Keeping It Fair

June 9, 2015 11:16 AM

You're sitting down with your friends to play a boardgame, and you find yourself in a conundrum: how do you choose a first player? Sure, you could roll a standard die and take highest number, but what if there's a tie? That could take forever! Besides, wouldn't you rather be mathematically sure that everyone has a fair shot at each spot in the turn order? Of course you would!
posted by tocts (57 comments total)

But...how do they pick who gets to pick the first Go First Die out of the bag?
posted by Elly Vortex at 11:23 AM on June 9, 2015 [9 favorites]

Spin 4 It 4 lyfe!
posted by Windopaene at 11:23 AM on June 9, 2015

Very interesting! That the first 4d12 "Go First" set was discovered by hand is surprising to me. I suppose it's just twelve orderings of four numbers (1, 2, 3, and 4 are always going to be the first numbers on separate die, etc.), but the checking by hand must be incredibly tricky.
posted by brecc at 11:23 AM on June 9, 2015

Overthinking a plate of beans dice.
posted by HuronBob at 11:24 AM on June 9, 2015 [1 favorite]

Youngest player goes first, do these people even boardgame?
posted by prize bull octorok at 11:28 AM on June 9, 2015 [8 favorites]

Is it Pandemic where the first go is the most travelled player? I'm sure there is some other fairly popular modern board game that is officially oldest first, which has paid off for me pretty well. No doubt this is now symbolic of the dead hand of the gerontocracy on our society.
posted by biffa at 11:31 AM on June 9, 2015 [1 favorite]

Cards Against Humanity has it right.
posted by jeffmik at 11:31 AM on June 9, 2015 [3 favorites]

My favorite method for deciding who goes first: The player that got up earliest in that morning.
posted by Gygesringtone at 11:32 AM on June 9, 2015 [1 favorite]

But...how do they pick who gets to pick the first Go First Die out of the bag?

By spilling the blood of a raven over a crystal chalice at midnight beneath the light of the Hunter's Moon. Galthor the Blood God will appear and tell you who goes first, and Galthor is always fair.
posted by Sangermaine at 11:34 AM on June 9, 2015 [12 favorites]

Easy, my whiny little son goes first. Otherwise we're all gonna have an awful time.
posted by bondcliff at 11:36 AM on June 9, 2015 [3 favorites]

Letter closest to the beginning of the alphabet goes first.

...wait, there are board games without letter tiles?
posted by Daily Alice at 11:39 AM on June 9, 2015 [3 favorites]

Is it Pandemic where the first go is the most travelled player?

According to the online version of the rulebook it's the player with the highest city population among city cards in their hand, but it was originally the player who was most recently sick.

For Forbidden Island it's the player who was most recently on an island. For Love Letter, the player who was most recently on a date (causes problems when played with couples).

Ah, sure enough there's a BoardGameGeek forum for this.
posted by jedicus at 11:41 AM on June 9, 2015 [2 favorites]

In Pandemic (at least the first edition), the first player is the one who was most recently sick.

In Forbidden Desert, it's the player who's thirstiest.

In Fiasco, it's the player who's from the smallest town. (In practice this tends to work out as 'person who's played Fiasco before goes first.)

None of these are games where being the first to go should give you any advantage where winning is concerned, though I'm sure with Pandemic and Forbidden Desert you could strategize who is the best player to go first based on the roles you drew...

...And die in the desert anyway...
posted by Jeanne at 11:41 AM on June 9, 2015 [1 favorite]

By spilling the blood of a raven over a crystal chalice at midnight beneath the light of the Hunter's Moon. Galthor the Blood God will appear and tell you who goes first, and Galthor is always fair.

But...how do you decide whose turn it is to bring the crystal chalice?
posted by Elly Vortex at 11:50 AM on June 9, 2015 [1 favorite]

Whoever guesses the 17-digit prime I'm thinking of, goes first.

