8 ms·
A pair of dice which never roll 7 (2004)
- rixed 5y agoYou could also allow some labels to be negative. For instances, dice (3, 4, 4, 9, 10, 10) and (-1, 0, 1, 1, 1, 2) result in all numbers from 2 to 12 without 7, but obviously not with the same outcome distribution. It's also not possible without repeating some labels.
- deleted 5y ago[deleted]
- OscarCunningham 5y agoYour negatives aren't necessarily. You can subtract 2 from everything on the first die and add 2 to everything on the second die.
- rixed 5y agoYes indeed, I hadn't noticed that.
- dang 5y agoOne thread from long ago: A Pair Of Dice Which Never Roll 7 - https://news.ycombinator.com/item?id=292070 https://news.ycombinator.com/item?id=292070 - Sept 2008 (9 comments)
- octonion 5y agoThis is a very tricky problem. We want dice that generate outcomes of two fair dice but no 7s, and every other outcome having the same relative probabilities. Note the generating function (x + x^2 + x^3 + x^4 + x^5 + x^6)^2 - 6x^7 has no nontrivial factors, so we must get creative. My first solution was to consider the generating function x^2 + 2x^3 + 3x^4 + 4x^5 + 5x^6 + 5x^7 + 4x^8 + 3x^9 + 2x^10 + x^11 = (x^6 + x^5 + x^4 + x^3 + x^2 + x) (x^5 + x^4 + x^3 + x^2 + x). So we can do it with a standard 6-sided die and a 20-sided die with 4 each of 1,2,3,4,5. If you roll a 7 or more, add 1. My solution is completely different from anything mentioned in the article. I actually like my solution much more, as it uses two readily available Platonic solids. You don't even need to renumber! For the D20, you can divide the face number by 4 and ceiling, or mod 5 and add 1.
- Veedrac 5y agoThere's a more obvious interpretation here. After you've rolled one die, there is exactly one other roll for the second die that could produce a 7. If you remove that possibility, you have a d5, still numbered 1-6 but with one of those digits missing.
- octonion 5y agoExcellent point!
- Pamar 5y agoWait, let me see if I got this right... I use a Red die and a Blue Die. Blue die is considered "secondary" (in the examples below, the second number is always taken from the blue die), and both dice are thrown together. - I roll 4+2 - result is 6 - I roll 4+6 - result is 10 - I roll 1+6 - result is 1 - I roll 3+4 - result is 3 - I roll 4+3 - result is 4 Correct?
- nihakue 5y agoBut this messes with the distribution (you now have two ways of rolling a 2: 1,1 and 2,5) and makes outcomes like '1' possible (1, 6), which shouldn't be
- 5y ago
- nobrains 5y agoWhy make face 7 blank? Why not keep 0 dots under it to make it the lowest priority? Would that mess up the probabilities?
- arketyp 5y agoYes. You would have to re-roll the C dye until not 7. Spared re-rolling both dice though.
- PostThisTooFast 5y ago
- BiteCode_dev 5y ago> re-rolling a pair of dice until you get a result you like seemed ugly. ... then proceed to: - create an entire new pair of dice for 2 turns of a game they play once in a while - one die now has 2 values on each face with separate meaning - for the first 2 turns, you have a special procedure to read the value of the dice that is quite convoluted I understand the fun of it, but that's also how I see code being written in the corporate world, and that makes me sad.
- scoot 5y ago> the dices "The dice". Single "die", plural "dice".
- BiteCode_dev 5y agoFrench here. Thank you.
- austinjp 5y agoJust to further complicate things.... native English speakers often use "dice" as the singular i.e. instead of "die". While technically incorrect, it's very common, probably more common than the "correct' form. The plural is "dice" and unfortunately "dices" is definitely incorrect :-) English is crazy.
- shibbidybop 5y agoI’ve even heard people use “die” as both the singular and plural! It’s the only singular/plural pair I know of where 3 of the 4 permutations show up in common parlance. I’ll be thrilled if I ever hear someone use dice as sing. and die as pl.
- debo_ 5y agoSome constructs in English can indeed feel a bit dicey.
- 5y ago
- outsidein 5y agoWhy not simply take the dice result not literally, but as index to a mapping table there 2 or 12 is swapped with 7?
- outsidein 5y agoOr use 1 dice 1..6 and one dice 5..10 The result should be (excel syntax) mod(d1+d2;12)+1. You can adjust the lowest start number of dice 2 to control which result gets the highest probability
- abdulhaq 5y agothat would change the probability distribution of the remaining numbers, which is to be avoided
- deleted 5y ago[deleted]
- nicexe 5y agoIf this is just for the sake of not rolling 7 you can have a die with just odd numbers like 1, 3, 5, 7, 9, 11. Having 2 of them guarantees an even sum. Of course you would have gaps between the possible outcomes but not rolling a 7 is already a gap.
