I’ve got a game idea kicking around in my head. Nothing may come of it. But if it does, it will use … dice!
Of course, it will need dice that do funky things. Specifically, the dice need to have a probability curve that looks like a capital-M, or two camel humps. The extreme results need to be more likely than the median.
Dice tricks are not my forte, so I’m a bit stuck. Any suggestions?
Dice tricks
Two sets of 2d6, with 7 as your nominal hump, would do it. But that’s awkward.
–Jason M
Re: Dice tricks
Well, that’s two camel humps that are located at the same spot.
2d4 and 2d8 would do it though.
Though, the collective hump would still be in the middle.
It seems impossible to me with one dice-pool.
Re: Dice tricks
each die pair represents one end of the scale. Seven, the top of the curve, is the most extreme outcome. radiating out from there are paired, but less likely, individual outcomes – 6 and 8, 4 and 9, etc. Distance from 7 is what matters.
I roll the first 2d6 and get an 11 – very far out and a very not-extreme result on that side of the trough. I roll the second 2d6 and get a 7 – maximally extreme on that side of the trough. A very lopsided camel.
Re: Dice tricks
Thanks for the suggestion, Jason. If I understand correctly, you’re essentially measuring the curves vertically, rather than horizontally. 7 becomes the “highest” value, with 2 and 12 being the “lowest” values. Interesting.
The only way I can see to make this work is to weight the extremes on all dice rolled more heavily than the middle.
Basically, when you roll (say) 2d3, you want to make it more probable that 2 and 6 will be the result than 3 and 5, and those more probable than 4.
You want to create something that pulls things towards one end of the scale more heavily than the other.
Let’s talk coin flips, since they’re easy, and have the smallest number of possible results. This is an exploration of an idea, I’m not sure if it works.
Think about what happens if you flip a certain odd number of coins (must be odd for this to work, I think), and then say you may only count the result that there are the most of — -1 for tails, +1 for heads.
Let’s toss three coins and consider. I’ll put brackets around results that get discarded.
Tails, Tails, Tails: -3; 12.5% chance of happening
Tails, Tails, [Heads]: -2; 37.5% chance of happening
-1: Can’t ever happen (one Tail gets you a +2, see below)
0: Can’t ever happen (not an even number getting flipped)
+1: Can’t ever happen (one Head gets you a -2, see above)
[Tails], Heads, Heads: +2; 37.5% chance of happening
Heads, Heads, Heads: +3; 12.5% chance of happening.
This gives you a result spread like this:
-3: xxx
-2: xxxxxxxxx
-1:
+0:
+1:
+2: xxxxxxxxx
+3: xxx
Basically, it says there will be a hole in the middle where certain numeric results never happen, and then the extremes will each have a spike at the closest-to-average-permissible result, with the curve sloping “down” (left) the more extreme the result.
You can do this with d6s, even, with the idea that if you have more results in the 1-3 range, you only count 1’s, 2’s, and 3’s, and if you have more results in the 4-6 range, you only count 4’s, 5’s, and 6’s.
Here’s a random sampling of 3d6’s rolled with this method:
6,6,5 = 17
2,1,2 = 5
1,[4],1 = 2
5,5,[3] = 10
4,6,[2] = 10
4,[3],4 = 8
3,3,1 = 7
2,[6],3 = 5
Etc.
So, high two-dice-majority combos will total anywhere from 8 (4+4) to 12 (6+6); low two-dice-majorities will total from 2 (1+1) to 6 (3+3). These ranges mostly correspond to the 37.5% -2/+2 bands from our coin-flip example, I think.
High three-dice-majority combos will total from 12 (4+4+4) to 18 (6+6+6), corresponding to the 12.5% +3 band.
Low three-dice-majority combos behave a little funky, because they’ll overlap the 2 to 6 chunk, getting us anything from 3 (1+1+1) to 9 (3+3+3). If you wanted to weight this differently, you could simply say that whenever three low dice are rolled, you take the value of the single highest die among them. So a 1,3,1 wouldn’t total 7, it’d be counted as a 3. I think that’d push the behavior back into something like the expected shape (similar to the coinflip example).
