What Are the Odds to “Draw 2?” Part 2

Part 2.  The Extension

The next questions was, how do these results vary from one game to the next?

With questions like these, it’s often useful to explore the extremes first.

Extreme #1.

Imagine a deck which only contains one special.  In this case, playing a special means that none remain and you have 0% probability of holding another.  Not very useful but worth noting.  We’ll bring this up again later.

Extreme #2.

Imagine a deck of seven cards which contains two specials in which you are dealt five cards.  If you play a special, you draw the rest of the deck and thereby guarantee that you’re holding the other one.  You have 100% probability of holding another.  This is actually more useful to note than Extreme #1.  Strategy in deckbuilding games like Dominion frequently revolves around building an engine that maximizes your chances of drawing all of your deck every turn.

So we have one extreme case in which the odds drop to 0%, and another extreme case in which the odds jump to 100%. What’s going on in the middle.  That’s what I set out to discover next.

The Restrictions.

To avoid ridiculous cases like Extreme #1 or Extreme #1, let’s set out a few assumptions.

First, we have a deck of size N and your starting hand size is n.  This deck contains a quantity k of special “draw 2 cards” cards.  To avoid the ridiculous extremes, let’s agree that the deck contains at least two specials and that the deck is large enough that after playing the special and drawing the extra two cards, there will be at least one card remaining.

Put mathematically, we have that

Probability Part 3 Equations 1

How much do the odds change when your opponent plays a special card and thereby draw two cards?  The quantity of specials which could be in her hand decreases by one.  The quantity of cards you have not seen decreases by one.  The quantity of cards in her hand increases by one.

The Formula.

The change in probability is given by these formulas:

Probability Part 2 Equations 2

Example:

The deck has 60 cards.  10 of these cards are “specials.”  Players are dealt 6 cards to begin.  When a player uses one of these specials, the odds drop by approximately 6%.

Probability Part 2 Equations 3

Example:

You are playing Dominion. Your deck has 25 cards.  10 of these cards have “Draw+2.”  Each round starts with 5 cards inn hand.  When you play one of these cards, the odds you are holding another drop by approximately 3%.

Probability Part 2 Equations 4

What do you think of “draw 2 cards” cards?  Have you incorporated them into your designs?  What did you learned from the experience? Do they improve a design or weaken it?  Share with your fellow readers in the comments below.  And if you’re enjoying what you’re reading, create an account with WordPress and follow this blog.  If you keep reading, I’ll keep writing.

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Triggered Effects, Part 5

The Story So Far…

Triggered card effects all fit under a general “when TRIGGER occurs, do EVENT” template. They can make a card situationally powerful.  They can give cardsets a mechanical theme.  They can create opportunities for counterplay.

We have taken a look at several categories of trigger and effect, including several from our insightful readers.  We have also taken a look at four different combinations and suggested a game which might might best serve each.

For reference, here is our working list of triggers and events.  Let’s try four more combinations.

Triggered Effects in Columns

 

 

 

 

Combination 05: B + E

Trigger (B): Receives Damage

Event (E): Cardplay

Here’s another combination that feels right for Duel.  Since battles can last over several plays, it would be interesting to create a card that grants cardplay each time it is damaged.  One of the deck concepts being developed for this game is “Gamers” and the idea of playing cards each time one of your cards is damaged certainly seems like a gamer-y kind of effect to me.

TCG PlayerTCG Player is my attempt at such a combination.  Strength is fairly high in Duel–to date, there are only two cards in nine decks with Strength greater than 10–so this should ensure that its ability kicks off at about twice on the average.  Since this card’s ability is reactive, there’s also good incentive to play it face down to entrap your opponent rather than simply playing it for its Strength.

Taking a second look at the card, there’s a rising concern that this card is overpowered.  Playtest will confirm or refute this concern of course.  Should the card indeed be too powerful, there are multiple ways to address the issue.  The TCG Player could be weakened or it could be left strong while the other elements of the deck are weakened to counterbalance its power.

 

Combination 06: A + H

Brushfire WarTrigger (A): Critical Mass

Event (H): Game State

This combination evokes thoughts of a card-driven political tension game and Twilight Struggle by Ananda Gupta/Jason Matthews is one of the classics.