I've been waiting 43 years to get this stupid game started.
posted by blue_beetle at 11:55 AM on June 9, 2015 [3 favorites]

Easy peasy. Thunderdome. Four players enter. One player leaves...And goes first!
posted by Samizdata at 11:56 AM on June 9, 2015

(Although this does remind me of the endlessly grognardy discussions about brands of dice and dice bias back in the day...)
posted by Samizdata at 11:57 AM on June 9, 2015

In Fearsome Floors, the player that looks most like the monster, Furunkulus, goes first.
posted by MsVader at 11:59 AM on June 9, 2015

Paper rock scissors or oldest player for grown-up games / youngest player for kid games.
posted by resurrexit at 12:00 PM on June 9, 2015

(Although this does remind me of the endless grognardy discussions about brands of dice and dice bias back in the day...)

Dice Bias is my favorite Grognards EP!
posted by jason_steakums at 12:00 PM on June 9, 2015 [3 favorites]

Is it Pandemic where the first go is the most travelled player?

Others have covered Pandemic, but if memory serves me correctly, the "most traveled" is Ticket to Ride.

Munchkin deliberately does not specify how to determine the first player, leaving it up to the players to argue agree to it. Thus it sets the tone of the entire game.
posted by Gelatin at 12:02 PM on June 9, 2015 [2 favorites]

Pinkie length.
posted by Artw at 12:07 PM on June 9, 2015

I have one game where the player who most recently ate fish goes first.
posted by jeather at 12:09 PM on June 9, 2015

The person who is explaining how to play the game goes first! That way you get a demo round.
posted by ApathyGirl at 12:17 PM on June 9, 2015 [3 favorites]

Artw: "Pinkie length."

Doesn't work if you leave anything choppy near me. Suddenly I am the only one with pinkies. Dunno what happens, but it does.
posted by Samizdata at 12:21 PM on June 9, 2015 [2 favorites]

The person hosting the game goes first out of courtesy. Unless somebody brought snacks. The person who brought the best snacks ALWAYS goes first.

If it's just family, the worst sport goes first so everyone else can just enjoy the game.
posted by kinnakeet at 12:22 PM on June 9, 2015

It’s the most comprehensive system ever devised for choosing who starts a game.
posted by a lungful of dragon at 12:28 PM on June 9, 2015 [5 favorites]

In Cartagena, the player who looks most like a pirate goes first. Funnily enough (but unsurprising, if you know board gamers) there will always be one player who looks a lot like a pirate.
posted by Paragon at 12:32 PM on June 9, 2015 [3 favorites]

I normally interpret "youngest goes first" to mean there's a slight advantage to going first, which makes sense in the context of a family game, but not as much when everyone's middle-aged.

A lot of games give some other silly rule for how to choose the start player, but a lot of the criteria aren't very dynamic (e.g., most traveled), and when you often play with the same group, it's nice to mix things up sometimes. We almost always just take a piece from each player, jumble them up, and pick one. In the rare case we want more apparatus, the iOS app Chwazi Finger Chooser is quick and fun.

Of course all this is just the pretense of the actual linked article, not the actual reason for it. The actual reason for it to nerd out about the math and probability and dice and stuff. For which I rate this a complete success!
posted by aubilenon at 12:33 PM on June 9, 2015 [2 favorites]

What up Eric! Aside from creating an extraordinary number of strangely smart dice, Eric is also one of the best puzzle designers in the world; I was lucky enough to work with him on Perplex City and The Code, among various other smaller projects. And then there's the small matter of his Lego work, which includes the head of Conan O'Brien.

My favourite Eric anecdote is when we worked on the Perplex City San Francisco live event. Having driven across the country in a couple of days, he proceeded to spend a large amount of time sleeping on the couch of our rented apartment. As is usual with the run up to live events, pretty much everything that could go wrong did go wrong, requiring the best and only solution we knew of: make more puzzles!

But what kind of puzzle? I thought out loud: "It's got to occupy a large group of people for a few hours... but it can't be some crazy encrypted code. It needs to be easily comprehensible."

Eric sensed we were in dire straits, roused himself from his slumber, sat in front of a laptop, and produced a jigsaw-maze that spread across hundreds of sheets of paper. At the live event, I was pleased to see all sorts of people, young and old, merrily working on the jigsaw-maze.
posted by adrianhon at 12:51 PM on June 9, 2015 [4 favorites]

Historically with me it's gone:

1. If you're playing Scrabble, everyone chooses a tile out of the bag. The person with the tile closest to the alphabet goes first.

