The Math of Rolling with Advantage (D&D/Baldur's Gate 3)

[@moonblaze2713]

The DM's guide tells them that if the character would have arvantage but its a passive perception check, to add 5 to their passive perception score. Its almost like the makers of the game knew the math. :p

[@ZoroarkLover98]

Beautiful

[@texasranger7687]

One more evidence that the first RPG guys were math neerd ! ^^

[@andrewhazlewood4569]

+5 is equal to advantage if the DC is 11.

[@favoniu9051]

@@texasranger7687 So much that. I remember in the first AD&D rules, there was an explanation of what a gaussian distribution was (the 'bell curve")...

[@karisaparolampinen]

Very helpful when choosing between constitution proficiency and advantage on saves in order to keep concentrating on spells

[@kesh_r]

Came here just for this lol. Proficiency bonus is just +4 at max level. So even in this scenario, warcaster is better?

[@karisaparolampinen]

​@@kesh_rit depends on your build, but let's say that you begin with CON 13 and take the resilient feat, bumping your CON to 14 and therefore getting a +2 + prof. to constitution saves. This would be the better option from level 5 upwards, when the total bonus becomes +5 (proficiency +3, con mod +2). In comparison, if you had advantage from warcaster and started with a CON 14 (+2), it still doesn't beat proficiency when you apply your CON modifier to both scenarios, according to this chart.

[@obsidianasmr2466]

@@kesh_r something to remember for baldurs gate is that taking the resilient feat also gives you a bonus to an ability score and since often scores are going to be odd numbers this effectively makes the bonus from the feat +5 1 from the asi and 4 from the feat. also even if you have an even score you can use withers to bump down your score to allow you to reallocate that into another ability increasing that abilities bonus aswell. Also warcaster only gives advantage on concentration saves whereas resilient gives the bonus to every concentration save including things like poisons. And while warcaster gives you an opportunity attack with shocking grasp thats such a niche advantage that it hardly ever outways the previously mentioned advantages of resilient. So imo reilient con is always better especially because your probably picking it up at level 8 where its weakness at earlier levels is already mitigated by a higher prof bonus because of how busted alert is.

[@joeracer302]

@@obsidianasmr2466 can also drink elixir to get advantage on con check, freeing up the feat for something else

[@Kutchy7765]

​@@kesh_rif you actually play dnd the bonux at max is +6

[@CaptainKrby]

This was actually really handy, as I'm currently refining my own ttrpg system. This is a great help with balancing abilities

[@TheChiptide]

Happy to help!

[@iamlucidess]

I feel like my hit rate just went up by watching this video. Very informative and fun to watch.

[@axelperez2917]

Unironically very helpful. I will consider this once I get started in dnd XD

[@haydenfreer8543]

We dungeoning these dragons bois

[@betoh7140]

She dungeon on my dragon till I &

[@grandlancer]

3:34 I'm pretty sure that's the underlying mechanic behind THAC0

[@embert.12]

🌮?

[@pseudonymous7557]

Ya that's just THAC0

[@tychozzyx9439]

To Hit Armor Class 0. D&D 2 used it as a player attribute/precalculated target. AC was 10 or below, even going negative and you add your target's AC to your THAC0 to find what you need to roll

[@satsujin-shathewitchkingof6185]

Very good video but there's actually a flaw with the math. The chance of winning a roll is 50%,either you do or you don't

[@satsujin-shathewitchkingof6185]

/j

[@TheChiptide]

Of course, how could I forget??

[@satsujin-shathewitchkingof6185]

@@TheChiptide Probably rolled to remember and lost. That cursed 50% chance

[@filval387]

@@satsujin-shathewitchkingof6185 In the words of a pokemon youtuber I currently can't remember the name of, "If it's not 100% accuracy, it's 50%."

[@GleamingGlint]

​@@filval387mandjtv - hail yeah

[@nerd8502]

One thing I'd like to add is that even though a +5 isn't better than Advantage when rolling for an 11, it isn't worst either. They have the exact same chance. Interestingly enough, that's the only point in which this happens in the graph. Even if you ignore the rule of "20 auto-succeeds, 1 auto-fails", its still the only non-trivial point where the chance of succeeding with a bonus and with an advantage is the same (non-trivial in this situation means a point which always succeeds or always fails, independently of the bonus or advantage)

[@Asiago9]

The equation at 11:00 actually simplifies quite nicely in my opinion down to -(x-21)(x-1)/20

[@ronnycook3569]

Here's an interesting piece of maths for you... Mirror Image vs. Shield. Shield gives a 1-turn +5 advantage until the end of your next turn, but is cast as a reaction. Mirror Image uses a regular action, but gives you several dummies as targets - so a successful hit has a 75% chance of hitting one of the mirrors on the first turn, and once the first mirror is gone that drops to 66%, then to 50% if THAT mirror is gone - with adjustments for dexterity. By my figuring Mirror Image is always better - as long as it's cast in advance. Of course, that uses an Action you could be using to do something else, and if cast in advance it guarantees a spell slot will be used whereas Shield only uses a slot if you're hit. So the maths is 100% in favour of mirror image, but Shield can be better tactically, especially if the character is unlikely to be targeted. That's not really surprising as MI is a 2nd level spell whereas Shield is 1st level. Plus, arcane casters don't typically get much chance to burn their reaction.