I confess that it’s been a few years since I’ve had the opportunity to enjoy this game but I believe a card of this type might look something like this Brushfire War.

 

 

Combination 07: I + G

Trigger (I): Forced Discard

Event (G): Component Condition

Right on ScheduleThis combination makes me think of a two player card-driven game about breaking out of prison. Perhaps it’s because we recently saw Guardians of the Galaxy and its delightful prison break sequence?  In any case, one player will play the guards while the other plays the inmates.

In an environment like this one, the Guard player’s deck would likely include a number of cards which counter Prisoner player’s cards or force the Prisoner to discard cards.  A classic trope of the prison break movie is the moment at which the prisoners subvert the Guards standard operating procedure, turning their plans against them.  In this spirit, we give the Prisoner deck this Right On Schedule card.

 

Combination 08: D + F

Trigger (D): Revelation

Event (F): Component Quantity

The idea for a theme is somewhat thin on this one but how about a worker placement/blind auction/deckbuilding hybrid in which the workers are cards?    In the majority of worker placement games, all workers are identical (Leonardo da Vinci and my own Zong Shi are exceptions) but if workers were cards, they could vary quite a bit.

Harbor MasterEach player is given a small deck of mediocre starting workers and the like–Copper and Estates for you Dominion fans out there. The central gameboard features spaces from which actions, goods, better cards can be drafted in a worker placement manner.  Cards (workers) are played face down with a marker to indicate ownership.  More than one player can choose the same space.  Once all cards have been played for the round, each space resolves.  The player with the best worker gets the full effect of the space while everyone else gets a minor, lesser, effect. Ties would be broken in favor of the lower–and therefore first–card

One card players can acquire in this environment might be our Harbormaster shown here.

 

Another Project

Continuing our back to school adventures, here’s another a nice homework assignment for you.  This time, I’m giving you the trigger, the event, AND the type of game this trigger must be used in.  See what you can think up and submit your ideas to our comment section.  Constraints breed creativity.  Go for it–you can do it!

Trigger (A): Critical Mass

Event (H): Game State

Game Type: Pick Up and Deliver

 

Gen Con 2014!

In addition to back to school season, it’s also Gen Con season!  Luther, John and I will be in attendance, primarily at Greater Than Games–booth 1949.  We’ll be running demos of Sentinel Tactics all weekend.  Come by, say hello, and let’s play a game!

 

We have now looked at eight of my “when TRIGGER occurs, do EVENT” examples.  How did I do?  What combination did you find most interesting?  What made you like it so much?  Which one did you like least?  What keeps it from being more enjoyable?   Share with your fellow readers in the comments below.  And if you’re enjoying what you’re reading, create an account with WordPress (http://wordpress.com/) and follow this blog.  You keep reading. I’ll keep writing.

Triggered Effects, Part 3

The Story So Far…

Triggered card effects all fit under a general “when TRIGGER occurs, do EVENT” template. They can make a card situationally powerful.  They can give cardsets a mechanical theme.  They can create opportunities for counterplay.

We have identified eight categories of trigger so far–Entrance, Tap/Untap, Exit, Acquisition, Revelation, Damage to the Card, Damage by the Card, Critical Mass.  I also pointed out that any of these effects could use the opponent as the trigger rather than the card holder.

We have addressed five categories of effect so far–Victory Points, Currency, Endurance, Cards, and Additional Cardplay.

I also challenged readers to identify any triggers I missed and to predict what other effects I would list.

 

Another Awesome Reader

Reader Jayson took on my challenge to identify missing triggers, suggesting four AND a modifier.  Jayson’s triggers were

(a)  “Play immediately when this card is drawn…”

(b)  “When you are forced to discard this card…”

(c)  “If X on this card is greater than Y…”

(d)  “When randomizer is X…”

There are all interesting triggers and each certainly has its place in design.  I find (b) particularly interesting and have been mulling that one over quite a bit since reading Jayson’s comment.

