Often a difficult decision: Do you purchase the construct, which you may or may not be able to use multiple times, or do you purchase the more powerful hero, which you will be able to user every time?

How often you will be able to use a construct depends mainly on the other players in the game. In a four-player game, with identical players, you would expect your opponents to defeat the construct-destroying monsters three times as often as in a two-player game.

This article will concern itself with the two-player game.

Assuming a 20-round game, with each player purchasing one card per hand (and defeating the relevant monsters which appear).

There are two monsters in CotG which can destroy your opponent’s constructs:
Corrosive Widow (4 power, each opponent destroys one construct) [4 copies]
Sea Tyrant (5 power, each opponent destroys all constructs but one) [3 copies]

So of the 100 cards in the deck, 7 of them allow you to destroy some (or all) of your opponents constructs.

In a 20-round 2-player game, with 20 purchases per player (15 center row + 5 Mystic/Heavy Infantry), 30/72*28 = 11-12 monsters will appear, or about 3 construct-destroying monsters.

So you would acquire your construct, spend between 2 and 4 rounds waiting to play it, then every 7 rounds, you may be forced to destroy it. For the sake of argument, we’ll assume 3 rounds of waiting, followed by 4 rounds until it is destroyed, meaning a construct (if purchased before the last 7 rounds of the game) will be played once and used 3 times more.

Now, some comparisons:
The All-seeing Eye (6 runes/2 honour construct, draw one card per turn)
Ascetic of the Lidless Eye (5 runes/2 honour, draw two cards)

I’m comparing the All-seeing Eye to Ascetic of the Lidless Eye because they have the same effect of +1 card overall.

Interestingly, if you get to use a construct 4 times, the construct is about 4 times as powerful, for only one more rune in cost (although that is 5->6 runes, which is difficult to do, especially in early game). Our playtesting agrees with this assessment. We actually removed this construct from our games because it was far too unbalancing if purchased and played early (our games tend to be ‘friendlier’, with less deliberate defeating of monsters to destroy the other player’s constructs, and two-player, which would exacerbate these effects).

(Commenting on the rune:honour ratio of individual cards is for a later post.)

Comparison 2, +power constructs:
Militia (0 runes (assumed)/0 honour, add one power)
Shadow Star (3 runes/2 honour construct, add one power)
Yggdrasil Staff (4 runes/2 honour construct, add one power, can trade 4 runes for 3 honour)
Void Thirster (5 runes/3 honour construct, add one power, +1 honour for defeating a monster once/turn)

Demon Slayer (4 runes/2 honour, add three power)
Muramasa (7 runes/4 honour construct, add three power)

So, it looks like it’s plus 3 runes here to make the +1 power permanent (along with the requisite honour). (Similar to the difference on cost between Apprentice and Mystic and Landtalker.) In this case, 4×1 power is much less powerful (hah!) than 1×4 power, and these cards have never felt too overpowered to me. Perhaps Muramasa, but it’s rarely out until the endgame, and there are a lot of other quite powerful 7 rune cards.

Comparison 3, +rune construct:
Apprentice (0 runes (assumed)/0 honour, add one rune)
Snapdragon (5 runes/2 honour, add one rune, +1 honour for playing a lifebound hero once/turn)

The Snapdragon looks like it’s supposed to be the rune equivalent to the Void Thirster, but even during design of the first set, the designers noticed that runes are more powerful than power (hah again!); looking at the cost of Mystics and Heavy Infantry will show you this, amongst others.

I’ve found that Snapdragon, if you can keep it in play, is a less-subtle-than-you-think help, especially early game. I can understand why you wouldn’t have the 3- and 4- rune equivalents, as they would tend to crowd out other strategies (and be even that much easier to purchase in the first couple of turns).

A final note of comparison. Using the math from above (and previous analyses), we can assume that each rune and power produced by a construct or hero produces 1/2 of an honour point.

