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This is the first installment of the Game Analysis format that I talked about last time. This first issue will cover the merits, failures, and ways to improve a fairly popular game called Love Letter. For the record, I am analyzing this game based off the version I played more than a year ago.

EDIT: Due to the large amount of off-blog discussion this has sparked, I have written a follow-up post to honor the points that have been brought up.

I will go over in more details about the game below, but let’s start with my overall impressions.

TLDR: I think the game is quite promising, but development and testing stopped too early and the game, for me, wound up disappointing. It’s probably worth picking up for most people, but be wary that it has some important issues with its design.

Merits

Love Letter is a very quick game to play. The rounds last around 5 minutes, and you can really play it as long as you wish.

The game only costs around $10.

The mechanics and concept are fairly simple and straightforward. You simply draw a card, choose which of your two cards to play, and use the played card to try to knock out your opponents or keep a particularly high value card in your possession. Once the deck is depleted, then the remaining players compare their hands to determine if they win the round or not.

It’s a pretty simple engine that has a fairly large space with which to design card effects to provide enough diversity of play to keep players interested.

Failures

To accurately depict where I think the game fails, I need to go over what the cards that you will be drawing and activating are.

A side note: I added TLDR statements below each section to describe the section if you are not interested in the small, but significant details.

Love Letter has a 16 cards numbered 1 through 8. I detail them below with the format: Number. Name xCopies: ability.

  1. Guard x5: Pick another player and name a card other than “Guard”. If that player has the card, they discard it and are now out of the round.
  2. Priest x2: You can look at another player’s card.
  3. Baron x2: Pick another player. Secretly compare your cards. Whomever has the lowest card discards their card and are now out of the round. In a tie, no one loses.
  4. Handmaid x2: Until your next turn, you cannot be targeted by other players (Guard, Priest, etc).
  5. PrinceĀ  x2: Pick any player. That player discards their hand and draws a new card.
  6. King x1: Trade your card with the card of another player.
  7. Countess x1: If you have the King or Prince, you must play the Countess. Otherwise, she has no ability.
  8. Princess x1: You are out of the round if you discard the Princess.

At a brief glance, it seems that there is quite a diversity of cards to play and choices to make. If you take more time looking at the abilities, and how many cards of that ability there are, you may start to get an inkling as to why I see some failures in the game.

Earlier, I stated “You simply draw a card, choose which of your two cards to play, and use the played card to try to knock out your opponents or keep a particularly high value card in your possession.” I would like to take the opportunity to say that, this is not an entirely true statement.

The game offers a choice to the players, but is this always, or even usually, a choice that you get to make for which card you choose to play?

General Statistics

I decided to make some spreadsheets to clarify why I believe the main fault with Love Letter is a lack of choice after having promised choice.

Let’s first look at the general probabilities of a random 2-card hand at the start of a match, when you potentially have the most choices. Also, let’s just see where your choices lie with the rules as they are stated on the cards.

LoveLgeneralHand

The numbers in the cells are how likely that hand is to occur (scale is 0-1). As you can see, if your other card (the columns) is the same number as the card you wish to play (rows), then you must play it. Also, if you have a countess (7) and either a prince (5) or king (6), then you must play the countess. Lastly, if you have a princess (8), you must play the other card. These are simply the cards’ abilities as they are stated.

An initial look at these do not seem terribly poor. Let’s even try adding how probable it is that you 1. cannot play the card, 2. must play the card, 3. have no choice in card play, and 4. have a choice as to which cards you can play.

1: you cannot play the card. To get this, we add all of the red numbers. I did these calculations through the spreadsheet in case there were significant remainders on the hand probabilities. The result is that you are 0.08 (8%) likely to draw a hand where you cannot play the card desired.

2: you must play the card. To get this, we add all of the yellow numbers. The result is that you are 0.19 (19%) likely to draw a hand where you must play the card desired.

3: have no choice in card play. This is simply the combination of 1 & 2. When you add them together, you are 0.27 (27%) likely to draw a hand where you have no choice in which card to play.

You may be thinking “Why did he include hands like, 1&2 as well as 2&1; they are equivalent. You are right, but adding the probability of drawing a 1 then a 2 to drawing a 2 then a 1 is the same result to what I did in this step.

4: have a choice as to which cards you can play. For this step, simply add all of the green cells. If I did my math right, this should also be equivalent to 1 – probability 3. For this case, the result is, indeed, 0.73 (73%).

27% chance of not having a choice in which card you have is already really significant. This means that, before any cards are played, you do not have a choice in which card you play more than 1 out of every 4 hands.

TLDR: Looking explicitly at the rules of the cards, if you drew 2 cards, at random, from the deck, you have a 27% chance of not having a choice in which card you play. Conversely, if you drew 2 cards from the deck, you have a 73% chance of having a choice.

Adding in the Guard

Ok, let’s now look at adding in some more squishy statistics, such as the probability of guessing correctly when using a guard (1) and blindly choosing another player to compare against with the baron (3).

First off, here is the table for the probability of guessing the correct card when you played the guard. Each column represents what your other card is. Each row is what you are guessing the player’s card is. The bottom row is the likelyhood that you drew this hand. As a side note, the probabilities of guessing correctly get more likely as cards get played.

