurs around Turn 8. In the 3-player games, given the smaller total economy of all the players, the curve occurs around turn 8 and 9, but is still present. This is also when players hit those Upper Level Environment Bonuses (Free Temp & Ocean). Even if not grabbed, another player may rush to get the last Ocean in place to prevent an opponent from getting the full benefit, which has the same net effect on our graph.

Turn 8, 9, 10, 12 - Decline and Game End
Typically by Turn 8 the TR purchases are in decline. Instead, players have changed to focus on grabbing the Awards, which are a big drain on the overall economy (-22 MC to purchase first two awards, -42 to purchase all 3 awards). In the end, there are only a few TR left to grab so player's position to maximize their score by purchasing Settlements next to Greenery, blocking opponent's, or pursuing VP maximizing cards.

Conclusions

Looking at the games, most 3 and 4 player games follow a definite pattern (although anomalies exist: keep reading if interested below). Although there is enough variation in the game to keep it interesting and challenging. Understanding the flow of a game will assist in recognizing what to expect in the game.

Lastly, it is important to recognize that most games end around the 10 Turn mark. Some finish earlier, some later, but a good game length is 10 Turns. This will become the standard used in calculating values in later blog posts.

Interesting Anomaly

 Look at the graph of a 3-player game below which is somewhat anomalous:

First, There is a huge initial TR grab on Turn 1. Second, the game was over by Turn 10, with almost no plateau, although one huge dip in Turn 7. Except for the Initial Turn 1 Grab, it looks like a fairly standard, if short, game.

The reason for this game is because of 2 of the corporations chosen by players and both choosing a similar strategy. The Corporations were Credicor and Teractor. Both of these have high initial MC (57 & 60 respectively). Both players decided to take no cards and, instead, just purchase Temp increases. These two players accounted for 8 of the 9 TR in the first turn (4 each). The 9th was purchased by the 3rd player. The two of them continued to purchase TR throughout the game until Turn 5. Around Turn 4 they switched to Oceans, and used ocean placement plants to power Greenery tiles.

Both players seemed in competition (the third player was never really in the running) until Turn 6. At that point Teractor switched strategies. While Credicor would continue purchasing Oceans and Heat, Teractor purchased Greenery outright and grabbed the Gardner milestone. On Turn 7 both players switched to Cities to try and gain the Mayor Milestone, which explains the sudden drop of TR. Teractor, due to Turn order, managed to beat Credicor to that milestone again, although Credicor did burst forth on Temp claimed Terraformer, it was too late.

At first glance, this game appears to defy the "average" game described earlier in the article. However, on closer examination we can see the same overall pattern. Except for the dip on Turn 6 and 7, this more closely resembles a 4 player game than a 3-player game. This is due to the players opting for the same strategy with two corporations with unusually high initial incomes.

Terraforming Mars: Cost of a VP

What to Buy

Last post looked at how VP are scored and their cost. Summarizing the results below:

Item	Number	Points each	Ind. Cost(MC)	Total Cost(MC)
Ocean	9	1	9	162
Temperature	19	1	14	266
Oxygen	14	2	23 (with greenery)	322
Totals	42	56		750

Next step is to determine the money value of a VP. The goal here is to achieve two things:

• "Normalize" the cost of all the cards to give an accurate determination of the card's values, which let's us determine...
• Which action is relatively "best" to take in terms of earning VP.

To start the evaluation, a baseline needs to be created. For this, imagine a game played with two simple rules:

1. Only permit Standard Projects,
2. Only spend mc to end the game. (greenery, Temperature and Water).

How much would each VP cost? This provides a good starting point to determine the value of each card, resource, and even the location of map board spaces.

Weighted Average

To figure this out, use a technique called weighted average (or Weighted Arithmetic Mean).

One wrinkle in Terraforming Mars is Greenery tiles. Greenery tiles provide 2 VP instead of 1 VP. Thus, a greenery tile will yield slightly better on average VP than, say, Temperature. Overall, its not difficult to figure out (the values are already in the graph above). To do so, divide the Total Cost (750) by the Total VP (56).

This yields: 13.39 MC/VP!

 But, what about...

The number above assumes purchasing every VP earned throughout the game. Terraforming Mars has a little "bonus" system which changes things up a bit. If Temperature is increased first, an Ocean tile gets placed for "free". Similarly, increasing Oxygen first yields a "free" Temperature. These bonuses change the amount of money spent. In fact, there are four scenarios to figure out:

1. Least Efficient Terraforming: Pay for everything.  
2. Semi-Efficient Terraforming 1: Pay for All Heat, 8 of 9 Oceans, and All Oxygen
3. Semi-Efficient Terraforming 2: Pay for All Oxygen, All Oceans, and 18 of 19 Heat
4. Most Efficient Terraforming: Pay for all Oxygen, 18 of 19 Heat, and 8 of 9 Oceans

Doing an analysis on each scenario creates the following table:

Least Efficient:	13.39
Least Semi-Efficient:	13.07
Most Semi-Efficient:	12.91
Most Efficient:	12.28
Average:	12.915

Normalized vs Actual Cost

To simplify analysis, a value of 13mc will be used as the baseline cost for a single VP. This is the "Normalized Cost", where everything is measured from this "normalized" value of 13mc/VP.