Looking at it again, under the following conditions:

No card banishing:
5,5 ->12 (2 completed turns ends with +2 cards, or 12 total)
5,5,2 ->14 (2 completed turns ends with +2 cards, or 14 total)
3,5,5,1 ->17 (3 completed turns, one carried over, ends with +3 cards, or 17 total)
4,5,5,3 ->20
2,5,5,5,3 ->24
2,5,5,5,5,2 ->29
3 (20 rounds)

Your construct would come out about 1.5 times, for 4 rounds each, and your hero would come out about 3 times, so your construct would be seen about twice as often.

Militia gives you 3 power, for 1.5 honour
Construct gives your 6 power, for 3 honour, at a cost of +3

Demon Slayer gives you 9 power, for 4.5 honour
Muramasa gives you 18 power, for 9 honour, at a cost of +3

Apprentice gives you 3 runes, for 1.5 honour
Snapdragon gives you 6 runes, for 3 honour, at a cost of +5

This feels slightly wrong, that the +1 power constructs don’t give you honour quite that often, so they’re probably pretty closely balanced with Snapdragon. Muramasa does actually feel 3 times as effective as the other constructs, so that’s fine. But all of this is based on so many assumptions, it should only be a guideline for whether you should purchase that construct at this stage in the game.

In our last segment in this series, we talked about the overall rune/power balance in Ascension: CotG: http://nayrb.org/~blog/2015/08/03/analysis-ascension-runes-vs-power/

In this segment, we’ll go into a bit more depth on the 1- and 2-rune cards in the set.

The cards are:

0 runes:
Apprentice* (add 1 rune, 0 honour) [factionless]
Militia* (add 1 power, 0 honour) [factionless]

1 rune:
Arha Initiate (draw one card, 1 honour) [Enlightened]
Lifeblood Initiate (add 1 rune and one honour, 1 honour) [Lifebound]
Mechana Initiate (add 1 rune OR 1 power, 1 honour) [Mechana]
Void Initiate (add 1 rune and may banish one card in hand or discard, 1 honour) [Void]

Starting with the 1-rune cards, reading http://boardgames.stackexchange.com/questions/7794/when-to-buy-cards-costing-1-rune-in-ascension, it says many things I’ve felt for a long time. The four cards here are not very balanced. I would even use stronger language, and say that the void initiate, if acquired early, can decide the game. I generally find that if I have two ‘banishing’ cards acquired early, I can winnow my deck down the just the essentials. This quickly becomes overpowering.

From a math perspective, one could assume the following (with no card drawing cards, assuming purchasing 1 card per hand):

No card banishing:
5,5 ->12 (2 completed turns ends with +2 cards, or 12 total)
5,5,2 ->14 (2 completed turns ends with +2 cards, or 14 total)
3,5,5,1 ->17 (3 completed turns, one carried over, ends with +3 cards, or 17 total)
4,5,5,3 ->20
2,5,5,5,3 ->24
2,5,5,5,5,2 ->29
3 (20 rounds)

With one card banisher in first two turns:
5,5 ->12 (2 completed turns ends with +2 cards, or 12 total)
5,5,2 -> 13 (2 completed turns ends with +2 cards, banish 1 card, for 13 total)
2,5,5,1 -> 15
4,5,5,1 -> 17
4,5,5,3 -> 19
1,5,5,5,4 -> 22
1,5,5 (20 rounds)

With two card banishers in first two turns:
5,5 ->12
5,5,2 ->12
2,5,5 ->13
5,5,3 ->13
2,5,5,1 ->14
4,5,5 ->16 (all Apprentices and Militia are banished now)
5,5,5,1 ->19
4,5 (20 rounds)

(Note that this may somewhat overstate the power of banishment cards, as we’re assuming perfect banishment, and being able to purchase two banishment cards in your first two turns. This has happened to me a number of times, though, so it’s not out of line as an assumption to make the math easier.)

So, with no banishment, you can get through your deck 6 times in 20 rounds. With one banishing card, you can get through it 6.5 times, which can be significant, as the later turns are much enriched in powerful cards, many of which can get you multiple honour points each. This strategy truly shines when you use two banishing cards, however. Note that your deck barely grows in size for the first half of the game. This allows you to go through your deck 7.5 times, being able to use your most powerful cards an extra time *each* more than even the one banishing card player.

