The HIDDEN Math Behind Dungeons & Dragons

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Why do we use dice? And why do we use the dice that we do? Do we need to use dice all the time?
#dungeonsanddragons #mathematics #dice #tabletopgames #roleplayinggames #rpg #probability #statistics #mathnerds #dndcommunity #dicerolling #gamedesign #mathematicalanalysis #dnd
This is a great tool for determining probability
anydice.com/program/1203
This is an article talking about advantage/disadvantage
onlinedungeonmaster.com/2012/05/24/advantage-and-disadvantage-in-dd-next-the-math/
This is an article talking about d6’s, and where I got some of the graphics.
www.thedarkfortress.co.uk/tech_reports/3_dice_rolls.php
Article on Hasbro Layoff’s if you feel like getting depressed:
techcrunch.com/2023/12/11/hasbro-layoffs-dungeons-dragons-wizards/
00:00 Why Do We Use Dice?
00:47 Why Do We Use D20's?
01:40 To Roll, or Not to Roll.
02:53 Why Skills Checks Suck
03:49 Why Should We Use the d6?
04:57 Average Dice Results
05:22 How Multiple Dice Affect Probability
06:15 Advantage/Disadvantage
08:01 Conclusions
09:14 My Cousin Marcus

Опубликовано:

11 янв 2024

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Комментарии : 48

@SimpusMax 8 месяцев назад

My table has incorporated the "take 10" rule (take 10 minutes to take a 10) for skill checks. Definitely helps those situations where bad dice lead to illogical results.

@AndrewStobb 8 месяцев назад

That's honestly such a simple and easy to implement rule. It's a wonder it's not in the core rules.

@Phsstpok 5 месяцев назад

@@AndrewStobb it was...

@hikarihitomi7706 9 месяцев назад

I so prefer 3.x over 5e. Many more options for influencing a roll. Also, scales from ordinary people to godhood.

@AndrewStobb 9 месяцев назад

Yeah I've found myself going back to 3rd edition from time to time for inspiration for different mechanics. Like there are actually robust rules for making a sentient magic item-- which are actually really cool. (just to be clear I was not gaming in the early 2000's, I just like some of the stuff presented).

@DragonsinGenesisPodcast 8 месяцев назад

That’s why we play Pathfinder 1E.

@hoi-polloi1863 8 месяцев назад

Had a game with three paladins. They came across an altar in the woods. All three failed their religion checks. Annoyed DM: "None of you can tell if this is a sincere shrine, or a monument to demon-worship." Embarrassed paladin: "We... musta fell asleep during paladin class that day"

@kontrarien5721 8 месяцев назад

Sounds like a case where that knowledge shouldn't be hidden behind a dice roll?

@westernbear2265 5 месяцев назад

Yeah, probably shouldn’t have been a roll to resolve on that one.

@quillogist2875 5 месяцев назад

There are several optional rules in the DMG that address how to have automatic success at routine tasks and bands of success or failure.

@99Michaelthom 8 месяцев назад

4d6 drop the lowest was first introduced in 1979 AD&D 1e DMG page 11.

@PMandrekar 8 месяцев назад

I remember explaining the differences between game systems and how the different mechanics play in to my favorite game system to my father (who was a famous probability theorist). This was great. (Dad was Professor VS Mandrekar 1939-2021) at Michigan State University (1968-2021)

@PMandrekar 8 месяцев назад

I run games in GURPS 4e. 3d6 mechanic

@TheShepherdFilms 7 месяцев назад

Quite a goodf video surprised you don't have that many subscribers...yet...it will come...your "to roll or not to roll advice" is excellent, I wish I had known when I started DMing, however something I definitely use all the time...even roll of 5 or just a backstory important thing can give you permission to tell your players stuff...also if it is backstory stuff and you say the magic words" "I'm not even gonna make you roll, you would know this" than I tell the important things...and it makes them feel special...

@AndrewStobb 6 месяцев назад

Yeah that honestly might be the most important thing in the whole video in my opinion.