LoveLguardGuess

There is not a lot of data that is usable for arguing why you might have a choice when playing this card. However, I thought the table was interesting and can help you think about what cards you should guess when playing a guard.

The more interesting thing to think about with the guard is that, since it’s fairly even for which cards you can guess, and since the guard is such a low number on the win-the-round ranking, you might as well play it when you have it. In the final analysis, I will consider playing the guard or not as a player choice.

TLDR: There’s not a lot of useful data when looking at the guard guessing probability, but you should probably play the guard since it’s a low-risk move.

Adding in the Baron

Now let’s look at the probabilities of winning when you play a baron (3) card. Each column represents what your other card is when you play the baron. There are 4 things to consider with the baron probabilities:

  1. How often do you get this hand? This is gotten from the first table.
  2. How often do you lose when playing the baron with this hand? This is determined by figuring out how many of the remaining cards beat your card.
  3. How often do you tie when playing the baron with this hand? This is determined by how many cards are equivalent to your cards, plus how many of the remaining cards yours beats. This should always be greater than or equal to the 4th item on this list.
  4. How often do you win when playing the baron with this hand? This is determined by how many of the remaining cards your card beats.

LoveLbaronGuess

I’ll discuss the results with a list according to the other card in your hand.

  1. Do not play the baron. You won’t lose 29% of the time, but you also will never win.
  2. You should probably not play the baron. You will win 36% of the time, but you’re 57% likely to lose.
  3. While it’s a coin toss as to whether or not you will win, you don’t have a choice since your other card has the same ability.
  4. Now we’re seeing when you’re more likely to win than not. Playing the baron when you have a 4 is still debatable, which is good.
  5. – 7. Playing the baron when you have a 5 or greater is probably going to get another player out. However, it may signal things about your hand since their card gets discarded face-up. For example, if you beat a 6, then everyone knows you have a 7 or an 8. For cards 5-7, it is really up to you if you want to play it.

8. You will always win, but you never had a choice about whether to play the 8 or the 3 because you lose when playing the 8.

TLDR: When you have a baron, you shouldn’t play it unless you have a 3 or greater. Be careful when you have a 4 since you’re only 57% likely to win, and 36% likely to be out of the running.

The Probability Table Now

LoveLresults

This is the same table, but I provided those answers to 1-4 from the first part on the bottom. Also, I included the fact that, if you use your king (6) to give someone your guard (1), they know exactly which card you got in return and, unless it’s a guard, you will get called out by the very card you gave them. I did a probability table for giving them the baron, but it is pretty much the same as the one above, but there are less 6s, so it’s not particularly useful data.

The pink is the probability that you do not have a choice in what card you play with a random 2-card hand. The reason the pink is 43%, which doesn’t make sense when the green is 58% is because it’s really 42.5% and 57.5%.

TLDR: The long and the short of all of this is that you have a choice in which card you play 57.5% of the time, but you do not have a choice 42.5% of the time.

Summary of Failure:

This is a really significant result because almost half of all 2-card hands are illusions of choice. This is my big issue with the game, and it all comes down to the abilities tied to each card. If the developers had done this probability analysis, or played it enough times, they would see this in their game and should have done something about it.

Ways to Improve:

So, after that looooooong discussion about why I’m disappointed in Love Letter, how can we improve it? The solutions I will mention are not fully analyzed, so be wary of taking them at face value.

One of the first things I would do is to look at where most of the probability of non-decision lies.

Most of the choiceless probability is around the guards. This is because there are far more of them than any other card. The solution around the guards is not particularly great, since having a card to point to any other player to guess who they are is a great ability to have on the lowest numbered card. If I was to do anything with the guards, I might remove 1 or 2 and make them into 2s. I wouldn’t want to make them other #s because the baron probabilities get pretty disturbed at that point, and I like where the baron is in terms of its power.

The second most probable choicelessness is when you have the princess (8). You have a 13% chance to draw the princess in your starting hand. From then on out, you do not have a choice in what you play. My solution would be to change the princess’ ability. Should it be a negative or positive effect? If it is a positive effect, the card becomes really powerful and provides a really significant conundrum for the player when they draw it as to whether or not they play or hold the card. On the other hand, if you make the effect negative, neutral, or very weakly positive, you make sure that the player never plays the princess because she is too valuable as an end-of-round card. Thus, you should make her have a positive effect.

The effect should not be super powerful, or else you randomly hand someone the game when they draw the princess. Instead, it should probably be around the power of the baron. Then, you can play it strategically and feel like you actually were playing the game instead of letting the game play itself.

Final Thoughts

I think Love Letter has a lot of promise. It can be a really fun game. Currently, it is a game that pretty much plays itself while you are there to turn its crank. If you change the princess card’s ability into a somewhat positive ability, then you actually get some of the player choice into the game that is desperately needed.

Should you buy the game today?

If you are looking for 5-20 minutes of amusement while you wait for your other friends to arrive, or are at a bar looking for something to play, you should probably buy this game.

However, there are other games out there that fill a similar niche, and you should maybe shop around for a better game or fix the princess card.