With this in mind, barring further math, I’ll make the assumption that a banishing card is worth 1 extra rune for each turn you would have used the card it banished. (This assumes that you replace an apprentice with a mystic, which will probably overstate the banishment power in the early game, but understate it in the later game.)

This means that the Void Initiate gains you 1 + (5+4+3+2+1+0)runes/6** = 1 + 2.5 = 3.5 runes!
Assuming that you can always gain 1 honour (in cards) per two runes, this works out to 1 honour + 1.75 per play!
Working this in to the equations for the other 1-rune cards:

Void Initiate: 1 honour + 1.75 honour per play
Lifeblood Initiate: 1 honour + 1.5 honour per play***
Arha Initiate: 1 honour and -1 card
Mechana Initiate: 1 honour + 0.75 honour per play****

Now, on to the 2-rune cards.

2 runes:
Temple Librarian (discard one card and draw two cards, 1 honour) [Enlightened]
Seer of the Forked Path (draw one card and may banish a card in center row, one honour) [Enlightened]
Spike Vixen (draw one card and gain one power, 1 honour) [Void]

The two Enlightened cards here, in true ‘Blue’ fashion, are starting to show the control aspects of their faction. The Temple Librarian allows you to cycle your deck faster, and the Seer of the Forked path alternately allows you to swap out cards in the center row you don’t want for maybe one that you do, or even perhaps more useful, to get rid of a monster that your opponent will attack you with next turn!

I’ll cover these cards in more depth when I cover drawing cards in more general.

For now, remember that deck winnowing is powerful. My favourite corollary to this is from the board game ‘Age of Renaissance’: https://boardgamegeek.com/boardgame/26/age-renaissance, which forces you to keep unplayable cards in your hand as an ‘unplayable misery burden’, which I think aptly describes low value cards in many deckbuilding games.

*I’m including Apprentice and Militia here for comparison for a couple of reasons. The most obvious is the correspondence with ‘Copper’ in Dominion. The second is that colourless cards in Magic: The Gathering are typically (slightly) less powerful than other cards at the same converted mana cost. Apprentice and Militia are listed as ‘0 runes’ because ‘Copper’ also costs 0, and it makes sense intuitively, but they might have slightly different actual ‘costs’, depending on how the math works out in later posts, when we work out how useful cards are, and give them fractional worth/benefit values.

**Yeah, I know. It’s not exact, and it doesn’t take into account the two-Void Initiate case.

***The high apparent value of this card under these assumptions suggests to me that the benefits of banishment are even higher than +1 rune each time a card that has been banished would have been played. Might be partially because +1 rune earlier is more important, as are runes >4-5 per turn…

****Assuming the flexibility is worth 0.5 runes per turn. In actuality, I’ve found that this card is seldom used, never mind used for its flexibility.

So, as you’re playing Ascension, you have a number of choices to make. One of the more important ones is how you balance your purchase of cards which give you runes vs. cards which give you power. (Myself, I enjoy the slower build and feeling of game mastery by playing a 120-point* game, so I tend to err on the side of runes.)

On first blush, it would seem that power would be the better (and simpler) strategy. You can purchase heavy infantry for two runes which will give you two power every time you draw them, vs. having to spend three runes for a Mystic which will give you a (seemingly) similar two runes.

There are more complex issues to get into, such as how each card you purchase affects your average draw and the histogram of your draws, but for now, we’ll focus on the list of cards in the first set, ‘Ascension: Chronicle of the Godslayer’.

Some people have very kindly made a list of all of the cards in this set, including the manufacturer: http://ascensiongame.com/game/card-database/, and some people on boardgamegeek.com: https://videogamegeek.com/thread/673668/how-many-each-card

We’re going to start with some basic statistics about the cards in the deck:

There are a total of 100 cards, 18 in each of four ‘colours’, and 28 ‘monsters’.

