Amidakuji, a lottery from Japan

December 24, 2010 6:11 PM

Amidakuji, or "Ghost Leg," is a lottery party game from Japan. At the top of a sheet there are a number of spaces for people to write their names. At the bottom there are prizes. There are an equal number of each. Between them is a map obscured behind a sheet. The map is made of straight vertical lines connecting the names and prizes. Connecting those lines at random intervals are horizontal lines. When it's time to pick winners, the sheet is removed and players can follow the lines to find their prize. You follow the line from your name down until you encounter any horizontal line, which you must follow, then continue down, continuing to follow all horizontal lines you encounter, until you reach your prize. No two horizontal lines can touch. Provided that, the process is perfectly deterministic and reversable. The same ends are reached whether you follow from the top down or the bottom up. If you have difficulty visualizing this, check the Wikipedia page.

It makes a great lottery setup for gatherings or parties. Many video games use a setup like this, with a visible map but a limited time to study the board, as a bonus, party, or mini-game. Bonus rounds in both Super Mario Land games use amidakuji, it's a staple of the Mario Party series, and Konami released an classic arcade game, a pretty good one too, called Amidar in which the board is a big amidakuji that the enemies move along.

posted by JHarris (18 comments total)

Ghost leg...reminds me of that episode of the x-files with bd wong and lucy liu.
posted by hal_c_on at 6:25 PM on December 24, 2010

The spider boss from Mega Man X seems like a clear amidakuji reference.

Wikipedia confirms.
posted by lumensimus at 6:27 PM on December 24, 2010

That makes sense of this.
posted by foursentences at 6:41 PM on December 24, 2010

I think a more fun version would involve showing everyone the names at the top and prizes at the bottom, then having everyone simultaneously and covertly submitting a slip of paper with 3-5 rung locations to add. That would allow for strategy and mind games in trying to get the best prize.
posted by painquale at 7:08 PM on December 24, 2010 [2 favorites]

Math's ruins everything.
posted by doublehappy at 7:24 PM on December 24, 2010

I've always seen this in manga and anime - especially for game matches and contests but assumed it was just a funky tiering system, I didn't realize it was also the method of selection. Awesome!
posted by yeloson at 7:31 PM on December 24, 2010

painquale, I'd suggest lowering that to just two per player, or maybe even one. It doesn't take a lot of rungs to make for a complicated board. You might need to devise a rule for when two people pick the same horizontal line though. Maybe determine beforehand which "rows" on the board a player's rungs will go?
posted by JHarris at 7:36 PM on December 24, 2010

The last time I saw this it was part of one of the minigames on the Disney Fairies Website (don't judge me!). In that one you have to add and remove the horizontal bars on the fly to make sure that falling items following the path wind up at the right target.
posted by Karmakaze at 7:42 PM on December 24, 2010

I think you want to give people enough rungs to give them the ability to cross long distances across the board. You're probably right that five is way too many though. I think it'd probably be sensitive to the number of players. And I think that if two players chose the same rung, you'd just place a rung there... it's overdetermined.
posted by painquale at 8:05 PM on December 24, 2010

Thank you for finally making sense of Amidst for me. For nigh unto a quarter century I have wondered how ape + paint roller = "Amidar" and you've put it together. A Xmas miracle!
posted by jtron at 8:21 PM on December 24, 2010 [1 favorite]

The number of horizontal rungs is apparently only a matter of complexity in constructing and tracing the board.

I'm curious about creating this as a dynamic structure for parties that accommodates three principles:

• Neither the host nor any other participant can have a chance of knowing how the board will turn out until the final participant arrives- so no precreated boards or legs
• The board is crafted (and in a sense, recrafted) using input from each new arriving guest, so that you don't have to know how many guests will arrive ahead of time to plan out the board (althoughly obviously the board cannot be completed until everyone has been placed)
• The guests themselves effectively create the board, as they arrive, to add an element of interactive randomness and participation

This also doesn't constrain to whether their are a pre-set number of prizes/presents p that may or may not be less than the number of guests g (i.e., you have 3 things to give away but many guests) or a white elephant style where everyone on the board supplies a gift, and g = p by definition.


Assume g is the number of guests, p is the number of prizes, and d is the depth of the board (the number of unique horizontal rows that will be created, assuming each leg by its placement defines a horizontal row). Once the board is created, each guest takes turns tracing their own line

The two basic variations would seem to be:

Horizontal:
If the board is g rungs wide, it can then be g legs deep. This equates to a g by g grid. The guest when arriving writes their name both atop one rung (presumably in the order they arrive, i.e. guest 1 is in rung 1). They would then write their name in a row on the left hand side (the y-axis), in the same order. This creates a grid of names that grows dynamically as guests arrive, starting as a 1x1, then 2x2, etc up to gxg. They then add their name to a scrap of paper, folded up and entered into a bowl. At this point their job is done until the time of the drawing, and they can go enjoy the party.

