Monthly Archives: July 2015

Analysis: Ascension (and Dominion) Basics

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.

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’, 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’.

Less Conventional 4-Quadrant Diagrams: The Horsemen of the Elements

So, 4-Quadrant diagrams are very common in the ‘make-something-two-dimensional-from-something-one-dimensional-and-name-it-after-yourself-and-sell-a-million-business-books’ field.

This series will cover some less commonly used 4-Quadrant diagrams.

First, the Elements:

  Gas   Condensed
|       |       |
| Fire  | Earth |  'Dry'
|       |       |
|       |       |
| Air   | Water |  'Wet'
|       |       |

Now for the Four Horsemen:

Activity Level:
 Human    Biological
|        |            |
| War    |Pestilence/ | Abundance
|        |Plague      |
|        |            |
| Death  | Famine     |  Lack
|        |            |

And as a special treat for those watching my Gold Box series:

 Includes     Does not
  'Pool'      include 
  in the     'Pool' in
  Title:     the Title:
| Pool     | Curse of   |
| of       | the Azure  | No Teleporters
| Radiance | Bonds      |
| Pools    | Secret of  |
| of       | the Silver | Teleporters! 
| Darkness | Blades     |

BOF V: “A Wolf in the Forest”

(This was my first experiment in creating a communal story, from Jan 5 to Jan 22/2013.)

(It’s interesting to look back on it, thinking “I thought of that?”.)

“You walk up to a wolf in the forest. It sits up on its haunches and looks at you. What do you do?”

