The Long Quest for a Cards-with-Numbers Game
For many reasons, I've been fascinated with card games that can be played with little more than a deck of sequentially numbered cards. Sometimes there are colors acting as perfunctory suits, like Uno or Reiner Knizia's Poison. The real gems are games like No Thanks or 6 Nimmt which have no suits, just numbers. There's something so seductive about the pure abstraction there.
On that note, dice games are heavy hitters when it comes to abstract purity – Yahtzee and Liars' Dice come to mind. Heck, even dice games with custom faces can be abstracted back down to algebraic notation... but let's talk about cards for now.
I must admit, part of the appeal is from a commercial perspective. Cards-with-numbers are easy to playtest, easy to lay out, require minimal art, and can be reproduced relatively easily. I think this creates a positive pressure on the design of the game itself. The mechanics and rules presentation must be well-executed since the components could be created at home with little trouble.
And that's why I've been orbiting around so many cards-with-numbers ideas lately. I'm looking at games like Stefan Dorra's For Sale, where cards are auctioned then used as bidding. I'm looking at Libertalia, where cards determine which special effect is activated first. I'm looking at Get Bit, where the cards are used for bluffing and deduction. In these games and others, a simple cards-with-numbers deck forms the slim, strong rebar supporting a robust game.
In a fit of frustration, I tweeted this ultra-minimal idea.
Idea: Spread number cards on a table. Players take turns taking one card. Turn order=Previous round's chosen cards, low-to-high. Score=Sum.
— Daniel Solis (@DanielSolis) November 4, 2012
This sounds really appealing at first glance. It's essentially self-balancing, with power-grabs mitigated by poor turn order in the later rounds.
But of course that just leads to the last round not really mattering. The "winner" would be determined by the turn order established in the previous round. Continuing this all the way backwards, the first round's turn order would essentially predict the endgame's winner or the final score would essentially be a tie. (Thanks to Mark Sherry for pointing this out.)
Granted, that projection is based on averages and random draws. People can be unpredictable, but with this sort of bug, you only win if your opponent makes a mistake. If everyone plays perfectly, the game simply ends in a tie.
However, if this formed the "rebar" of another game, it might be useful. Say you're trying to straights or all evens or all primes. When you toss in other information on the cards, you get even more opportunities for set-building. (I like how 6 Nimmt puts bulls on key cards in a regular pattern, so that some the pattern occasionally lines up so some have two bulls, some have three, and so on. It feels like a constellation.)
How about this:
- Spread the numbered cards across the table, 5 per player. (If there are 3 players, there are 15 cards on the table, each numbered 1-15.)
- Players take turns taking one card, then moving up the score track that many points.
- The turn order of each round proceeds from the trailing player, up to the leading player.
- Straights are worth the lowest number in the set. So a 2 3 4 5 6 is only worth 2 points. Thus, if you see an opponent has a 2 3 and a 5 6, you really want to force them to take the 4.
- There are enough cards to play through 5 rounds. After that, the player with the highest score wins.
Even when there is a bug in a cards-with-numbers game, you can design around it to make something more substantial and satisfying.
Anyway, my quest for designing a cards-with-numbers game continues. Do you have any favorite cards-with-numbers games?
The analysis isn't quite that simple. Here's how it goes:
ReplyDeleteIn the final round, you don't have any concern about turn order, so you might as well just take the largest card available. This requires a minimum of rationality on the part of the players. Obviously, the person who goes first will be taking the biggest card, but if they're going first, they must have taken the 1 card the previous turn, so their score for the final two rounds will be n + 1 (where n is the number of cards/players). Second player takes the n-1 card, but they must have taken the 2 card the previous round, so their score for the final two rounds is also n-1 + 2 = n + 1. Continue this process and everybody gets a score of n + 1 in the final two rounds, regardless of what card take took in the 2nd last round (and consequently, what order they went in).
Which means that the final two rounds don't actually matter, so in the 3rd last round, you should just take the largest card available. By an argument similar to above, in the 4th and 3rd last rounds combined, everybody earns another n+1 points. Not on average, but exactly. The only reason someone wouldn't is if somebody was angling for a better position going into the last two rounds. It won't do them any good, but it might free up a nice card to give someone n+2 or n+3 points that round, and possibly secure them a victory. Again, the only way to win is if someone makes a mistake.
You can continue with this reasoning, removing rounds two at a time, since if played properly, each pair will just score each player n+1 points. If there's an even number of rounds total, it will be a complete tie. If there's an odd number of rounds, the whoever took the largest card in the first round wins.
As a result, the trivial greedy strategy works: always take the largest card you can. If there's an odd number of rounds, or an opponent makes a mistake, you'll win. If not, you'll at worst tie.
What if you introduce an economy that slightly divorces victory points from tempo? Suppose you introduced money -- each card has a point value, and a currency value. Players all start with a hand of cards (some starting currency). Flip two cards from the deck, and let people make a blind bid to take those cards. Paid cards go on the discard pile; unpaid cards. Everyone must bid at least one card. When the deck is exhausted, the person with the most points on cards (not the most currency value) wins. Then you can mess around with the currency values assigned to which cards.
ReplyDeleteThis post was me -- the pitfalls of having more than one Disqus account. 8P
ReplyDeleteThe game I'm working on 'Opening Day' is in essence a 'cards-with-numbers' game. I need to show it to you. I'd love your feedback.
ReplyDeleteNo idea about your design, just to say on my side I'm fascinated by textless card games, wich gives me this sensation of abstract purity. Textless here means no text of any kind, no icons, no symbols, nothing but a freaking nice illustration. My favorite is Hanafuda - and in fact, no other comes to my mind. Ok, it is a bit cheating with the principle of purity because you have to remember all the families and combos you can make, but the visual experience when the game is played is just awesome. Most of the card games are now designed with icons, to make the first games easy, to help the players to play it with nothing to remember. Ergonomy. On the contrary, Hanafuda asks for a little bit of effort, but the result worth the cost. As a graphic designer and a game designer, that made me meditate, and sometimes reverse the balance between the "look & feel" rendering instead of "ergonomy first".
ReplyDeleteAlways ready with some excellent math analysis. Thank you, sir!
ReplyDeleteI highly recommend Sid Sackson's For Sale! Here's a Vasel review. http://www.boardgamegeek.com/thread/378884/
ReplyDeleteLet's trade! Happy to meet up somewhere between us for a mutual playtest.
ReplyDeleteHave you played Jaipur or Divinare? Both are games featuring cards with mechanically relevant text or numbers, just illustrations.
ReplyDeleteRiffing on the old board game Rithmomachia, how about building game mechanics based on factoring the numbers?
ReplyDeleteRithmomachia had 4 means of attack on its board:
1. Surrounding a piece with any others
2. Sums (placing 2 pieces adjacent to a piece between them that they added up to)
3. Multiplying - attack by distance (a 4 piece could take a 12 piece that was 3 away)
4. Move - each piece had a number and a shape (circle, triangle, square), so a circle moved 1, triangle 3, square 4, so if the other player had a matching piece at the proper range, you could zap them.
To stick with your pure number theme, drop the suits/shapes, and you still have 3 interesting interactions.
... and then there are dominoes - cards with 2 numbers on them. Equally easy to produce and a rich vein for game designs.
Take a look at Rack-O.
ReplyDeleteI did. Jaipur is one of my favorite 2-player game. ;)
ReplyDeleteSmall point: For Sale is a game by Stefan Dorra, not Sid Sackson.
ReplyDeleteOh goodness. Thanks for catching that!
ReplyDelete