Jayson went on to point out that many triggers could be modified in the negative case “If X does not…” which may be seen as a special case of the Critical Mass trigger discussed in the last column but is certainly worth keeping in mind nonetheless.

 

More Effects

Triggered card effects fit under the “when TRIGGER occurs, do EVENT” umbrella.  We have addressed five categories of effect so far.  Today’s blog expands our list to include game component effects and internal effects.

 

Game Component Effects

Obviously, card effects can be used heavily in card games.  But cardplay mechanisms can also be used as part of a larger game.  This opens up a world of card effect opportunities for the intrepid designer to explore.

Glittercats correctly anticipated this area with the comment “A lot of games use card effects to control non-card mechanics. So the card’s effect may be to move tokens on the board, or re-roll dice, or some other interaction with non-card components.”  Let’s take a closer look at the options this gives us.

 

Component Quantity

Card effects in a  board game could direct us to add components, remove components, move components, or swap component locations.  These effects will say things like

“…place a control marker in your weakest area.”

“…remove 2 voters from the most populated area.”

“…you may move all of your workers from the defeated area.”

“…swap the position of two adjacent racers.”

 

 

Component Condition

Card effects in a  board game could direct us to alter the components themselves.  These effects might say things like

“…advance the toxicity marker one level.”

“…you may immediately reroll one of your dice.”

“…refill an empty farm.”

“…flip a die over to its opposite face.”

 

Game State

Similar to component condition, our effects could change the overall state of the game.  We could achieve this by altering the topology of the game board, exhausting areas, refreshing areas, or even changing the odds.  These effects might look like

“…add +1 to all die rolls for the rest of your turn.”

“…add a map tile from the supply.”

“…remove a depleted mine from the board.”

“…open one gate.”

 

Internal Effects

BerzerkerUp to now, we’re focused entirely on outwardly-directed effects.  But what about triggered effects which target the card itself?  This ground has been well-trod by constructed deck games but what about applying these effects to other types of games?  These effects could have our players

“…give this card +1/+1.”

“…remove a timing stone from this card.”

“…untap this card.”

“…remove all enemies from this card.”

These were my other categories in the “when TRIGGER occurs, do EVENT” formula.  Next time, we begin combining triggers with events.  Which which games use which combinations best?  Come by Friday and find out!

What effects did I leave out?  If so, what were they?  What game trigger do you find most interesting?  What made you like it so much?  What game triggers do you dislike?  What keeps it from being more enjoyable?   Share with your fellow readers in the comments below.  And if you’re enjoying what you’re reading, create an account with WordPress and follow this blog.  You keep reading. I’ll keep writing.

Triggered Effects, Part 2

The Story So Far…

Triggered card effects all fit under a general “when TRIGGER occurs, do EVENT” template. They can make a card situationally powerful.  They can give cardsets a mechanical theme.  They can create opportunities for counterplay.

Part one of this series identified six categories of trigger–Entrance, Tap/Untap, Exit, Acquisition, Revelation, and Damage to the Card.  I also pointed out that any of these effects could use the opponent as the trigger rather than the card holder.

I also challenged readers to identify any triggers I missed.

 

My Awesome Readers

Several astute readers took on my challenge, identified missing triggers, and shared them in the comments section.

ConspiratorJacob Titus Sanders pointed out that while I had discussed damage dealt to a card, I had completely overlooked damage dealt by the card.

studio228 suggested critical mass effects of the form “if you have 6 or more cards in your graveyard…,” or “if you’ve played three or more actions this turn…,” or  “if either player deals 12 damage in a single turn…”

Readers Rob and willbanalog pointed to resolution mechanisms–the “stack” for triggered effects found in M:tG and the immediacy of triggered effects in Marvel Dice Masters.

Regular reader, frequent contributor, and all-around spiffy dude Carl Klutzke remarked that triggered effects could be used to clean up otherwise wordy card effects.  Carl, we’d love to see a few specific examples from you.