I: “Good dog.”
Me: “The wolf looks at you askance, somehow implying with a glance that comparing it to a dog is somewhat similar to comparing a rocking horse to a racing stallion. What do you do?”
S: “Misunderstanding the somehow-implied metaphor, I draw a small saddle from my pack and hold it out to the wolf, awaiting further instruction.”
A: “I take Fat Neil’s cloak and sword and run into the forest.”
JW: “Can I make a diplomacy check?”
Me: “A: You reach the wolf, who now has two other people standing around it. You are carrying a wooden sword and a towel. What do you do?”
JS: “Run to grandma’s house.”
A: “I wrap the towel around myself and commence eating fish.”
Me: “JW: The wolf seems pleased to see you. It points its nose West, deeper into the forest. What do you do?”
Me: S: The wolf motions for you to turn around. What do you do?
Me: JS: You are now wearing a red cap. You approach a small forest cottage. What do you do?
JW: I pack up my equipment, leave a ration of venison on the ground in thanks to the wolf, and walk of to the west cautiously.
S: Saddle still in hand, I turn around, grumbling slightly about how good Alex’s lunch smells.
Me: A: You finish chewing your wooden sword in two. You now have two sticks, suitable for framing a two-dimensional picture, or perhaps propping up a small tent. What do you do?
Me: S: The wolf reaches around, deftly takes the saddle from your hands, and places it on your back. It then ties the buckle. It seems to want to get on. What do you do?
Me: JW: The wolf breaks the venison in two, eats half, and puts the other half in its pouch. It takes a piece of paper from its pouch, limps over to you, and hands it to as you walk away. As you are walking, you see paths off to the right and left. What do you do?
S: I glance around and declare, “Nay,” scuffing the ground with my boot to emphasize my lack of interest in this plan.
Me: S: The wolf limps over and looks at you sideways, in a pleading fashion. You also smell the delicious taste of venison. What do you do?
JW: I stop and look at both sides of the piece of paper.
PSL: I call out the game master for taking taste as subject to the olfactory sense.
Me: JW: One side has what appear to be coffee stains in the shape of a dolphin. The other side has what appears to be a map of the forest, with paths marked in two different colours. From your memory, you discern that you walked along one of the light green paths to reach the wolf. The path to your right leads to what looks like a cloud of warm colours, the path to the left leads to what appears to be jagged steel slashes. There are numerous dark green lines crisscrossing the paths. What do you do?
Me: PSL: Your character walks up to the nearest tree and smells the bark with his tongue. What do you do?
S: I crouch with a sigh and point at the saddle.
JW: I try to remember why I came to this forest in the first place.
Me: S: The wolf climbs on, straps itself in, and somehow conveys that it wants to go East. What do you do?
Me: J: You’re not sure. Sometimes you go into the forest to try to find the fabled contemplation glade, sometimes you go to hunt for food, sometimes to visit your friend the druid, sometimes just to explore. What do you do?
S: Again misunderstanding the wolf’s attempt at communication, I run in a circle and jump over a downed tree, then wait for my venison reward.
Me: S: The wolf softly nips at your left ear while at the same time tapping its left leg on your left side. What do you do?
S: I shriek, complain a little about unjust desserts, and start running in the direction the wolf indicated.
JW: I follow the path to the right, thanking the druid again.
Me: S: You find that as you start to run, your stride begins to lengthen, and your rum starts to feel more like a gallop. You move through the undergrowth, which seems to part for you, and come upon a large tree. The wolf motions for you to stop. What do you do?
Me: JW: You walk through the forest for a while, until you come to a small cottage. There is smoke coming out of the chimney, and delicious smells wafting from the open door. What do you do?
Jamie Wells I try to figure out what it I am smelling.
Me: JW: It smells like delicious baked cookies, along with a hint of mint. You catch a glimpse of red through the window. What do you do?
PSL: I gallop after S, because that seems to be where a narrative is beginning to develop.
JW: With baked cookies with a hint of mint being one of my favorite things, I can’t help but get drawn to the open foor, peak my head in, and say “Hello? May I please have some cookies?” (in whatever the common language happens to be in this forest).
Me: PSL: You crash through the underbrush and end up in a meadow. You see a woman with a wolf on her back looking at a large tree. What do you do?
Me: JW: Peering around the doorjamb, you see an older woman taking a baking pan out of the oven, and a younger woman wearing a red cap sitting at the table chopping mint. The older woman says “Of course!” The younger woman in the red cap says: “Would you like some fresh mint sprinkled on top? It’ll probably be the last for a while, so make sure you savour it!” What do you do?
PSL: I instagram.
Me: PSL: You focus your will, and a small weight appears out of thin air into your hand. What do you do?
S: I pull over, feeling strangely exposed, as if a bit of my soul has been stolen. I peer up at the tree, then back at the wolf.
PSL: I toss the weight at the thick of the tree overhead (or rather the next one over, I’m not *that* hopeless) and wait expectantly.
Me: S: Up the tree, you see a small human dwelling, wedged between the branches. The wolf motions to you and then up the tree with its snout. What do you do?
JS: Part of my brain questions the sanity of taking food from a stranger, however it is overridden by the “COOKIES!!!” portion of by brain. I gobble up three of them (with mint sprinkled on them).
Me: PSL: The weight transforms into a small rabbit and a watch in the air. They gently graze the next tree over and fall lightly to the ground. What do you do?
PSL: I tie the chain on the pocket watch to the rabbit and hold the watch as the leash handle. Then I enter the forest.
Me: JW: This is the MOST DELICIOUS MINT that you have ever tasted. The younger woman in the red says “I know, I’m never able to savour them, either.” “It’s too bad that with the forest going dark, we can’t get any more of that mint.” “Say, you wouldn’t be willing to do something for us, would you?” What do you do?
Me: PSL: You walk into the forest, with the rabbit happily hopping behind you. You feel a faint ticking in your hand each time the rabbit hops. You come to a clearing. There is a circle of mushrooms in the center, and numerous holes in the ground around the perimeter. What do you do?
PSL: I hurriedly pack my belongings and wonder why my office atop Robarts Library closes at five when Christmas seems weeks ago. Then I shrug and eat the first mushroom.
JW: I say “How may I help you?”.
Me: PSL: You successfully escape Robarts Library just before it wakes from its slumber. Huge stony concrete wings unfurl from behind, and two red circles of light appear near the top of the central tower. They seem to be intensifying. The mushroom tastes odd, as if it had been sprinkled with something. You feel the ground getting closer. You have a great desire to eat another one of the mushrooms. What do you do?
Me: JW: The older woman intones: “In the days before humans came to these woods, there was a great darkness that covered the land. It was fought off only through the great valour and sacrifice of a group of noble animals. A wolf, a bear, a rabbit, and a hawk. Their story fills many volumes, and we do not have time for it now. It has been said that the darkness can not encroach as long as they stand vigilant, but they are injured and scattered. We have not heard from any save the wolf in weeks. If you can clear a small path to the mint, and retrieve some, along with the fireweed that grows there, we can perform a divination to figure out the next task.” What do you do?
