# How to make sure a player will not draw their own character card as target?

In my current design each player needs to kill an other player assigned to them. They have a character card and a target card which shows which character they have to eliminate to get points. Both the identities and the targets are hidden. The players get clues about their target during gameplay.

My problem is I don't know how to make sure during the setup of the game that no one gets themself as target (that is the identitiy and target cards show the same character). Reshuffling every time when someone realizes they got themself would be lame. Especially that in case of n player this is expected to happen in every nth game.

An idea I got is to shuffle the same id and target cards together, then take the first id card (face down) and put it into an other pair, then the original character card of that pair is taken to another pair, etc. until all pairs are done. Finally shuffle them again and give them to the players. This seems a bit long (and maybe overcomplicated?) to me.

A mobile application would be an easy way to solve this problem, but I would rather not force the players to use their phones to play this game.

Is there any better way? Is there maybe any existing game which had a similiar mechanic?

• Does a player have only 1 target (after target is dead, do they immediately have another)? Can a player be targeted by more than 1 other player? – JonTheMon Jun 9 '16 at 20:31
• Can you use a rule like "Kill any two players if you draw your own card" or "Attack the player on your right if you draw your own card?" Or have every player draw two target cards, and let them choose one as their target and put the other back on the top of the pile so they know a little about the next/last player. – jejorda2 Jun 9 '16 at 20:33
• Nit: The expected number of matches is 1 regardless of N. So, as N gets large, your probability is significantly higher than 1/N as you asserted. Important thing is you recognize the problem... – John Jun 9 '16 at 20:37
• @John, oops, I calculated it wrong, you are right. Even worse then..:) – britsplease Jun 9 '16 at 22:41
• @JonTheMon, in the current state, after the target is dead, no other target is drawn, but the killer still needs to survive the round. – britsplease Jun 9 '16 at 22:43

Get cards corresponding to pairs of targets and killers, and arrange the pairs so that the target card is above the corresponding killer card.

E.g. Each killer and target pair is designated by a letter

Target A - Killer A, Target B - Killer B, Target C - Killer C, Target D - Killer D

Put the pairs in unmarked envelopes. Shuffle the envelopes.

E.g. Pairs in envelopes are in parentheses

(Target B - Killer B), (Target D - Killer D), (Target C - Killer C), (Target A - Killer A)

Take out the cards from the envelopes and place them in a stack in random order while preserving the original order within each envelope.

E.g. Stack from top to bottom

Target B, Killer B, Target D, Killer D, Target C, Killer C, Target A, Killer A

Move the top card of the stack to the bottom of the stack

E.g. Target B moves from the top to the bottom of the stack

Killer B, Target D, Killer D, Target C, Killer C, Target A, Killer A, Target B

Deal out pairs of the killers and targets to each player while preserving the new order of killer card on top of the target card

E.g. Player card pairs in parentheses

(Killer B - Target D), (Killer D - Target C), (Killer C - Target A), (Killer A - Target B)

Each player is now assigned a unique role as killer and a unique target.

Inspired by a similar post from board game geek.

• This seems to work and it is not too complicated, I like it. Also thanks for the detailed explanation. I guess I will tag this answer as accepted, since this is a direct answer to the question, though the other comments and answers are great alternatives. – britsplease Jun 10 '16 at 13:50
• If I understand this correctly, won't you know that you are targeted by the person who was dealt before you and that your target is the person after you? I believe that you need to deal into envelopes at the end and shuffle the envelopes. – Dane Jun 10 '16 at 21:21
• By the way, this procedure, including the final envelope step I mentioned, is how we ensured a complete circle in a live-action game called Assassin we played at my school, where you adopted your defeated target's target until you ended up with two players, each targeting the other. – Dane Jun 10 '16 at 21:23
• Also, using this method, the targets will always form a cycle. It cannot happen that A and B have to kill each other and C and D have to kill each other. That might be what you want, but maybe it isn’t. – Eike Schulte Jun 11 '16 at 8:51

A game with a similar mechanic is Lifeboat. In that game normally you get points if your target dies, but if your target is yourself then instead you are a "psychopath" and get points for anyone who dies (but fewer points in other ways).

One solution for your setup could be to put both player ID and target on a single card: "You are player 1; kill player 2", "You are player 2; kill player 3", through "You are player n; kill player 1".

• I love Lifeboat, but it literally does nothing to prevent someone from loving or hating their own character. The rules for being a narcissist/psychopath are necessary because it's still possible to have yourself as a target for one/both. – The Chaz 2.0 Jun 2 '17 at 15:34

Here is another possible option. Instead of handling each player a card with single target you can give them ordered lists of targets, than deduce specific targets once all lists are revealed. Sounds confusing? Let's look at example!

Suppose it is a 4 player game with players Alice, Bob, Charlie and Doris (A,B,C and D for short). We create 4 lists with targets in order: #1[A,B,C,D]; #2[B,D,A,C]; #3[C,A,D,B]; #4[D,C,B,A] and give them to players randomly. Let's say we have a situation when Charlie has list #1, Alice got #2, Bob has #3 and Doris #4. Then at some point of game all lists are revealed. We'll look at this as a table:

``````Player   Charlie  Alice   Bob    Doris
List     #1       #2      #3     #4
Case1    A        B       C      D -X
Case2    B        D       A      C -V
Case3    C        A       D      B
Case4    D        C       B      A
``````

Now we check cases one by one. Case 1 is invalid, since Doris has to target herself. Fall through to case 2... Bingo! Everyone has a valid target!