Granite OniCarl also noticed that I’d completely omitted start/end of turn effects which is tragic when you consider how frequently such effects appear in the Sentinels of the Multiverse card game.  Reflecting on such effects, I might still leave them off the list however.  So many games which include start/end of turn that phases are commonly reserved for just this purpose whereas what I was hoping to address in this series are effects which are not so evident.  Of course, I did include tap/untap so maybe start/end of turn should be these as well.  there’s certainly something there to think about…

 

Approaching Effects

Triggered card effects fit under the “when TRIGGER occurs, do EVENT” umbrella.  Having taken a revised look at the variety of triggers that exist, we now begin a take on the other half–effects.

 

Victory Points

Many games keep score with victory points of one kind or another.  The simplest and most obvious effects then would say things like

“…gain 3VP.”

“…all opponents lose 2 VP.”

“…all opponents must give you 1 VP.”

 

Currency

If your game has an economic element in which items must be bought or sole, currency is another obvious effect.  Overt currency effects tend to say things like

“…you have 5 extra silvers this turn.”

“…each opponent must give you 1 coin.”

“…all your Shekels count double this turn.”

 

Endurance

Venerable MonkMost Constructed Deck Games (CDGs) are dedicated to survival.  Players of these games generally think highly of any mechanism which extend life.  Because some CDGs use the deck itself as a measure of life while others track life separately and the daddy of them all M:tG does both, these effects may be overt or covert and say things like

“…gain 2 life.”

“…all opponents lose 1 life.”

“…target opponent loses X life and you gain X life.”

“…shuffle your discard pile into your deck.”

 

Cards

warehouseFor many card games, the cards are a currency in and of themselves.  Gaining or losing cards can then be quite important.  Effects of this type might read like

“…draw a card.”

“…all opponents must discard a card.”

“…all opponents must discard the top card of their deck.”

“…draw a card at random from each opponent’s hand and add it to your own.”

 

Additional Cardplay

Sometimes it is not so much how many cards you have but how many cards you can play.  In these games, players would be quite enthusiastic about effects which give the opportunity to play more cards.  Cardplay effects read like

“…+1 Action.”

“…gain 3 green mana.”

These are the first five card effect categories in our look at the “when TRIGGER occurs, do EVENT” formula.  Next time, we go after the rest.  See you Monday!

What effects did I leave out?  If so, what were they?  What game triggers do you find most interesting?  What made you like it so much?  What game triggers do you dislike?  What keeps it from being more enjoyable?   Share with your fellow readers in the comments below.  And if you’re enjoying what you’re reading, create an account with WordPress and follow this blog.  You keep reading. I’ll keep writing.

Icons vs Text, Part 4

You have read several of my design group’s conclusions about the place of icons and text in game components through this series.  Last column examined color, art, and keywords. Today we look at two other methods and get at several concrete examples of published games.  We generally learn more from our mistakes than from our successes.  What can we learn from the games on our shelves?

 

A Standard Deck of Cards

Is there any more ubiquitous gaming component than a deck of cards? I believe there are probably more homes with a card deck in them than even a set of dice.  And how many games can be played with them? Certainly the number is in the thousands. The repository of all things card game Pagat contains about 30 games just beginning with the letter “A.”

https://i2.wp.com/playingcards.wdfiles.com/local--files/bicycle/Bicycle%20faces.jpg

Standard cards have no text.  They have numbers.  They have letters. They have colors.  They have suits.  These are the icons of the standard deck. Each game which uses them defines those cards to its purpose.

 

 

X-Wing Miniatures Game

X-Wing uses both text and icons. Pilot cards give all stats, actions and special abilities.  Stats are designated with an icon and a color, actions are designated with an icon in black, special abilities are detailed with text.

 

y-wing-layoutEach ship in play has a tile on its base which specifies its stats and pilot’s name. The pilot’s name functions as a keyword if you have learned that pilot. Otherwise, you can look it up on the pilot’s card.

Each ship is itself an icon. Every ship of the same type shares the same set of stats. Thus, if my opponent places a Y-Wing on the board, I know immediately that it rolls two attack dice, rolls one defense die, has 5 hull and 3 shields, can focus and can target lock.  I will still need to read its pilot name on the base to know if it also has any special abilities but I know quite a bit simply by looking at the mini.

