random.md: wip

Signed-off-by: Ian Jackson <ijackson@chiark.greenend.org.uk>

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 RANDOM INITIAL BAG NOTES
+========================
+
+We don't understand the balance implications, which are likely to be
+nontrivial, so both players should get the same starting bag.
 
 
 I. Garlic
+---------
+
+# Assumption 1
+
+(Pretty certain.)  The total amount of garlic is important.  It must
+be 11 (4x1 + 2x2 + 3) until the 1 extra gets added.
+
+# Assumption 2
 
-Assumption 1. (pretty certain): The total amount of garlic is
-important.  It must be 11 (4x1 + 2x2 + 3) until the 1 extra gets
-added.
+(Doubtful, may needs testing.)
 
-Assumption 2. (doubtful, may needs testing): the amount of "big"
-garlic vs "small" garlic chips is important.  Reify this as: the total
-number of garlic chips must remain (roughly) the same.
+The amount of "big" garlic vs "small" garlic chips is important.
+Reify this as: the total number of garlic chips must remain (roughly)
+the same.
+
+# Options
 
 With assumptions 2, there are only the following garlic compositions
 possible:
 
-  2x 3-garlic                5x 1-garlic
-  1x 3-garlic  2x 2-garlic   4x 1-garlic   <- standard
-  0x 3-garlic  4x 2-garlic   3x 1-garlic
+X.  2x 3-garlic [4]                     5x 1-garlic
+Y.  1x 3-garlic [2]   2x 2-garlic [2]   4x 1-garlic   <- standard
+Z.  0x 3-garlic       4x 2-garlic [4]   3x 1-garlic
 
 (Proof: there are 7 garlic chips, each of at least 1 garlic.  That
-leaves 4 "surplus" garlic to distribute amongst otherwise-identical
-chips.)
+leaves 4 "surplus" garlic ("[]") to distribute amongst
+otherwise-identical chips.)
 
 With assumption 2 weakened to "roughly" (ie, +1/-1) there are the
 following additional possibilities:
 
-1 fewer garlicky chips (more lumpy garlic, 5 "surplus"):
+1 fewer garlicky chips (6, more lumpy garlic, 5 "surplus"):
+
+P.  2x 3-garlic [4]   1x 2-garlic [1]   3x 1-garlic
+Q.  1x 3-garlic [2]   3x 2-garlic [3]   2x 1-garlic
+R.  0x 3-garlic       5x 2-garlic [5]   1x 1-garlic
+
+1 more garlicky chips (8, less lumpy garlic, 3 "surplus"):
+
+S.  1x 3-garlic [2]   1x 2-garlic [1]   6x 1-garlic
+T.  0x 3-garlic       3x 2-garlic [3]   5x 1-garlic
+
+With assumption 2 removed entirely, there are many other possiblities
+but they seem very strange.
+
+
+# Suggested Variant Garlic A
+
+Prepare, for each player, one each of X Y Z.  Choose secretly and
+randomly.
+
+# Suggested Variant Garlic B
+
+Same, but include P..T.  Players are entitled to count their
+chips so they will know the difference between XYZ/PQR/ST.
+
+
+II. Non-garlic
+--------------
+
+Standard load is 1 pumpkin (¤3) plus 1 green (about ¤5).
+
+Options would seem to include:
+
+ * Replace the green with a red, blue or locoweed.  These are
+   available at this point and relativity uncontroversial (although
+   probably of higher value, albeit that the locoweed is not very
+   interesting).
+
+ * Replace the green with a black.  This is interesting because 
+
+
+
+
+III. Mechanics
+--------------
+
+# Random choice
+
+To choose secretly and randomly between identical-looking sets of
+containers (let's call them bags, supposing they're XYZ from "Garlic",
+above).
+
+A computer will be involved.  It will produce two sets of secret
+output, one for player 1 and one for player 2 (WLOG there are at least
+2 players)
+
+All players collaborate to parepare bags, one for each player,
+according to each of XYZ.  So now (for eg two players) we have bags:
+  X0 Y0 Z0
+  X1 Y1 Z1
+Place these in pairs in locations labelled X, Y, Z.  So we ahve:
+  X: bag, bag, ...
+  Y: bag, bag, ...
+  Z: bag, bag, ...
+
+Everyone but player 1 leaves the room.  Player 1's secret output
+instructs them to move bag-pairs X Y Z to new locations alpha, beta,
+gamma, according to a random permutation.  Now we have:
+  alpha: bag, bag, ...
+  beta:  bag, bag, ...
+  gamma: bag, bag, ...
 
-  2x 3-garlic  
+Everyone but player 1 leaves the room.  Player 2's secret output
+instructs them to select one of alpha, beta, or gamma.  The others are
+put aside:
+  selected: bag, bag, ...
+  discarded: many bags
 
+At the end of the game, everyone must reveal their bags.  Perhaps we
+declare that at the start of round 5 (at the extra garlic) everyone
+must do so, and after that people may look in their bag.
 
 
+# Combination
 
-Without assumption 2, there are many other possiblities.
+If multiple choices must be made, containers other than bags can be
+used.  Eg 35mm film canisters.  They must be unloaded into the bags by
+the players, without looking at them.