So, to sum up, here’s a method:
1. Roll 3d6
2a. If 2 or more dice are 4 or higher, discard the ones below 4 and total the remaining ones.
2b. If 2 dice are 3 or lower, discard the single high die and total the remaining two dice.
2c. If 3 dice are 3 or lower, discard all dice 4 or higher, and count only the single highest die remaining.
It doesn’t QUITE get you a double camel hump, but it’s not far off.
Wow. Thanks for the idea, Fred. I really like the idea that the central values are impossible to roll. That might fit the aesthetics of my idea better than the original M-shaped curve.
It got me thinking outside the box. I think the below idea might be easier to implement at the table and give a curve kinda like a V with the middle part impossible.
1) Roll 1d12.
2) If the result is 5-8, reroll.
3) If you roll 1-4, subtract the number of rerolls, and use that as your final value.
4) If you roll 9-12, add the number of rerolls, and use that as your final value.
Sure. I’d probably go for a narrower reroll band, just to make it a bit more managable. Basically:
1) Roll 1d12
2) If the result is 6 or 7, reroll
3) If you roll 1-5, subtract the number of rerolls you did, and use that as your final value.
4) If you roll 8-12, add the number, etc.
This makes a reroll happen 1 in 6 times instead of 1 in 3 on a single die toss.
NOTE! Basically the goal/result here is bisecting your standard bell curve and moving the halves away from each other. You could probably get a similar result by rolling a 1d12 and a 1d4, and using these rules:
1) Roll 1d12 and 1d4
2) If the d12 is showing 7+, add the d4 result (generating a range from 8 to 16)
3) If the d12 is showing 6-, subtract the d4 result (generating a range from -3 to 5).
This gives you a single-throw method, without having to do the rerolls, and produces a result similar to the “rerolling one in six” ruleset I offered above: you won’t ever get a 6 or 7 with this method.
If you roll two d6 and take the highest odd result, or if there’s not an odd, the lowest even result, you get:
1 19.44%
2 13.89%
3 25.00%
4 8.33%
5 30.56%
6 2.78%
That’s a pretty wide left hump though.
Paul
That’s an interesting idea, and seems like it would be easy to use at the table. I originally wanted symetrical humps, but now I’ve got to reconsider. Thanks, Paul
Are you looking for an M or a V?
If an M, something as simple as a fudge-die roll (or any other curve, like 3d6) with an extra die to serve as a coinflip can do it. roll 3d6 and if the extra die is heads, then treat the value as positive.
For a V, that gets a little wackier. Need to think about that a little more.
For a V, 2d6 take the higher, with a coin toss. Or an opposed single-die vs single die roll, high absolute value wins.
Hi, Rob. The coinflip die is so direct and simple, I like it. I’m not sure how I feel about using negative numbers. I know you fans of Fudge have had much success with it, so maybe I’ll give it a try. Thanks!
Dice tricks
Two sets of 2d6, with 7 as your nominal hump, would do it. But that’s awkward.
–Jason M
You could do an opposed roll. Roll 2d6 positive vs 2d6 negative, and the higher absolute value wins. Results range from -12 to +12, with -8, -9, +8, and +9 being the most likely outcomes.
Well … a tie is the single most likely outcome, so you’ll want to decide what to do with that. “Ties go to the positive” wouldn’t do any harm, make the right-hand hump a smidge higher is all.
Comparing absolute values is straightforward and simple. I don’t know if it’s right for this game, because I’m not too fond of using negative numbers, but if I ever play Feng Shui again, I’m definitely using this! It’s far superior to that game’s dice system as written. Thanks, Vincent.
Re: Dice tricks
Well, that’s two camel humps that are located at the same spot.
2d4 and 2d8 would do it though.
Though, the collective hump would still be in the middle.
It seems impossible to me with one dice-pool.
Re: Dice tricks
each die pair represents one end of the scale. Seven, the top of the curve, is the most extreme outcome. radiating out from there are paired, but less likely, individual outcomes – 6 and 8, 4 and 9, etc. Distance from 7 is what matters.
I roll the first 2d6 and get an 11 – very far out and a very not-extreme result on that side of the trough. I roll the second 2d6 and get a 7 – maximally extreme on that side of the trough. A very lopsided camel.