The X-Wing Miniatures Game did make one major graphic design error–the dice. Fantasy Flight elected to have red attack dice and green defense dice. Red/green colorblindness is the most common form.  This has not been a major issue in my plays with a colorblind player–he simply asks me for the appropriate dice–but the fact remains that FFG would have been wiser to use white and black dice.

 

Dominion

Color is used throughout Donald X. Vacarino’s Dominion to indicate card type–gold for treasure, green for victory, white for actions, blue for reactions, orange for duration, red for shelters, brown for ruins. Consistent application of these colors is a handy reference for most of us.  Because each card also has its type printed at the bottom of the card, component color is not mandatory and Dominion remains perfectly playable by the color blind.

Like its booster pack-based forebears, Dominion also uses text to describe most game effects and card art may be seen as an icon for each card.

 

Gem Dealer

Reiner Knizia’s Gem Dealer From Eagle/Gryphon games is an excellent example of failing to consider the implications of using color to indicate category.  Nate Walker did the side-by-side comparison shown below and kindly posted it to BoardGameGeek.  Under anything but strong lighting, these colors are completely indistinguishable no matter how good the player’s vision may be.  If each gem also had a different shape, no issue would exist.  Color can be an asset to identifying components. It is not good enough to be the only means of identifying them.



Glenn Drover’s Age of Empires III

Era 2 BuildingsAoE III perfectly missed the opportunity to use art as an icon.  To the right, we see the set of Era II building tiles. Notice that Fortress and Military Academy have exactly the same effect–+1 soldier per turn but different art while Privateers and Taxation have completely different effects but the same art. How easy would it have been to use the same building art for Fortress and Military Academy, then use the musket-bearing figure to represent our Privateers. Rather than clarifying, the art here obfuscates the purpose of these components.


John Eyster and I were discussing this blog series a few nights ago.  He pointed out that AoE III also has a mass-o-plastic issue.  The generic workers and the specialists tend to blend together on the game board.
He’s not wrong.  This is particularly troublesome since relative quantities need to be assessed and reassessed throughout the game. To be frank, I’d forgotten this issue since I replaced all the basic units with wooden cubes in player colors ages ago.


These issues are particularly unfortunate in the case of AoE III.  It’s a solid game.  My first plays were of a preproduction copy at Origins Game Fair. That version still used cubes as workers (which was the source of my inspiration to do the same) and was so enjoyable that I made an effort to get in a second play before the end of the convention. There are many games at Origins begging for your attention so finding one you want to play repeatedly is quite unusual.  


AoE III was rereleased as
Glenn Drover’s Empires: the Age of Discovery. I haven’t had the opportunity to try it out but hope that these design issues have been resolved.  It’s quite a good game and deserves to have equally good art.

 

 

Lessons Learned

What do these successes and failures teach us?  They show that any method can be used well and it can be used poorly.


So what should you do? I believe the correct answer lies in redundancy. Use multiple methods to reach your players.  Include icons and make them match the card effect.  Make keywords and include brief reminder text.  Give your cards/tiles art and make that art evocative of the item’s meaning in the game. Use distinct minis or meeples that stand out from their neighbors.  Rather than giving each player five different meeples, give each of your five players meeples which have unique shape as well as color.  You will have a much greater chance of being clear when you employ more than one method to convey information.

1955-mil-transport
Nich Vitek did a phenomenal job of employing redundant information while developing the graphic design of 1955: The War of Espionage. Each card conveys information in several ways.  Consider this
Military Transport card.  We see by its flag that it is allied with France.  We see by the number in the upper corner that it has strength 2.  This information is repeated in the lower-left edge by its two blue stars.  The image of troopers dropping from a transport plane implies the card’s special ability, which is also spelled out in the card text.  An icon appears in the left banner and at the top right of the card, both as a reminder of the card’s effect.

 

How about you?  What game do you think used text, component art, or icons most clearly?  Which one did it worst?  Share with your fellow readers in the comments below.  And if you’re enjoying what you’re reading, create an account with WordPress and follow this blog.  If you keep reading, I’ll keep writing.


Next time we get together, my second book report! Have a great weekend and I’ll see you Tuesday!