- wartijn_ 5y agoBut it's not just for the sake of not rolling 7, it's about avoiding only that number to improve Catan. If you can't roll any odd number in the first few rounds, tiles with those number become way less valuable, which changes where you want to place your villages, which affects the entire game.
- goldenkey 5y agoThe 7s can be replaced with 0s to fill in some of the gaps and allow for odd number rolls.
- deleted 5y ago[deleted]
- kej 5y agoFor a while they sold a pack of 36 cards as a Catan accessory, labeled with 2 through 12 in the same frequencies as two six sided dice, and instead of rolling the dice you flip over the top card and then you shuffle them and start over when you reach the bottom. It's an interesting change to gameplay, since the numbers are no longer independent and the gambler's fallacy ("I haven't had a 12 for a while, so it's more likely to come soon") actually makes sense here. You could restore independent numbers by reshuffling the entire deck after each turn. That seems like an easy way to get the results from the article, without worrying about biased dice or repainting. If you want to alter the deck's probability you can just add or remove cards.
- wartijn_ 5y agoO that's really interesting. I've been thinking about making something like that myself, didn't know there was an official extention. I think it should improve the game when you remove a bit of luck with this.
- asciimov 5y agoThe dice deck is alright, but just alright. Even if you include the card that tells you to reshuffle the deck, the bell curve is just too smooth. If you have a roll drought, you know that deluge is on its way. The best thing I have done for dice in my Catan set is to include a bag with a random assortment of 6 sided dice. At the beginning of a new game we randomly pick two dice. The random sizes, materials, and origins of manufacture keep the clustering of rolls inconsistent from game to game, which makes the game more enjoyable.
- wes-k 5y agoCatan universe has a “card stack” mode where they take two sets of those 36 card decks and randomly remove 18. You end up with some randomness but much better bell curves on dice distribution. My friends and I debated for a while but once we switched to using card stack we never went back.
- mizzao 5y agoI thought I was going to read some article that explained some sort of Stuff Made Here type electronically loaded dice that communicated with each other to avoid landing in positions that added up to 7. The mathematical approach is more elegant, but less hacker
- deleted 5y ago[deleted]
- foobarian 5y agoI had some fun with something similar by printing a 6-sided die with one of the numbers appearing twice, and one missing. If one is not looking for it it is very hard to spot randomly. I had the kids roll the trick and store-bought dice some 200 times, and record the rolls on a chart. At some point it clicked :) Also a good demo of randomness and what it actually looks like in practice to be "fair" vs. "not fair".
- fho 5y agoThe board game Glow kind of does this. There are only five symbols of interest which allows for having color coded dice with an additional side of that color (eg red dice have an additional fire symbol). Beautiful artwork, 4/5 game play, definitely recommended.
- thfuran 5y ago>Now the procedure is: roll both dice. To find the total, choose whichever of the two uppermost faces shows more dots. To find the red number, take the red number shown on the even (R) die, and modify it by the amount shown on the odd (C) die if any. If an addition takes you above 6, subtract 6 from the result; if a subtraction takes you below 1, add 6. [...] The mechanism I've described above works nicely on paper, but unfortunately it has a practical disadvantage, which is that it's unusually sensitive to imperfections in the dice. While this is interesting, it hardly seems like potential nonuniformity due to unbalanced dice is the big issue here. I'd consider this an unusually complicated and awkward dice counting mechanic in a ttrpg. For a casual boardgame, it is beyond the pale.
- riversflow 5y agoI agree, cool problem solving, but ultimately a contrived solution. I found the next bit after your quote quite funny after thinking of this solution right away while reading. >A really obvious alternative approach would have been to roll a d6 (labelled 1-6 as usual) and a d5 (also labelled 1-5 in the obvious way), add the results, and then add one if it was 7 or more. . . I initially discarded this approach because it felt inelegant; I wanted my dice to roll (say) a 9 by producing something which was obviously a 9, rather than producing something that looked like an 8 and requiring you to remember to convert it into a 9. Because one simple rule is so inelegant compared to dice with numbers, dots and sometimes a second number, riiight.
- alar44 5y agoYeah I mean if you want elegant just reroll the fuckin dice. The solution is kind of interesting I guess, but it's so impractical I don't think you can even call it a solution.
- halfsquatch 5y agoIt's a colloid.
- kleiba 5y ago