"Actual Cost" is how much something would cost to normally generate. For example, while 1 Temperature has a "Normalized Cost" of 13mc, the "Actual Cost" for Temp is 14mc as indicated on the Standard Project's Chart.

Effectiveness

From these two costs it is possible evaluate a "Return" rating, which is simply the Normalized Cost divided by the Actual Cost. In a manner of speaking this is the "return on investment" for performing a specific action. Looking at the Standard Projects which generate Victory Points, we have the following chart:

	Actual Cost	Normalized	Return
Greenery (w/ oxygen)	23	26	1.13
Greenery (no oxygen)	23	13	0.57
Temperature	14	13	0.93
Water	18	13	0.72

1 Greenery may be played to generate Oxygen, or after Oxygen is maxed, thus the two entries.

The greater an Action's Return, and with no other external considerations, the more valuable the Action. Thus, from the chart, and with no other factors affecting it, Greenery when the Oxygen is not capped provides the greatest Return than all the other options. If one had 28mc to spend and could only spend it on Standard Projects, it would be smarter to purchase a Greenery tile than all other options listed.

Summary

We learned the following from the above:

1. Cost of a VP = 13mc
2. "Actual Cost" is the stated cost to perform an Action
3. "Normalized Cost" is the cost evaluated against the accepted cost of a VP.
4. "Return" is a measure of relative value of an Action, with the better actions having higher Return, if no other considerations exist.

Terraforming Mars: Reaching the End Game Condition

Making Mars Habitable

The first step to understanding Terraforming Mars is understanding the Terraform Rating (TR). There are three basic ways to increasing the TR of a player:

• Increasing Oxygen from 0% to 14% (each Step is 1%)
• Increasing the Temperature 2 degrees from -30°C to +8°C (each Step is 2°C)
• Placing an Ocean tile onto an Ocean space (each Ocean is a Step)

Each increase of a Step increase of one of the above increases the player's Terraforming Rating 1 step. Terraforming provides two things for a player. First, it is the player's base "score". Second, at the start of a Generation (a round of Terraforming Mars) it provides the player with some base income. Unlike most games, a player's Terraform Rating begins at 20.

Breaking Down the Steps

Ocean Steps

There are 9 Ocean tiles which need to be placed on the board. Placing an Ocean tile on the board typically grants some other benefit based on where the Ocean is placed. The Standard Project to add an Ocean costs 18MC.

Temperature Steps

Temperature increases along the track on the right hand size of the board. There are 19 Steps of Temperature, but three particular Steps provide additional bonus. At -24°C (Step 3) and at -20°C (Step 5), the player's Heat Production increases. At the 0°C mark (step 15) the player also gets to place a free Ocean tile, if there is an Ocean available.

There are two means of increasing Temperature, Heat and Standard Projects. The Standard Project cost for Temperature is 14MC.

The second way is to spend Heat. As the game progresses from Generation to Generation players gain Heat equal to their Heat production. Once a player has collected 8 Heat, they may trade that Heat into 1 Temperature increase.

Oxygen Steps

Oxygen is tracked along the top on the Oxygen track. There are 14 steps of Oxygen, but Step 8 grants a benefit of bumping up Temperature 1 Step as well, if available. Oxygen is typically increased by placing Greenery tiles. Every Greenery tile adds 1 Step when it is placed on the board. Greenery tiles are added either through the Standard Project (cost 23MC) or by trading in 8 'Plants'.

Plant production works similar to Heat. You gain Plants based on a player's Plant Production each generation. When a player has collected 8 plants, they may be traded in for a Greenery tile.

Greenery Tiles

Despite their expense, Greenery tiles offer an additional benefit. Every Greenery tile on the board gives the player who placed it an additional VP at the End of Game Scoring. Thus, although they cost 23 MC, they provide the player with 2 VP: one for the Oxygen increase and one for End Game Scoring.

Bringing It Together

Terraforming Mars ends once all the above Steps are met. Thus, in a game, there is a minimum number of VP available to the players:

Item	Number	Points each	Ind. Cost(MC)	Total Cost(MC)
Ocean	9	1	9	162
Temperature	19	1	14	266
Oxygen	14	2	23 (with greenery)	322
Totals	42	56		750

Yes, there are 42 Steps to Terraform Mars (which answers some questions). Using just Standard Projects, this gives us 750MC to put them into play, and will yield a total of 56 VP to be divided among the players.

This is the starting point for analysis of the game's economy, which we will perform in our next post.