@swordsnstones 5 месяцев назад

our game uses 1D6 each round for initiative. 1-3 PCs attack, 4-6 PCs defend. this is basically determining advantage as well, but we use situational advantage occasionally if a party or monster is surprised, nothing too complicated. using the initiative each round increases the chance of death to PCs and monsters as there is no guarantee they will be on the attack each turn.

@BabylonZeus 8 месяцев назад

I ended deconstructing the Advantage system and introduced +x or - x. Much more fluid and free to build situations

@TwinSteel 8 месяцев назад

You should show the diminishing returns of stacking advantage and the effect of advantage on other dice like d6

@AchanhiArusa 2 месяца назад

=0.5*#Faces*(High + Low)/#Faces (Gauss's Summation formula divided by the number of faces) =0.5*(High + Low)

@SkittleBombs 7 месяцев назад

I also like group checks if everonyone want a to do the thing just make them all roll and they need 50% or more players to succeed

@Demonskunk 8 месяцев назад

While advantage is statistically very powerful, it doesn’t feel as good as a flat bonus because it’s unreliable. With advantage you can still roll a 3 and a 5, where as with a +5 you can’t effectively roll below a 6.

@AndrewStobb 8 месяцев назад

The real difference (and the reason they went with advantage, to my understanding) is that before 5e, you would get multiple stacking +2’s, which was a headache for all sorts of reasons.

@archlittle6067 8 месяцев назад

The PC that is proficient with the skill in an ability check should almost always Help another PC do the check, so they get advantage. If the PC has Expertise, then they probably should do the check. A smart party should have a PC that can cast Guidance for an additional +1d4. So, advantage +1d4 (+ any ability modifier) should always be the norm.

@MemphiStig 8 месяцев назад

Alternatively, to get any die or dice combo average, add the lowest number to the highest and divide by two. (that's your +0.5) Average of d6 = 1 + 6 / 2 = 3.5'; 2d8 = 2 + 16 / 2 = 9; etc. Also works for odd combos like 2d8 + 2d10, or odd dice, like 5d7 + 3d30, but do you really need all that math all the time? No. Just dice. (I'd drop some dice emojis but *apparently* yt isn't as representative as we thought!)

@AndrewStobb 8 месяцев назад

That's another great shorthand method.

@SkittleBombs 7 месяцев назад

Have a chat about the math of mixed success like ironsworn 1d6+adds vs 2x 1d10 target numbers. Or the dagger heart 2d12 with 50-50 hope/fear

@ieshadover 8 месяцев назад

Yes it is, the best tactic is alway go for advantage or getting an oppenent disadvantage. If you can get both the battle quickly becomes a sweep. It is why silvery barbs is often banned or modified by GM's.

@AngryPict 8 месяцев назад

I used to prefer a flat + to a roll. But on reflection, more dice rolled is always more fun. We also use this mechanic with other things, not just to hit rolls. Poor quality makeshift weapon? Damage with disadvantage. Blade made by legendary smith? Damage with advantage. Not RAW but means players are more keen to find good gear that isn't necessarily magical.

@AndrewStobb 8 месяцев назад

That's actually a really good way to do makeshift weapons. I think the traditional would be -1 to attack and or damage, but that is way easier to implement. I might use that for my next campaign.

@kevoreilly6557 6 месяцев назад

Easier to just think about advantage as the combine probability of failure so 55% change of success on 1 dice is 1-combined change of failure 1- (.45)*(.45) = 1-(~.20) ~80% For disadvantage multiply the change of success, not failure, so it is just (.55)*(.55) ~30%

