As a card game enthusiast (in this case, 52-card deck card games), I think it’s really cool to discover new card games that are not just the “play a seven on a seven, slap your opponent in the face, announce ‘UNO’, and win the game”. “High-Low” is one of these games discovered recently, and I decided to do an analysis of the game of how to win as a sort of fun thought experiment.
High-Low Rules
Here’s kind of how to play the game. It’s a guessing game, kind of like Hedbanz or any of those trivia games.
- Each player gets a card which everyone but them can see.
- Going around in a circle, each person tells the group what they think the relative rank of their card is. Ex. “I think I have the third highest card.”
- Once everyone has gone once, each person in order then tells the group what they think the rank of their card is in addition to what they think the value on their card is.
- If everyone correctly guesses the rank of their card on the second round, the game is won.
Additional Notes/Rules
The rules are kind of not enough, so here are some of the edge cases (if I didn’t forget any).
- Ace is the highest rank, going all the way down to 2.
- At the beginning of the game, someone usually says the number of duplicates they see in order to give players some more information (as duplicate values are very difficult to distinguish without this).
- Players should give their absolute rank among the group (ex. if two players have an A and another player has a K, they would be the third highest rank and both A players would be the highest rank).
- Players cannot give a rank that is not possible (to prevent someone from just saying “I think I have the 10th highest rank” to tell the player next to them that they have a 10 when there are only 6 players). I guess this can be done with 10 players because honestly there is no way to stop it without introducing arbitrary and subjective rules.
Reasons I like the game
There are a few things that I really like about this game.
- It’s cooperative yet challenging.
Since there is very limited information, you have to think about what the other players are thinking when they make their guess. What’s great about this game in particular is that you always have to think somewhat about what your card is, but it is usually never completely out of your reach. And the thing about it being cooperative is you never feel like you are hopeless because the rest of the group is always trying to help you.
- It’s simple to learn but difficult to master.
I love games that take whole days to play, but when it comes to introducing the game to players who have never played before, usually teaching the game requires at least one playthrough of the game, and things like Terraforming Mars means you need at least 8 hours of commitment before you actually get to play the game with people who know how.
General Strategy
Spoilers for anyone wanting to just try the game out for themselves.
With groups of more than 10 or fewer than 5, it is significantly more difficult/boring to determine your rank (due to existence of duplicate values), but from personal experience I feel like it is way better to have more people than to have fewer.
Intuitively, the first person has no information besides some basic probability, so usually they would guess that their card is some arbitrary value. Usually, 8 is a good heuristic to start at, but honestly the only important thing is that it gives some amount of information to the next player. The rest of the players can kind of just count how many players that the first player can see and then guess which number they would have to make the other players guess that. If they see five extremely low numbers, and their guess was second highest, then you can probably determine that your number is high.
The next few people would do similar things. This would restrict the guessing pool enough so that by the time the first player has to guess again, they should know approximately where their rank is.
How to Cheese the Game
That being said, games like these are ridiculously easy to cheese with a predetermined strategy. Each player has n degrees of freedom in which they can give information. However, we have an upper bound of 13 * n possible card combinations. This means that with four or more players, it is possible to always give all information about any players’ card to every player.
Despite the fact that the game has a solution, I still think the game is super fun to play and any logic nerds wanting to try something new should try it out.