2. If you're playing any other game, one person just declares that they'll go first and everyone else decides not to care because it is just a board game for the love of gods and little fishes
posted by EmpressCallipygos at 12:51 PM on June 9, 2015

Easier solution: chess. White always goes first.
posted by graymouser at 1:03 PM on June 9, 2015 [1 favorite]

Didn't read the article. I Ctrl-F "finger" and get no hits. Why on Earth would you use dice for something so simple?

My friends called this "roshambo" when they taught it to me, although I seem to find it described on the Wiki page about "Morra".

Pick someone at random to be "Zero" - it doesn't matter who. As in "Rock Paper Scissors", everyone together hits their fists 3 times. Instead of holding out a rock, paper, or scissors, each holds out the random number of fingers of their choice (0-5). Count how many total fingers the group is holding out. Then, start counting that many from person zero.

I believe this is as simple, perfectly random, and fair as can be.
posted by polecat at 1:12 PM on June 9, 2015

Youngest player goes first, do these people even boardgame?

No, not for games more complex than things like Candy Land.

This is actually my least favorite thing about the board gaming renaissance, the tendency of designers to suggest different whimsical ways to pick who goes first, but actually put them in the rules, so they look like they should have the force of law. I'm sure you're a design genius, Mr Name-On-The-Box, and you claim there is no advantage to going first so why not use some silly way to determine turn order?

Well because in practice, the means suggested is such that one player always goes first. Player who comes from the city with the most people? Player with longest beard? Player who's most recently been abroad? In practice, this changes very rarely, and so the same player usually goes first. And while he might not have a direct advantage, it does restrict the interest of the game, by exposing players to fewer situations.

And as for the youngest player going first, that implies the game is such that first player gets an advantage, which is often not the case, or at least not directly so. Instead, the youngest player, who would be the most likely to need help to learn and play the game, should ideally go last, as he'll see how the game is played from the example of the other players, and they may also be able to suggest a good action to him based on the progress of the other player's moves.

If you're playing any other game, one person just declares that they'll go first and everyone else decides not to care because it is just a board game for the love of gods and little fishes.

Not for the current class of serious board games. Even if there's no direct advantage to going first, some strategies may only be viable for the first player, or it may cost other players some resource to usurp the first player position. For Monopoly, well, who cares? But for Agricola, or Caylus, or Puerto Rico, or Power Grid (beloved Power Grid), choose randomly.
posted by JHarris at 1:15 PM on June 9, 2015 [4 favorites]

JHarris - I think my point is that my friends and I aren't as entirely caught up in the strategy element of board games, nor are we in the habit of playing board games that require so much strategy, so we kind of don't care.

(Actually, the one board game I play most of all is a two-person game where you actually play two rounds, one as black and one as white, and the winner is "whoever lost the fewest number of pieces when you were white" or something).
posted by EmpressCallipygos at 1:19 PM on June 9, 2015

My friends called this "roshambo" when they taught it to me, although I seem to find it described on the Wiki page about "Morra".

The method described is not random at all, just like Rock, Scissors, Paper isn't random, but is instead vulnerable to player psychology, and the fact that the number of player seats isn't the same as the number of fingers the players have. Dice are cheap and plentiful. Roll dice. Or get this, someone use their smartphone to Google "roll a die," which will prompt the search engine to instantly give you a random number from 1 to 6. Reload the page several times and there you go.

You still have to decide who is player "zero," and because it does ultimately matter, statistically, who that is, the problem remains, if somewhat diluted.
posted by JHarris at 1:23 PM on June 9, 2015

Is okay EmpressCallipygos, if it seems like I'm unusually invested in the answer to this question, it's because we have to answer it very frequently, on the average of more than once a week, and sometimes several times in a day.
posted by JHarris at 1:25 PM on June 9, 2015 [1 favorite]

A fair point, JH.
posted by EmpressCallipygos at 1:34 PM on June 9, 2015

This method also suffers from at least 2 players giving each other the finger each time. At least in my experience.
posted by biffa at 1:43 PM on June 9, 2015

The player who goes first is the player who has gone the longest without directly quoting a piece of pop culture.
posted by jason_steakums at 1:50 PM on June 9, 2015 [6 favorites]

Bruges has the fairest start method of the games I own - the player who most recently ate Belgian chocolate. On the other hand this can sometimes come down to the halfsecond if your group is eating Belgian chocolate directly before playing.