@jamestaylor3805 8 месяцев назад

Advantage is a +4(20% improved success rates) in a system that mostly peaks at +3 on any single adjustment. It is not broken, it is a great example how extremely a situation can affect odds, and no matter how good you are at something the environment plays a roll in the outcome too. The problem with advantage and disadvantage is when the modifiers are doubled. For example if the DM has increased the difficulty of a check to account for the environment, and something happens that applies disadvantage to the roll, the odds of success become very low. The inverse is true too, in that an act that would normally be nearly impossible can become almost unfailing if the DC is reduced for environeny and then advantage is stacked on top. We need to understand that advantage and disadvantage are a replacement for other roll modifiers, and shouldn't be 'in addition to' other roll modifiers. Base difficulty + /- skill adjustment +/- situational adjustment +/- advantage, potentially replacing minor(less impactful) situational adjustments of similar origin It should be very uncommon for all potential adjustments to align where any single roll only has positive adjustment or only negative adjustments. Those are very much "when the stars aligned" moments.

@bonzwah1 5 месяцев назад

The issue is that advantage/disadvantage was designed to be a replacement for environmental/situational modifiers...but then a lot of class features give advantage or disadvantage. - Personally I think that was a big design mistake. I think advantage/disadvantage should have been a strictly narrative/situational modifiers determined by the table in the moment. And all class features should have added bonuses or imposed penalties. - I think DND 5e has an identity conflict. The premise of advantage/disadvantage is to eliminate the idea of multiple sources of situational modifiers. It was a deliberate call for tables to not think beyond one major situational influence over the outcome of the roll. But the way DND combat is designed, it is clearly meant to be tactical and crunchy. So I really think the best of both worlds would have been to make advantage/disadvantage off limits for class features. Instead they should have been like bless or shield of faith. They should have exclusively added small dice or flat modifiers to the roll. That way, advantage/disadvantage would have been left in the exclusive domain of narrative improv at the table, and mostly implemented when the table is approaching the game in a rules lite narrative approach. I don't mind that DND 5e has both chocolate and peanut butter, but I would have preferred if they did not mix.

@jamestaylor3805 5 месяцев назад

@@bonzwah1blame there falls entirely on the rogues design requirement of advantage to trigger their primary ability. With that one step they had to make advantage manageble for players in a way that doesn't require a DMs call at the table.

@jamestaylor3805 5 месяцев назад

Rogue is the only one of the big three classes(Rogue, Wizard, Fighter) that even mentions advantage among its base class features.

@stephenkolostyak4087 8 месяцев назад

7:10 - I never liked d% charts, and now I may have realized why for the first time: dice are not ordinal but we treat them like they are for these games.

@mikko272 8 месяцев назад

The skill should give an answer when you are good at then let the character build the solution to the problem. d20 takes a lot away from the character use what makes sense in the story.

@SkittleBombs 7 месяцев назад

If you like shadow dark you’d probably like ICRPG and how they do easy/hard instead of adv/Dadv

@mykediemart 4 месяца назад

Well explained

@patty4449 8 месяцев назад

I dont use 3 or 5... Too limited... I outsource the foundation and adapt the dice rolls to situations and more... Just like Dimension 20... It feels much better if you have a normal roll with a propper outcome without doing all the wrong choices... I also like to include Karma rolls (If my party decides to make unholy murder things) and Nature throws (so if a house is burning does anything happen, similar to Baldurs gates Nature rolls btw) I also like to shift the rule balance between situations... For example you are less likely to trick someone if they are from hell, in hell or anything of that sort due to being used to it so deception checks are a lot harder or even impossible if that being can read minds etc... It really depends a lot on situations and characters but also I think having random interactions like that make the situation so much more immersive... And honestly I don't feel like an asshole all the time when the enemy rolls a nat 20...

@A-MR.E 8 месяцев назад

Big fan.

@ashleyhoughton8592 8 месяцев назад

No.

@CraigS- 8 месяцев назад

Would have been a great video if you didn't make the stupid yelling so damn loud compared to the rest of the video.

@AndrewStobb 8 месяцев назад

Do I look like I know how to balance Audio? I just want a picture of a Goddang Hotdog! Jokes aside, I'm sorry if that ruined the video for you, it's something I hope to improve on.