19 October 2016

Bluffing games have a single defining characteristic: The game is about lying to the other players and not getting caught for it. There's one particularly well-known bluffing game called Bullshit (or BS, or some number of other more politically correct names). You've probably heard of it, but I'll briefly outline the rules.

The game is played with a standard deck of playing cards, which are initially dealt equally among the players. The players then take turns playing cards face down and claiming what they played. So you might put down two cards and say "two sevens". On each turn, the rank of the claim must go up by one. So after one player claims to play sevens, the next player must claim eights, then the next player nines, and so on. After kings it goes to aces, then twos, and so on.

After each play, anyone can challenge it before the next player plays. If someone challenges, then the played cards are revealed. If the player lied, then they take all the cards in the play pile. If the player was telling the truth, then the challenger takes all the cards. A player wins if they successfully play all of their cards.

Despite its prevalence, Bullshit is an awful bluffing game. A game of Bullshit will usually start out with a reasonable amount of lying, but by the end you'll probably find that lying is essentially impossible, and so you'll just tell the truth when possible, and get challenged when you can't. At that point, the game becomes a game of luck. Why does this happen?

### Increasing information

As a game of Bullshit progresses, more and more information becomes available to the players through the challenge reveals. You'll quickly notice things like one player can't possibly have any fours, so you can immediately challenge him if it gets to his turn with fours. You might even get a four of a kind, which means that if that number shows up on anyone else's turn, you can challenge them. As a result, a lot of challenges are not based on reading your opponent, but rather proving that they can't be telling the truth.

### Forced lies

What happens when it comes to be your turn and you need to play kings but you don't have any? You're required to put down some number of cards. Maybe you put down one card and hope that nobody challenges because they don't know you have any. Maybe you're a bit bolder and play two cards because you think your opponents will think you'd play only one card if you were lying.

These ideas work fine in the early part of the game, but the increasing information means that eventually you'll be forced to lie in a spot where you know that your opponents know that you'll be lying. At that point, nothing you do matters, and you'll just be taking the pile regardless. This also means that you may as well challenge the previous player, so now they won't want to lie either.

### Low incentive to lie

Imagine it's your turn to play sixes, and you have two sixes in your hand. What benefit do you have to lying? You get to play other cards instead of sixes. But after this turn you're going to be getting a turn with every other rank before getting back to sixes. So really, sixes are the least important type of card for you.

Plus, getting caught lying has a huge downside of getting a pile, whereas telling the truth is a guarantee that you won't pick up the pile immediately. If someone else is forced to lie before you are, then the pile will go away and you won't have to worry as much about it. Overall, there's a lot of reasons to tell the truth, and not many reasons to lie.

What fun is a bluffing game where bluffing is almost always wrong, and "reading people" just consists of looking at your hand and seeing if their play is literally impossible? It's not fun, and most people who have played the game will tell you that. However, there is a less well-known but similar game which is an example of how these issues can be avoided.

I don't know if this game has a standard name. I know it as Bluff, but a Google search for that mostly turns up the game of Bullshit that I described above. Just like Bullshit, the game starts with dealing out a deck of cards evenly among the players, and turns consist of claiming a number of a rank and playing cards face down, and those plays can be challenged. However, there are a couple key changes.

When playing on an empty pile, you are allowed to play any rank of your choosing. When playing on a non-empty pile, you must play the same rank as the previous player. That means that when a pile builds up, every single card there has been claimed as the same rank. Finally, you are allowed to pass your turn. If, after someone plays, every other player passes, the pile is set aside without revealing any of the cards (these cards are permanently removed from the game), and the player who made the last play starts a new pile.

What makes this game better?

### Decreasing information

Let's imagine a two player game of Bluff. At the beginning of the game, you have perfect information. You have half of the cards, and your opponent has all the cards you don't have. Now say you claim to play two eights and your opponent does the same. You pass and those four cards have been removed. You don't know that those two cards that your opponent played were really eights. So you no longer have perfect information. Over time, this effect compounds on itself and you end up with an overall decreasing information trend.

### No forced lies

The passing option means that if you believe that your opponent knows that you have none of a card, then you can pass and take a compromise. You weren't able to play any of your cards, and your opponent gets the power of choosing the next rank, but you aren't just forced to take a huge number of cards.

### Lying pays off immediately

Contrary to Bullshit, where you have to wait 13 turns before playing the same rank, in Bluff you're expecting to play that same rank on your very next turn. So maybe you have two eights. You could get rid of two other cards now, then next turn play your actual two eights. But maybe your opponent is wise to your tricks, so you could play your eights now. Even if you played out all your eights already, maybe your opponent will think that you lied to them earlier and pass instead of calling you out on a lie.

I won't claim that Bluff is a particularly amazing bluffing game, but it is one that can be played with just a standard deck of cards, works with two players, and actually incentivizes bluffing. The differences between Bullshit and Bluff look small from a rules perspective, but they have a profound impact on how the game is played. These ideas are worth keeping in mind when designing a bluffing game, or even other types of hidden information games.