From: Ian Jackson Date: Fri, 26 Nov 2021 00:07:41 +0000 (+0000) Subject: random.md: wip X-Git-Url: http://www.chiark.greenend.org.uk/ucgi/~ianmdlvl/git?a=commitdiff_plain;h=313b8e2b641960807ac7ed8664c6db509c969380;p=quacks.git random.md: wip Signed-off-by: Ian Jackson --- diff --git a/random.md b/random.md index 8bd6ef5..cfcf257 100644 --- a/random.md +++ b/random.md @@ -1,35 +1,127 @@ 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.