Once everyone has arrived, the board is created dynamically: each person goes up to the board in the order they arrived (or any other order decided) and for some limited number of integers (say 3 or 4) they draw a name from the bowl and enter a leg that goes to the right of that player's rung. So if Alice, Bob, Carol, Dave, and Eugene are playing and arrive in that order to the party, Alice walks up first, picks Dave's name out of a hat, and in the first row connects a leg from Dave - Eugene. Then she draws her own name, and makes a leg Alice -> Bob in the first row, etc. When she's done there should now be 3-4 legs across the first row of the board, in random places. Alice then puts the names she's drawn back in the bowl, it's shaken up, and Bob now goes up to draw 3 or 4 names the same way, entering them in the second row, and so on. In this way, a board is created by the players themselves.

Since there are only g - 1 gaps between rungs, anyone who draws Eugene/the rightmost name would have to either create a wrap-around leg (an interesting variation, essentially turning the board into a rolled up tube- I assume this is mathematically as valid as a 2D board), or simply have Eugene's name removed from the bowl permanently when it's first drawn. Since two legs in the same row across consecutive rungs is an issue, this could also be solved with a redraw.

Also, for large numbers of participants the board would take a lot of time to assemble as g people would have to go up and draw 3-4 names, and then another round of g people going up and tracing to their price once the board was assembled. Party guests might find this boring to do in two rounds, although I guess you could sense when the drawing is coming near and any new arrivals are basically out of the game, and have people start leisurely taking the first round.

A variation then might be that party guests upon arrival write their name on the top and left in the order they arrive, put their name on a slip of paper in the punch bowl, and the board stays unfinished. However, over the course of the party everyone is encouraged to go up and draw a leg anywhere on the board they want, provided it's not connected to a leg in the next row. When the time comes for the final drawing, one player is picked at random to start, and draws a single name from the punch bowl (which stays removed). They then find this name, and not their own, on the top, and trace down. Once they've finished, they then hand control over to the person who's name was drawn, and that person draws a new name, traces down, and hands control over, etc. In this way the board is assembled with legs such that- despite seeing and controlling the board layout, no guests know which rung they are on until they're up at the board, tracing their path out.


Vertical:
A vertically driven arrangement has the benefit that the number of guests g is relatively unimportant, as the depth d can be predetermined (however, for mobility reasons I'd think you'd want a depth large enough to ensure the last arriving guest has the possibility of traversing to the first rung). Each person as they arrive writes their name on the board at the top in the next available rung, and also picks or randomly chooses (rolling dice, drawing from a hat, etc) a limited number of integers, say 3-4, from the set of 1 to d. They then draw those legs in the appropriate rows connecting their rung to the next rung (and again, the final person to arrive will have to either not participate, or do a "wraparound" rung). Depending on whether the prizes/presents at the bottom are known ahead of time- and if their are a limited number- if the players are choosing their numbers they might be able to game the board to some extent. This might be defeated by simply writing d out in random order on the left hand side before they pick, so they can't see where their actual choices are going to place.

This has the advantage over the horizontal method of having players create the board upon arriving and not have to worry about it after that point, as well as ensuring that the first arrival has something to do, and the board resizes dynamically as people arrive.

In addition, the last variation of the horizontal method could work here: let people draw in the board as they arrive and forget about it, but add their names to a punch bowl as well such that people trace from the name they draw, and not their own.


I think for a gathering where the turnout is going to be wildly variable, the vertical method of board assembly works best; for those where the number of guests are likely to be fewer in number and/or likely to not vary by more than 1-2 from what the host expects the horizontal method could be fun. In both cases the "draw a name to decide where you trace from" adds a layer of chance that avoids frustrations that people can game the board.
posted by hincandenza at 9:47 PM on December 24, 2010 [2 favorites]

Man, this is a seriously beanworthy plate. I love it when minutiae like this turn out to be so gloriously overthinkable.
posted by nebulawindphone at 9:58 PM on December 24, 2010

You could use it as kind of a blind secret santa chooser, too, using the bottom row as a reflector. Cover the names, have everyone draw in a rung or two. The coordinator would trace from your name to the bottom, move one to the right on the bottom list (wrap around to #1 from the last one), then trace back up to find the match. Nobody would get themselves, and the person you give to would be guaranteed (i think) not be the person that gives to you.
posted by ctmf at 10:45 PM on December 24, 2010

I've encountered this game in Korea, where it is called sadari (ladder). Typically, instead of allocating prizes it's used to distribute the cost of something like eating takeaway food on a Friday afternoon at the office. Instead of just splitting up the cost evenly, you can end up eating cheaply or expensively, depending on your luck. It also selects someone who eats for free, but actually has to go and buy the food.
posted by L.P. Hatecraft at 10:56 PM on December 24, 2010

The only problem with that, hincandenza, is that it completely obliterates amidakuji's prime virtue: simplicity. If you're going to do all of that, then why not just draw from a hat and assign prizes based on that?
posted by JHarris at 11:50 PM on December 24, 2010

It also selects someone who eats for free, but actually has to go and buy the food.

Exactly the person who really shouldn't be buying....
posted by JHarris at 11:51 PM on December 24, 2010

My six-year-old son, who, it seems, is Japanese, did this about 10 days ago to choose who went first in a board game.
posted by planetkyoto at 6:46 AM on December 25, 2010

Almost exactly the same as the "Rabbit Trap" game I used to play in the US as a kid.
posted by cdc at 8:45 PM on December 26, 2010