Reiner Knizia is one of my favorite board game designers. One thing I really admire is that he’s willing to noodle on a theme (e.g. his four early tile-laying games) until he’s satisfied with it. He’s gone through a few versions of Lost Cities, including Keltis: Das Kartenspiel (hereinafter, “Keltis” — there are a few other Keltis variants, but this is the one I’ve been playing.

First, I’ll briefly explain the rules of Lost Cities, and then the changes in Keltis. Then I’ll explain why these changes produce lower variance. Finally, I’ll explain why I’ve been thinking about this.

The Lost Cities deck consists of twelve cards in each of five suits. Nine cards per suit are numbered 2-10; the rest are identical “investment” cards, which multiply a player’s score in that suit. Each player has a hand of eight cards. On their turn, they either play or discard. Plays and discards are both by suit. After playing, they draw either from the deck or any discard pile. As soon as the last card is taken from the deck, the game ends. There are two things that make the game interesting: 1. You can only play cards in each suit in-order: first any investment cards, then the numbers in ascending order (with gaps permitted). 2. If you don’t play any cards in a suit, you get zero points for that suit. Otherwise, your score in a suit is negative twenty points plus the sum of the values of the cards played in that suit. This generally means that you only open a suit if you’re pretty sure you’re going to make 20 points in it.

Keltis has a few differences from Lost Cities, but from our perspective, the most important ones are: 1. The value of each card is approximately the same. Cards still have numbers, but the point value for a suit depends only on the number of cards in that suit. 2. You can play a suit in either ascending or descending order.

Here’s how this leads to lower variance: In Lost Cities, opening with a hand of, say, the 9 and 10 of each of four suits is somewhat unlucky. You don’t want to discard anything, because your opponent will snap it up from the discard pile. But you also don’t particularly want to open a suit, because you’re guaranteed to lose a point on it. In general, getting cards in the wrong order can turn what would be a good suit bad. There’s nothing more frustrating than ending the game with the 7-8-9 of a suit and missing six points just because of bad timing. In Keltis, that would be an acceptable opening hand, since the 10s are all immediately playable.

And in Lost Cities, if you have 3-4-6 in a suit (13 points already), you’ll surely open that suit since you expect to get approximately two of the 7-8-9-10 cards. But in a quarter of games you’ll get just one, and in a quarter of games you’ll get three. And it’s possible to get zero or all four. In Keltis, this is approximately true as well (the card distribution is a bit different, so not exactly). But in Keltis, this will result in a swing of a few points — not 30 points (or more with investment cards).

It’s always nice to have data to back up a theory, so I found this page. It claims that, in fact, Keltis (listed as “Keltis Card”) is lower-variance. Well, more precisely, it makes a more-complicated claim about Elo ratings, but I think the effect is the same.

Subjectively, I think Lost Cities might be a slightly more fun game, and this says bad things about me. There’s a real excitement as things come down to the wire: will I suck out and get that blue ten (which is now worth 40 because of investments), or won’t I? That part of the game is pure gambling, and while it’s fun, it’s not something I feel proud of enjoying. But at least I’m not alone: Keltis gets 6.7 on BGG, while Lost Cities gets 7.1.

I have been thinking about this because I just had opposite feedback about dynamic range in two of my prototypes. In Sekhmet, the range was considered too low: a given tile could score between 1/2 and 2 points. In Banshee, the tile values are between 1 and 10, and the player who happened to draw the 10-point tiles was very likely to be able to use them and win. Similar problems don’t necessarily demand parallel solutions, so while I’m going to replace all the 1s with 2s in the next test of Banshee, I’ll probably fix Banshee by completely replacing the way that tiles score — and in the process, maybe reduce the range.

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