But what if Bob and Alice happen to swap lists and now it looks like this?

``````Player   Charlie  BoB     Alice  Doris
List     #1       #2      #3     #4
Case1    A        B       C      D -X
Case2    B        D       A -X   C
Case3    C -X     A       D      B
Case4    D        C       B      A -V
``````

First case is still no go, second one now is invalidated, we would then check case 3.. Also invalid because of Charlie suicidal tendencies, so we are left with case 4, which works fine in this case. You got the idea. If you arrange lists correctly, there will always be an option.

Why one might prefere this convoluted system over something like in Floyd Navarro's answer? Well, this one doesn't necessary result in cyclical hunting when A hunts B hunts C hunts D hunts A, etc. It leaves possibility for A vs C and B vs D duels, if that's something you want. Obviously, this has also it's flaws. This one is more convoluted.

If you don't want to reveal targets, there are workarounds on that too (though a bit more convoluted). Basically, you don't need to reveal lists, only make sure current case is valid. This can be done with help of secret voting sistem a-la Resistance. With N players you have N possible cases. Give each player one "NO" card, since there are only 1 invalid case for each player in their list - selftarget. Then give N-2 "YES" cards (There are N-1 possible voting rounds total, because in worst scenario last case will be selected automatically, and one "NO" card is already given to each player), and players vote for each case. If case not valid for a player, that player selects "NO" card, otherwise it is "YES". Then cards are shuffled and revealed one by one. If all cards are "YES" - the case is valid. If there are at least one "NO" card, the case is invalid and players vote for next case. Note: you shouldn't reval all votes at once because of possible all "NO" scenario, which allows to easily deduce all player's targets. All you need to know is that case passes or not, no more.

Also, now I'm interested myself, are there any games which feature similar system?

Mathematically, if you want to avoid a player drawing their own identity as a target, what you're hoping for is a "derangement" of the targets compared to the identities; a "derangement" is a permutations of a reference set such that no element is in the same place as the reference set. A set of 3 elements {1,2,3} has 5 other permutations, but only two possible derangements: {2,3,1} and {3,1,2}. The number of derangements of a set of n unique elements is given by the subfactorial !n = round(n!/e). As the number of permutations of n unique elements taken n at a time is n!, the probability of a random permutation of the reference being a derangement is n!/e/n! = 1/e ~= 36.788%.

So, in nearly two-thirds of deals (regardless of the number of players) where character identity and target are assigned randomly without replacement, at least one person will end up drawing their own character as a target. This is why Benjamin Cosman's example of "Lifeboat" builds in this eventuality as a special role in the game. The ideal recommendation is for you to do the same, if at all possible.

If you absolutely must prevent a person drawing themselves as a target, the draw has to be "rigged" to remove the person's own character identity from the pool of potential targets. The usual problem with this is that to do so, each person must gain knowledge about the selection process so far, which will be inherent in verifying that their own identity card is not available for selection as of when they choose a target.

What you need is a double-blind. In board games, especially without "electronic enhancement", this typically takes the form of a mediator, someone who ends up inherently knowing everything about the character and target selection process, and therefore cannot participate in the game as a normal player. This person can, behind everyone's back, "manage" the pool of target cards to ensure each person cannot pick themselves, without each of those people knowing whether they're still in the pile or not. However, depending on your game design, this person may have little else to do for the duration of play.

The fairest solution I can think of is:

• The board starts with a character card, a target card, and an envelope (like the one in Clue) for each player, in separate piles.

• Each player in turn will take a character card at random and put it in a new envelope.

• The envelopes will be shuffled.

• Each player will then take an envelope and a random target card, and after verifying the two cards are not the same character, put the target card in the envelope. No other player should know which cards are in that envelope.

• If the last player to put a target in with an identity finds that they are the same (this can happen with an odd number of players; it should not happen with an even number), he'll announce this (without saying which character it is) and will choose one other envelope at random, switching out that envelope's target card (which will now guarantee all the cards are different in each envelope). Nobody else should know any of the cards involved, and ideally, the switcheroo can and should be done so that the person swapping them out does not know the character or target of the envelope he chooses.

• The envelopes are shuffled again, and then everyone draws an envelope giving them both their identity and their target.

Each person will know one character's target, and one person might know two characters' targets. This information is only minimally useful, and only if that person subsequently draws an envelope containing a known character as their target; they will then know which player is their target based on who that player kills. Unfortunately, based on the same math determining whether someone will draw themselves as a target, at least one player will have this knowledge in 2/3 of draws. Overall, however, this method "leaks" much less information to each player than other possible methods of controlling the target pool, without requiring that one participant not be a player because they know too much.

• It sounds like the desired solution is for the players to select a derangement for the game, but not to know which derangement has been picked, only their target. If there are a lot of permutations of which character Ids can be in the game, this could be quite difficult. Never mind the problem that with three players, I know that the player I'm not targeting is targeting me. – Rupert Morrish Oct 6 '17 at 1:06

Is it necessary to have everyone else as a target? If not (because the player number is high enough) just split the players in two equal teams and let each draw only from the other team.

If you have a left over person (for example with a player count of 13), split in half with one left over as third "team", let him draw from one team and then shuffle his name into that pile to make the count correct again.

Is way less effort than the envelope procedure, but has as drawback that you know some people who are "safe" to not have you.