Looking at the monsters first, there are:
– 10 monsters costing 3 power
– 8 monsters costing 4 power
– 6 monsters costing 5 power
– 3 monsters costing 6 power
– 1 monster costing 7 power

A simple test for the maximum effort you should put into cards which give you power is what is the maximum number of honour points you would expect to gain from that? You can always trade two power for one honour (cultist), but given that that is the default, you shouldn’t expect it to be the optimal move very often.

Assuming you go through the entire deck, and your opponent kills no monsters:
– 10 monsters costing 3 power give 1,1,1,1,1,1,1,2,2,2 honour, for a total of 13 honour
– 8 monsters costing 4 power give 3,3,3,3,4,4,4,4 honour, for a total of 28 honour
– 6 monsters costing 5 power give 3,3,3,5,5,5 honour, for a total of 24 honour
– 1 monster at 6, 1 monster at 7, for 3 and 4 honour, respectively, for a total of 7

So, that’s a total of 72 honour from center-row monsters, plus however many from cultists.

So that seems reasonable, 72 honour to compete with between you and your opponent. However, at the same time, you have to compete with the center row cards which cost runes:
– 12 cards costing 1 rune each
– 8 cards costing 2 runes each
– 13 cards costing 3 runes each
– 17 cards costing 4 runes each
– 11 cards costing 5 runes each
– 6 cards costing 6 runes each
– 4 cards costing 7 runes each
– 1 card costing 8 runes

And give you honour:
– 30 cards which give you 1 honour
– 20 cards which give you 2 honour
– 12 cards which give you 3 honour
– 4 cards which give you 4 honour
– 6 cards which give you 5,5,6,6,7,8 honour (all mechana constructs)

for a total of: 30+40+36+16+37 = 159 honour possible from purchasing center row cards.

So, including cultists (and a few other cards), you would expect to get twice as many honour points from rune-requiring cards as power-requiring cards.

This suggests to a first-order approximation, that you may be able to ignore power-requiring cards, but you very likely cannot ignore the rune-requiring cards.

Next time, we’ll discuss 1-rune and 2-rune cards!

*120 honour aquirable honour points at the start of the game. The standard game has 30 points per player, so for the two-player games I usually play, that would be 60 honour points. The game doesn’t end up twice as long, as the number of honour points you acquire per turn is closer to exponential than linear**.

**Don’t quote me on this, I have not mathed it out, yet.

Ascension is officially* my favourite modern** deck-building game (the genre started by Dominion).

The game was designed by a guy who had been a U.S. Magic: The Gathering champion, to try to capture more replayability by harnessing a quasi-drafting style of play.

http://ascensiongame.com/files/2015/05/Ascension-article.pdf

This article is not about that. It is about the play balance of cards, and how you may be able to use math to help predict what works and what doesn’t.

It was in an article about Magic: The Gathering that I first heard about this, about ‘boons’ http://mtgsalvation.gamepedia.com/Boons, where the original designers came up with the idea of trading one mana (and a card) for three of something. Unfortunately, the 3 of somethings ended up being quite unbalanced, with respect to each other, so they ended up restricting or stopping the print run of most of them.

They had some more success with their ‘1 mana per attack/defense’ rule for creatures, with an ostensible balance with Fireball/Disintegrate, where you had to spend one mana per damage dealt.

Anyways, back to Ascension. You may recall from Dominion, the Fibonacci series for costs of Copper/Silver/Gold/Platinum:

Copper: cost 0 for 1 purchasing power
Silver: cost 3 for 2 purchasing power
Gold: cost 6 for 3 purchasing power
Platinum: cost 9 for 5 purchasing power

This works because in a normal length game, as your deck gets larger, you get about as much total purchasing power from each copper as you would from Gold:

Start of game: EEECCCCCCC -> (3.5/hand)
Turn 1,2 buy silver: EEECCCCCCCSS -> (4.58/hand)
Turn 3,4 buy silver: EEECCCCCCCSSSS -> (5.36/hand)
Turn 5,6,7 buy silver,gold,gold: EEECCCCCCCSSSSSGG -> (6.76/hand)
Turn 8,9,10 buy gold,gold: EEECCCCCCCSSSSSGGGG (7.25/hand)
Turn 11,12,13 buy gold,province,province: EEEPPCCCCCCCSSSSSGGGGG (6.95/hand)
Turn 14,15,16,17 buy duchy,duchy,province,province, ending the game (assuming 2 or 3 players).