We will deal, though.
posted by xiw at 2:23 PM on June 9, 2015

Loot Letter has the player go first who most recently encountered a wandering monster in the wild. I like this because it encourages story-telling.
posted by daisyk at 2:31 PM on June 9, 2015 [1 favorite]

LotR LCG solo player here. First player is always me.
posted by turbid dahlia at 2:32 PM on June 9, 2015 [2 favorites]

Here's a low-tech method for randomly sorting players:

Cut up a piece of paper to make cards or tickets, and make as many numbered tickets as people in the game. So if there's five of you, make five tickets with the numbers 1, 2, 3, 4, 5. Put them in a bag or box. Take turns to take one out at random (except the last person, who can only take the last one). As long as the pieces of paper are not distinguishable, and nobody cheats by looking at which ticket they're picking, the result is a random ordering of the players.

Proof: What's the probability that you will draw number 1?

- If you are the first to draw, it's 1/n. In the above example, 1/5.

- If you're the second to draw, it's the probability that the first player didn't get number 1 (n-1/n, or 4/5 in the above example) multiplied by the probability that you will get it: 1/n-1, or 1/4. 4/5 * 1/4 = 1/5.

- You're the third to draw. The probability that neither the first nor the second players got number is (and I will only do the example numbers from now on) 4/5 * 3/4, or 12/20. The probability that you will get the number 1 ticket is 1/3. Multiplied, that's 12/60, or 1/5.

- You draw fourth. The probability that ticket number one is still in the pot is 4/5 * 3/4 * 2/3. That's 24/60, or 2/5. Your probability of picking one ticket out of two is 1/2. That makes your chances 1/5.

- You draw last. You can't choose, you just pick the one that's left. I could do the same calculations as before, or just note that, by the time you've taken your card, number 1 will have been drawn, with 100% probability. Since each of the four previous players drew a ticket sight unseen with probablity 1/5 of taking number 1, your chances that the number 1 is still there are 1 - 4/5 = 1/5.

So all five players have the same chance to get number 1, and by the same reasoning, to get number 2, number 3, etc. for any number N of players. If you don't trust the other players and you have a small child around, you can ask a small child to draw the numbers in turn for each of the players.

However, many people may not have a small child lying around. Also, most people don't know or won't want to understand probability, and will feel this is an unfair way to random sort any number of players, and will claim that the first person to draw had an advantage over the last person, and will want to buy the cool random ordering dice, which are cool but not half as cool as knowing and using probability, and building and using your own ad-hoc tool.

In theory, the short straw method is also fair on everyone, including the last player, except that you can very easily force choices on others, so in practice it never is. Numbered tickets in the pot is better.
posted by kandinski at 3:00 PM on June 9, 2015 [3 favorites]

The third-edition of Once Upon a Time has my favourite, and not just because I thought of it: draw a card from the story-deck, and the player who most closely resembles the picture on it starts the game.

Oh, the arguments. The denials. The severely pissed-off goth guy in a demo game who everyone agreed looked exactly like the Stepmother card...
posted by Hogshead at 4:24 PM on June 9, 2015 [3 favorites]

Polecat's method is similar to the "remainder game" called "a random method" in the So Long Sucker [pdf] description.

If it's good enough for Hausner, Nash, Shapley, and Shubik, it's good enough for me. I heard Nash knows something about games.
posted by ctmf at 5:41 PM on June 9, 2015

I recently learned of a "card game" called Start Player that will give you fun conditions for picking the start player. Also an iOS version. Examples:

The player with the most 7's in their phone number is the Start Player.
The player who has most recently spoken to his or her mother is the Start Player.
The player who owns the most computers is the Start Player.
posted by segfault at 5:55 PM on June 9, 2015

Pick someone at random to be "Zero" - it doesn't matter who.

It does, actually. If you allow zero fingers then Player Zero benefits, because Player Zero gets to win on zero, whereas all the other players can only win if there is at least one finger showing.

Also and otherwise, there may be some bias in the average number of fingers people use. If such a bias exists (I think it probably does) then the results will be biased towards Player Zero and against players furthest away from Player Zero.

E.g. If players always hold out two (or three or four) fingers then Player Zero would always win.
If players almost always hold out two fingers, but occasionally one or three, then Player Zero will win if all players have held out two fingers or if the number of players holding one finger balances the number of players holding three fingers. Und so weiter.