PSL: I eat another mushroom.
KMV: Suggest it might look good as a grandmother.
CH: Thinks you all have made too many assumptions. *YOU* are obviously a bitch, and a HOT one at that. You and the wolf make passionate love under the full moon, howling in paroxysmal, delight, tearing into one another as clumps of fur lay strewn across the freshly fallen snow. . . [excerpt from Fifty shades of the Grey Wolf]
RG: I cast Animal friendship or Charm animal depending on the edition we playing.
MC: don’t walk up to a wolf in the forest unless you are a wolf. If you are a wolf then smell the wolf’s butt.
Me: PSL: You see the ground come up at you *really* quickly. You feel the rabbit pulling you away from the mushroom ring towards one of the holes around the clearing. What do you do?
Me: KMV: You see the wolf make the ASL for ‘red’, somehow. It points with its snout down one of the forest paths. What do you do?
Me: CH: You wake up from a very strange dream and find yourself on a strangely computer science-based Jeopardy show. You hear the words: “50 shaders of grey for 100, Alex.” What do you do?
JW: I say “Just show me where to go, and I shall complete this task”.
Me: RG: You cast ‘charm animal’ on the wolf. The wolf seems to shimmer as if something passed through it. Its tongue lolls out as if it is sharing a joke with you. What do you do?
Me: MC: The wolf speaks to you in Wolf: “Praytell, would you join me in a quest to push back the darkness? We must first find my companions, to assist us in the many tasks ahead.” What do you do?
Me: CE: The wolf looks at you as if it was sitting at home, drinking an import. What do you do?
Me: JW: The woman asks you to open your map, and points out one of the dark green lines which ends in a circle of green wavy lines with flames in the center. “You must follow this path to the mint grove. We do not know how far the darkness has spread. You must focus sunlight to clear a path. Take these two sugar crystals. They should focus the light enough to clear a path.” What do you do?
JW: I take the sugar crystals and take the path the woman indicated on the map down to the mint grove. On the way out, I snag a couple of more cookies and leave 5 silver coins in payment.
PSL I stick my arm up the first hole up to the shoulder.
Me: JW: On your way out, the woman runs after you and hands you back your silver coins. “You’ll want these to help reflect and focus the sunlight!” “Enjoy the cookies! If you need a brief insight later, try eating them!” You wonder why she always speaks with exclamation marks, but you continue on. Going down the path, you reach the point where the path goes from light green to dark green. The Dark green path seems to be a small path through the underbrush. You crawl along the path. After going a short ways into the underbrush, you sense more than see a dark cloud up ahead. What do you do?
Me: PSL: As you reach down to the hole, you realize that the hole has gotten bigger, and is about the same size as you. At approximately the same time, you realize that the rabbit has gotten much larger and is pulling you into the hole. You fall over, and are rolling down the hole after the rabbit. What do you do?
JW: I set up the sugar crystals in a resonating cavity, reflect sunlight into the cavity using a silver coin, and aim the output beam into the cloud (ie. I shoot the beam of light into the darkness).
WYC: You deal them a hand of cards, and play go fish with them.
Me: JW: The sun shines into the cavity, and is somehow focused and *changed*. The beam slashes into the dark cloud, exploding it into shards in a straight line in front of you. You can now see a brightly lit path to a meadow. What do you do?
Me: WYC: The wolf motions you over to a magical pond with fish frolicking inside. There are slots on the side of the lake for cards. Looking at your cards, you see that they now each have a number of fish on them. The wolf asks if you have any kipper. Looking at your cards, you do not. What do you do?
GW: I sit down and look back at it
PSL: I reach out for a protruding root and manage to bring my descent to a halt.
YG: I cast Magic Missile into the darkness.
EG: Smile and say hello.
JW: Into the meadow I go!
LMH: Sounds like time for a makeout session…
PSL:Also, I throw up my mushrooms.
Me: GW: The wolf looks back at you. You see it motion towards the ground. You see something glinting there. What do you do?
Me: PSL: You successfully slow your descent, but the rabbit is too large and pulling you too fast for you to fully stop until you reach the end of the hole. It opens into a large underground room. There are four exits: the way you came in, which looks like a daunting climb, a passageway to the left, which seems to have a flickering light, a passageway straightforward, which the rabbit seems to be pulling you towards, and a passageway to the right, which smells faintly swampy. What do you do?
PSL: Go right.
Me: YG: You make a small temporary hole in the dark cloud, and a few shards break off and fall to the ground. You feel like you might need something larger. There are dark shards on the ground. What do you do?
DL: I call the midwife who tells me to chill out. I look at facebook. I double check the snack bag. I look at facebook again.
GW: I walk over and examine what is glinting on the ground.
Me: EG: The wolf swishes its tail as if to say hello. It points its nose towards a tree. You see something sparkling in a hole in the tree about 10 feet up. What do you do?
Me: JW: You enter the meadow. Bursting out of the brush, you see that the brightly lit path extends into the meadow. You see a large cluster of herbs growing in the center of the clearing. The green cluster seems to be moving. You feel more than see the dark cloud around you starting to fluctuate. What do you do?
Me: LMH: The wolf licks your face repeatedly. It seems to like you. What do you do?
Me: PSL: You throw the extra mushrooms you were carrying up in the air and catch them. Nothing seems to happen. You start down the right passageway. The rabbit seems to be pulling you back the way you came, and eventually pulls away from you and waits at the end of the tunnel, back at the four-way room. The tunnel starts to glow green as you continue. A miasma starts to fill the air. You reach an underground grotto with glowing green moss covering the walls, and a small pond. What do you do?
Me: DL: The Wolf pads over and sits down, trying to distract you to help you relax. It pulls a vole out of your snack bag and chews contentedly in companionable silence. What do you do?
Me: GW: It seems to be a ring. Picking it up, it has a picture of a wolf on it. What do you do?
PSL: Eat moss.
LMH: Begin excreting toxins through my sebaceous glands…
GW: I look the ring over and try it on. Unfortunately it is too big to fit on any of my fingers, so I offer it to the wolf.
EG: I attempt to climb the tree but the first branch is too high for me to reach. After a few painful jumps, I collapse against the tree and fall asleep.
JW: I pick some of the mint, then eat one of the cookies to get some insight on where I might find the fireweed.
BSG: I wander into the mint meadow and am surprised to find someone already there picking mint.

Analysis: Archer: The Danger Zone!

So, we played this game last night:

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.
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]:

Level 1 1/6 (16.7%) [XV 0.167]
Level 2,3,4 Impossible
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
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:

Level 1 1/6 (16.7%) (+0.25 insults) [XV 0.417]
Level 2,3,4 Impossible
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
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:

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):

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]
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)
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…)