The only way I can see to make this work is to weight the extremes on all dice rolled more heavily than the middle.
Basically, when you roll (say) 2d3, you want to make it more probable that 2 and 6 will be the result than 3 and 5, and those more probable than 4.
You want to create something that pulls things towards one end of the scale more heavily than the other.
Let’s talk coin flips, since they’re easy, and have the smallest number of possible results. This is an exploration of an idea, I’m not sure if it works.
Think about what happens if you flip a certain odd number of coins (must be odd for this to work, I think), and then say you may only count the result that there are the most of — -1 for tails, +1 for heads.
Let’s toss three coins and consider. I’ll put brackets around results that get discarded.
Tails, Tails, Tails: -3; 12.5% chance of happening
Tails, Tails, [Heads]: -2; 37.5% chance of happening
-1: Can’t ever happen (one Tail gets you a +2, see below)
0: Can’t ever happen (not an even number getting flipped)
+1: Can’t ever happen (one Head gets you a -2, see above)
[Tails], Heads, Heads: +2; 37.5% chance of happening
Heads, Heads, Heads: +3; 12.5% chance of happening.
This gives you a result spread like this:
-3: xxx
-2: xxxxxxxxx
-1:
+0:
+1:
+2: xxxxxxxxx
+3: xxx
Basically, it says there will be a hole in the middle where certain numeric results never happen, and then the extremes will each have a spike at the closest-to-average-permissible result, with the curve sloping “down” (left) the more extreme the result.
You can do this with d6s, even, with the idea that if you have more results in the 1-3 range, you only count 1’s, 2’s, and 3’s, and if you have more results in the 4-6 range, you only count 4’s, 5’s, and 6’s.
Here’s a random sampling of 3d6’s rolled with this method:
6,6,5 = 17
2,1,2 = 5
1,[4],1 = 2
5,5,[3] = 10
4,6,[2] = 10
4,[3],4 = 8
3,3,1 = 7
2,[6],3 = 5
Etc.
So, high two-dice-majority combos will total anywhere from 8 (4+4) to 12 (6+6); low two-dice-majorities will total from 2 (1+1) to 6 (3+3). These ranges mostly correspond to the 37.5% -2/+2 bands from our coin-flip example, I think.
High three-dice-majority combos will total from 12 (4+4+4) to 18 (6+6+6), corresponding to the 12.5% +3 band.
Low three-dice-majority combos behave a little funky, because they’ll overlap the 2 to 6 chunk, getting us anything from 3 (1+1+1) to 9 (3+3+3). If you wanted to weight this differently, you could simply say that whenever three low dice are rolled, you take the value of the single highest die among them. So a 1,3,1 wouldn’t total 7, it’d be counted as a 3. I think that’d push the behavior back into something like the expected shape (similar to the coinflip example).
So, to sum up, here’s a method:
1. Roll 3d6
2a. If 2 or more dice are 4 or higher, discard the ones below 4 and total the remaining ones.
2b. If 2 dice are 3 or lower, discard the single high die and total the remaining two dice.
2c. If 3 dice are 3 or lower, discard all dice 4 or higher, and count only the single highest die remaining.
It doesn’t QUITE get you a double camel hump, but it’s not far off.
I can think of a number of methods:
2d6 – 7 This gives you a range of -5 – 5, with the hump at either end, value-wise.
2d6 and take the one furthest from 3; on ties, reroll You’ll never get a 3 with this, but otherwise it’s nice.
These are both cool, easy-to-handle ideas. I particularly like the second one with its abyss at 3. Thanks, Alexander.
If you roll two d6 and take the highest odd result, or if there’s not an odd, the lowest even result, you get:
1 19.44%
2 13.89%
3 25.00%
4 8.33%
5 30.56%
6 2.78%
That’s a pretty wide left hump though.
Paul
Are you looking for an M or a V?
If an M, something as simple as a fudge-die roll (or any other curve, like 3d6) with an extra die to serve as a coinflip can do it. roll 3d6 and if the extra die is heads, then treat the value as positive.
For a V, that gets a little wackier. Need to think about that a little more.