It's possible that biases can favor other players, but that's a more complicated analysis which I will gladly leave to the reader while I get some coffee.
posted by Joe in Australia at 6:06 PM on June 9, 2015 [1 favorite]

Hogshead, at least that beats the "longest beard" criteria from an earlier edition.
posted by JHarris at 6:21 PM on June 9, 2015

Do you all not have decks of cards in your game box? Cut for lowest or highest; suits in bridge or 99 order.

jedicus: "For Forbidden Island it's the player who was most recently on an island."

But what if you are on an island?
posted by Mitheral at 7:13 PM on June 9, 2015 [1 favorite]

But what if you are on an island?

Leave the island immediately.
posted by aubilenon at 7:24 PM on June 9, 2015 [5 favorites]

I decided that I would test the "roshambo" method I described above with an Excel spreadsheet. I don't know if this is an effective way of file sharing, but I uploaded the spreadsheet on Gigasize.

If each of N players can choose 0-5 fingers, and each player chooses randomly with equal distribution, then the probability of each total is the same as the probability of a number being rolled from N 6-sided dice (where N is subtracted from the totals because the dice have numbers 1-6 instead of 0-5). After fetching the probabilities of rolling 1 die through 5 dice from http://anydice.com/ , I created tables to compute the probability that each player gets to go first.

Conclusions:

* The probability of any player getting to go first is equal, or else damn close.

* The probability of who goes first is not conditional on which number you yourself pick.

* Since each player gets equal probability, it does not matter who is player 0.

I'm actually a little bit surprised, because until now I my assumptions about this were based on a very intuitive sense that is was plenty-random-as-need be. However, it seems to be very rigorously and precisely fair.

Take a look at the spreadsheet and let me know if you see a flaw in my assumptions. The only flaw I can see is that players won't choose their number of fingers with equal distribution. However, I'm pretty sure that I've just done at least a hundred times more analysis of this problem than anyone I'll ever play with, and given that the payoff of working this system is almost certainly very low, I'm doubt I or anyone else is going to bother coming up with some rule for how to fractionally increase one's own chance of having a better standing in the game.

Now to go have a look at ctmf's link...
posted by polecat at 8:48 PM on June 9, 2015 [1 favorite]

OK, thanks, ctmf, for the link. Now I know that this is commonly called "The Remainder Game" (also known as Horsengoggle). I find it repeatedly advocated by this guy who has also brought it up in numerous discussions on boardgamegeek.com. Here is the most (tediously) in-depth discussion of it that I've found. Nobody shows their work (what I really want is to see somebody show their work), but there is a consistent claim that it is slightly biased toward player 0 and those closest after. I found somebody matched the same 24.85% 25.00% 25.15% 25.00% values that I computed for 4-player. Not perfect, but close enough for my purposes.
posted by polecat at 9:35 PM on June 9, 2015 [1 favorite]

Wouldn't the zero-bias be solved by just making all-zero the only disallowed result? All-zero, everyone drinks, do over.
posted by ctmf at 10:06 PM on June 9, 2015

Some of these are house rules and some official.
Pandemic: Who was sick most recently.
Ticket To Ride: Who's been to the most destinations on the map.
Carcassonne: "Roll" all your meeple. You get one point for each one standing on an edge (not flat on its side). Most points wins.
Tzolk'in: Player who most recently sacrificed something (game is themed around the Aztecs).
Love Letter: Player who most recently went on a date.
posted by EndsOfInvention at 3:22 AM on June 10, 2015 [1 favorite]

The linked article gets lost trying to find a set of die that are permutation-fair for 5 and 6 people. But I can only remember a few times when we've reseated ourselves to be in a certain order, and unfortunately I cannot remember why we bothered in those cases. It seems far more common that we all get seated, and merely decide who goes first, and play in the order seated.

Do other people usually reseat themselves to be in order for fairness, or is my board game group not nearly as hardcore as I like to imagine?
posted by fragmede at 3:24 AM on June 10, 2015

Trains: Last person who was on a train

Haven't checked the first player rule for Trains: Rising Sun. Presumably the last person who was on a train...in Japan?

(Trains is awesome btw)
posted by turbid dahlia at 5:15 AM on June 10, 2015