Each copper is used ~6 times, silvers are used 5+5+4+4+3 = 21/5 = 4.2 times, making them worth ~8.4 each. Gold is used 3+3+2+2+1/5 = 11/5 = 2.2 times, making them worth ~6.6 each.

So, this shows:
1) The coins are approximately balanced
2) Early game silvers help more than other coins, assuming the game is as short as possible.

So, really back to Ascension now. Apprentices are the clear analogue to Copper, Mystics the clear analogue to Silver. I’m guessing they considered having an analogue to Gold either overpowering or boring, hence the fact that Landtalker only appears once in the deck in the standard set. (The higher cost and rune production cards in Ascension are quite interesting in that they get non-linear after a cost of 6 (perhaps to accommodate the 7 and 8 ‘automatically get or defeat something’ cards).)

That’s it for now!

*And unofficially…
**Magic: The Gathering is currently considered ‘old-school’, and also is a ‘collectible trading card game’.

So, we played this game last night:

https://boardgamegeek.com/boardgame/137336/archer-danger-zone-board-game

The game is a good game for terrible people, although nowhere near as terrible as Cards Against Humanity, but as many of the reviews say, those who don’t know the show ‘Archer’ will likely not enjoy it anywhere near as much.

But this is not a review. This is a design and decision blog post.

During the game, your character chooses to attempt various challenges. To attempt a challenge, you roll 1,2, or 3 dice. You have four skills (Booze, Guns, Sex, and Smarts), one of which you will need to use for each challenge. Each of your skills allows you to roll a number of dice to overcome that type of challenge. The challenges (mostly) come in the four types above, and three difficulty levels.
Level 1 challenges earn you 1 victory point, and require you to roll 6 or higher.
Table:
Level: 1, 1VP, roll 6+
Level: 2, 2VP, roll 8+
Level: 3, 3VP, roll 10+
Level: 4, 4VP, roll 14+

(Level 4 challenges are considered ‘personal’, and you can use any skill to overcome them.)

So, this decision tree seems pretty simple. For a game of sufficient length, you can just play the odds and go by the best expectation value [XV]:

1d6:
Level 1 1/6 (16.7%) [XV 0.167]
Level 2,3,4 Impossible
2d6:
Level 1 26/36 (72.2%) [XV 0.722]
Level 2 15/36 (41.7%) [XV 0.834]
Level 3 6/36 (16.7%) [XV 0.500]
Level 4 Impossible
3d6:
Level 1 206/216 (95.4%) [XV 0.954]
Level 2 181/216 (83.8%) [XV 1.676]
Level 3 135/216 (62.5%) [XV 1.875]
Level 4 35/216 (16.2%) [XV 0.648]

So, with no special abilities/powers, the expectation values (for a game of sufficient length) suggest the following ranking:
3d6 for level 3
3d6 for level 2
3d6 for level 1
2d6 for level 2
2d6 for level 1
3d6 for level 4
2d6 for level 3
1d6 for level 1

Which kind of makes sense, where you have characters playing to their strengths, makes each character different and encourages role-playing. (My character, Krieger, spent almost all his time in his lab, trying to insult any character who got too close.)

All of this becomes more complicated when you factor in a few other game rules.
1) ‘Insults’. Whenever you roll a 5 or 6, you get to draw an ‘Insult’ card which either increases your score or decreases someone else’s score. The increase to your score is in average 1/2 point. The average decrease to others’ score is also about 1/2 point. (As you generally only decrease one other character’s score, this is less useful, unless there’s only one character in front of you, and it’s mean.) We’ll allocate 0.75 expectation value to this, assuming there are two characters in front of you, on average. So, 1d6 would add 0.75*2/6, 2d6 0.75*4/6, and 3d6 would add 0.75*6/6 XV, respectively

This gives you:

1d6:
Level 1 1/6 (16.7%) (+0.25 insults) [XV 0.417]
Level 2,3,4 Impossible
2d6:
Level 1 26/36 (72.2%) (+0.5 insults) [XV 1.222]
Level 2 15/36 (41.7%) (+0.5 insults) [XV 1.334]
Level 3 6/36 (16.7%) (+0.5 insults) [XV 1.000]
Level 4 Impossible
3d6:
Level 1 206/216 (95.4%) (+0.75 insults) [XV 1.704]
Level 2 181/216 (83.8%) (+0.75 insults) [XV 2.426]
Level 3 135/216 (62.5%) (+0.75 insults) [XV 2.625]
Level 4 35/216 (16.2%) (+0.75 insults) [XV 1.398]

This makes the 3d6 skills even stronger, giving the ranking:
3d6 for level 3
3d6 for level 2
3d6 for level 1
3d6 for level 4
2d6 for level 2
2d6 for level 1
2d6 for level 3
1d6 for level 1
(Not sure if you can roll for impossible missions, just enough to deliver insults)

2) The ‘Break Room’ allows you to roll 3d6 for any type of challenge, but if you don’t overcome the challenge, you lose one VP. This changes the decision to the following:

3d6:
Level 1 206/216 (+1 95.4%), (-1 4.6%) [XV 0.906] + 0.75 from insults = 1.656
Level 2 181/216 (+2 83.8%), (-1 16.2%) [XV 1.514] + 0.75 from insults = 2.264
Level 3 135/216 (+3 62.5%), (-1 37.5%) [XV 1.500] + 0.75 from insults = 2.250
Level 4 35/216 (+4 16.2%), (-1 83.8%) [XV -0.190] + 0.75 from insults = 0.56

Giving the ranking:
3d6 for level 2
3d6 for level 3
3d6 for level 1
3d6 for level 4

Making this strategy more risk averse, but probably higher scoring, if you’re getting a lot of challenges which are not suited to your skills, such as if you’re sitting right behind the other character who has the same strong skill as you. (Each character has 1 skill at 3d6, 2 skills at 2d6, one skill at 1d6.)

3) The ‘Applied Research Lab’ allows you to re-roll each of your dice once. This is quite powerful… The question is which dice you re-roll when? This should really be a table (a *large* table):

1d6:
1-5 1/6 chance (16.7%)
If you miss, re-roll on 1,2,3,4 (5 gives you an insult, which is worth more (0.75) than re-rolling (0.42).
[Overall XV 0.167->0.333]
[Including insults: 0.42->0.64]
2d6:
Level 1 challenges (6+)
If you miss, re-roll any dice with 1,2,3
[Overall XV 0.72->0.93]
[Including insults: 1.22->1.55]
Level 2 challenges (8+)
If you miss, re-roll any dice with 1,2,3
[Overall XV 0.83->1.45]
[Including insults: 1.33->2.16]
Level 3 challenges (10+)
If you miss, re-roll any dice with 1,2,3,4 (you can re-roll only 1,2,3 in some cases, but easier to remember to just re-roll 1,2,3,4)
[Overall XV 0.50->1.19]
[Including insults: 1.00->1.97]
(Level 4 challenges are impossible with 2d6)
3d6:
Level 1 challenges (6+)
If you miss, re-roll any dice with 1,2
[Overall XV 0.95->0.998]
[Including insults: 1.70->1.78]
Level 2 challenges (8+)
If you miss, re-roll any dice with 1,2,3
[Overall XV 1.68->1.96]
[Including insults: 2.43->2.82]
Level 3 challenges (10+)
If you miss, re-roll any dice with 1,2,3 (you also choose only to re-roll the 1 if you have 1,3,5 and need 10, interestingly…)
[Overall XV 1.88->2.71]
[Including insults: 2.62->3.67]
Level 4 challenges (14+)
If you miss, re-roll any dice with 1,2,3 (if you get 4,4,4 or 4,4,5, you should re-roll one 4)
[Overall XV 0.65->1.76]
[Including insults: 1.40->2.88]

Conclusions? Left as an exercise for the reader… 🙂 (Best summary in the comments gets a secret prize, which may include glory…)