One thing I forgot to mention... In the video, I note that when rolling 1d20, a positive adjustment to a target number can alternatively applied to the die roll, and vice versa. 1d20+2 vs DC 12 is the same as 1d20 vs DC 10, for example. This only works for single die rolls (linear distributions). Because the probability weight of a modifier to a combination dice roll (normal distribution) depends on the value being modified, a modifier of +2 to a roll is not the same as dropping the target number by 2. This is why most games that use combination dice rolls for resolution modify either the target number (a la BattleTech) or the roll (a la Traveller, with its accumulated Die Modifiers/DMs), very rarely both. If you do, you're involving some fairly complex probabilities, and the results can be difficult to manage. This in turn limits the tactical usefulness of the game's mechanics. Play goes from "playing the odds" by manipulating the situation as best you can in your favour, to just hoping the numbers work out through blind luck. So remember: - Target and roll modifiers are interchangeable when rolling single dice. - They are not interchangeable when rolling combinations. - Combination dice resolution systems that modify both target and roll become less predictable and useful.
Another great video. I have been working on my own system that has a some oddities that this has me thinking about. I am allowing the players to choose dice they roll within a defined range of 2-14. While I was aware the of the different probability curves between D6+D8 and D10+D4 calculating it out is different. Especially when it comes of odd dice like 2D7 or D3+D11. It sort of requires me to rethink some of design.
Playing with curves can really give some novel results, but getting players to choose a combination to use is... Well, it's an interesting concept - I'm just not sure, as a referee, I'd like a game to be that unpredictable. Anyway, yes, different combinations will give different results. For example, the old Monster Manual II random encounter chart I show at the end of the video uses 1d12 + 1d8 to generate 2-20. So why not 2d10? The answer, of course, being 2d10 gives a "triangular curve" (same shape as 2d6), while 1d12 + 1d8 gives a flattened peak between 9 and 13. That means you have five spots of equal probability in the middle of the table for your "Common" creatures to go. If I was given the choice of dice to roll to produce a given range, it'd be mismatching dice all the way! Anyway... I'm intrigued and a little scared of your idea!
@@WillyMuffinUK In some cases the player may want to roll only one of the dice and keep the other in reserve, perhaps using the big dice for attack and saving the small for extra defense. I also was thinking I would have the player roll their Big or Small dice for other things. I think seeing the flat curves I need to rethink how I use those those rolls.
One thing I forgot to mention...
In the video, I note that when rolling 1d20, a positive adjustment to a target number can alternatively applied to the die roll, and vice versa. 1d20+2 vs DC 12 is the same as 1d20 vs DC 10, for example.
This only works for single die rolls (linear distributions). Because the probability weight of a modifier to a combination dice roll (normal distribution) depends on the value being modified, a modifier of +2 to a roll is not the same as dropping the target number by 2.
This is why most games that use combination dice rolls for resolution modify either the target number (a la BattleTech) or the roll (a la Traveller, with its accumulated Die Modifiers/DMs), very rarely both. If you do, you're involving some fairly complex probabilities, and the results can be difficult to manage. This in turn limits the tactical usefulness of the game's mechanics. Play goes from "playing the odds" by manipulating the situation as best you can in your favour, to just hoping the numbers work out through blind luck.
So remember:
- Target and roll modifiers are interchangeable when rolling single dice.
- They are not interchangeable when rolling combinations.
- Combination dice resolution systems that modify both target and roll become less predictable and useful.
Gary Gygax would be proud of what you've done in this video. That's the highest praise I can think of. Well done sir.
High praise indeed - thank you.
Another great video. I have been working on my own system that has a some oddities that this has me thinking about. I am allowing the players to choose dice they roll within a defined range of 2-14. While I was aware the of the different probability curves between D6+D8 and D10+D4 calculating it out is different. Especially when it comes of odd dice like 2D7 or D3+D11. It sort of requires me to rethink some of design.
Playing with curves can really give some novel results, but getting players to choose a combination to use is... Well, it's an interesting concept - I'm just not sure, as a referee, I'd like a game to be that unpredictable. Anyway, yes, different combinations will give different results. For example, the old Monster Manual II random encounter chart I show at the end of the video uses 1d12 + 1d8 to generate 2-20. So why not 2d10? The answer, of course, being 2d10 gives a "triangular curve" (same shape as 2d6), while 1d12 + 1d8 gives a flattened peak between 9 and 13. That means you have five spots of equal probability in the middle of the table for your "Common" creatures to go. If I was given the choice of dice to roll to produce a given range, it'd be mismatching dice all the way!
Anyway... I'm intrigued and a little scared of your idea!
@@WillyMuffinUK In some cases the player may want to roll only one of the dice and keep the other in reserve, perhaps using the big dice for attack and saving the small for extra defense. I also was thinking I would have the player roll their Big or Small dice for other things. I think seeing the flat curves I need to rethink how I use those those rolls.
@@jamesrickel3814 Ahh, so players have a sort of pool to work with.
This was very helpful. Thank you.
You're welcome - I'm glad you found it useful.
have you seen anydice it let's you type out dice using standard dice notation and outputs the graphs for you
Handy tool for game designers!