You could do an opposed roll. Roll 2d6 positive vs 2d6 negative, and the higher absolute value wins. Results range from -12 to +12, with -8, -9, +8, and +9 being the most likely outcomes.
Well … a tie is the single most likely outcome, so you’ll want to decide what to do with that. “Ties go to the positive” wouldn’t do any harm, make the right-hand hump a smidge higher is all.
For a V, 2d6 take the higher, with a coin toss. Or an opposed single-die vs single die roll, high absolute value wins.
I can think of a number of methods:
2d6 – 7 This gives you a range of -5 – 5, with the hump at either end, value-wise.
2d6 and take the one furthest from 3; on ties, reroll You’ll never get a 3 with this, but otherwise it’s nice.
Re: Dice tricks
Thanks for the suggestion, Jason. If I understand correctly, you’re essentially measuring the curves vertically, rather than horizontally. 7 becomes the “highest” value, with 2 and 12 being the “lowest” values. Interesting.
Wow. Thanks for the idea, Fred. I really like the idea that the central values are impossible to roll. That might fit the aesthetics of my idea better than the original M-shaped curve.
It got me thinking outside the box. I think the below idea might be easier to implement at the table and give a curve kinda like a V with the middle part impossible.
1) Roll 1d12.
2) If the result is 5-8, reroll.
3) If you roll 1-4, subtract the number of rerolls, and use that as your final value.
4) If you roll 9-12, add the number of rerolls, and use that as your final value.
That’s an interesting idea, and seems like it would be easy to use at the table. I originally wanted symetrical humps, but now I’ve got to reconsider. Thanks, Paul
Hi, Rob. The coinflip die is so direct and simple, I like it. I’m not sure how I feel about using negative numbers. I know you fans of Fudge have had much success with it, so maybe I’ll give it a try. Thanks!
Comparing absolute values is straightforward and simple. I don’t know if it’s right for this game, because I’m not too fond of using negative numbers, but if I ever play Feng Shui again, I’m definitely using this! It’s far superior to that game’s dice system as written. Thanks, Vincent.
These are both cool, easy-to-handle ideas. I particularly like the second one with its abyss at 3. Thanks, Alexander.
Sure. I’d probably go for a narrower reroll band, just to make it a bit more managable. Basically:
1) Roll 1d12
2) If the result is 6 or 7, reroll
3) If you roll 1-5, subtract the number of rerolls you did, and use that as your final value.
4) If you roll 8-12, add the number, etc.
This makes a reroll happen 1 in 6 times instead of 1 in 3 on a single die toss.
NOTE! Basically the goal/result here is bisecting your standard bell curve and moving the halves away from each other. You could probably get a similar result by rolling a 1d12 and a 1d4, and using these rules:
1) Roll 1d12 and 1d4
2) If the d12 is showing 7+, add the d4 result (generating a range from 8 to 16)
3) If the d12 is showing 6-, subtract the d4 result (generating a range from -3 to 5).
This gives you a single-throw method, without having to do the rerolls, and produces a result similar to the “rerolling one in six” ruleset I offered above: you won’t ever get a 6 or 7 with this method.
Dice Tricks
What you’ve described here is a little different than what I remember you describing at DexCon. I’ll raise two thoughts based on what I remember.
If you want to be able to have players choose between high risk and low risk options, you could use a 2d6 curve for low risk (tending to generate values in the middle of the range) and flip it for the high risk version. For example, roll 2d6 for low risk and 12-2d6 for high risk.
Also, larger dice would give you a steeper curve, so if you want more extreme results that’d be something you could use to get there (2d20?).
Re: Dice Tricks
This is Scott. Sorry, I’d meant to sign the original post.
Dice Tricks
What you’ve described here is a little different than what I remember you describing at DexCon. I’ll raise two thoughts based on what I remember.
If you want to be able to have players choose between high risk and low risk options, you could use a 2d6 curve for low risk (tending to generate values in the middle of the range) and flip it for the high risk version. For example, roll 2d6 for low risk and 12-2d6 for high risk.
Also, larger dice would give you a steeper curve, so if you want more extreme results that’d be something you could use to get there (2d20?).
Re: Dice Tricks
This is Scott. Sorry, I’d meant to sign the original post.