[@TheChiptide]

That’s interesting! So it seems like shield is more of a risk-reward type of thing, while Mirror Image is more consistent, but requires more resources. Might be an interesting thing to look into!

[@ZorgoXorgon]

I once saw a mathematical proof that on average advantage equates to a little over +2 on a single roll, and I have used that logic when deciding which to pick for single rolls if I have a choice. But this video shows that the average is not the best metric because most DCs in the game that matter are in the 15-25 range. According to your chart, if the DC is 19-21, the +2 would be statisticly better, and outside that range, the bonus has to be higher and higher until +5 which is best for almost all rolls (15-25). Very helpful video!

[@Scary_Balthazar]

The math is pretty easy if u know the formula. The average is 14.5 if I remember rights so except the nat 1 and 20, we can consider it a +4.5 to the roll

[@PhoenixShadow13]

I wanted to say thank you for this video. I had a loss in Dwellings of Eldervale, and was curious about the rolls with advantage. Your formula helped out figring out the calcs

[@betasprite4239]

Very cool to see all of the math put together. After my years of playing, i kind of had an instinct around which bonus numbers were "better than advantage", but i never had an explanation. This was cool to see.

[@WesleyMcLain-kj5if]

I’ve always heard that advantage is the equivalent of a +5 and now I know why. Thanks!

[@ntorix599]

If you already have a bonus out side of the plus five or advantage then the whole chart effectively moves to the right by a number of spaces equal to your normal bonus. For example if you have +3 and you have to choose between an additional +5 or advantage, then the first square where the +5 is better is 9 instead of 6 on the chart.

[@benjaminpatrickpatrickgarr9291]

If anyone wants a good example of Triple Advantage in D&D 5E, Assassin Rogue with Elven Accuracy (requires Half-Elf or Elf) is a great one. Sadly, BG3 does not have Elven Accuracy as a feat.

[@wirelessbaguette8997]

BG3 does allow for quad advantage (and higher) though, via inspiration. The "taking the higher" bit doesn't matter, but the "at least one success in X rolls" bit applies to inspiration with advantage. You can roll up to 10 dice for a given skill check. Rolling that many dice, the auto success on 20 really starts to influence the power of advantage.

[@Marre2795]

2:58 True, but to justify this with a concrete examples, there are different feats (at level 4, 8 and 12) where you gain advantage or a flat bonus, and these feats are rare enough that you usually don't want to spend 2 feats to improve a single type of check. Example: Resilient (Constitution) vs. War Caster. Resilient (Constitution) lets you add a bonus to Constitution Saving Throws. War Caster lets you roll Concentration Checks, the most common Constitution Saving Throw (by far), with Advantage.

[@cwolf1221]

This is nice to visualize because assuming advantage adds about 3.3 to every roll never felt quite right

[@TheChiptide]

Yeah, while the average for a roll with advantage is technically around 13, it’s not the same as adding a bonus because each roll isn’t equally likely. Unlike a regular dice roll, you only have a .25% chance of getting a 1 with advantage, but over a 9% chance to get a 20!

[@Stoat2319]

The new game theory

[@TheChiptide]

This is Game Theory in the most literal sense!

[@tekbox7909]

Also something to consider for the example of attack rolls is that on a Nat 20 you get a critical hit which means extra damage so a 20 roll is desirable even if something lower could hit though trying to account for that will result in a big headache considering that everyones attacks do different amounts of damage and the way the damage is calculated even if the average is the same between two attacks makes a difference to the average damage on a critical hit.

[@jm.519]

For me, I'm going to use this very thing in setting my DCs for players, and knowing when to give them advantage or disadvantage.

[@VulcanGray]

I dont ever roll two D20s. I just roll a D400 with an appropriate distribution of faces

[@jameshealan2881]

My head exploded about halfway through but I think I got the gist at the end

[@PokeWater007]

Super interesting video! Would love to see your take on rolling with disadvantage and how that factors into the decisions

[@Pystro]

It really also depends on what challenges you face. If your GM only throws challenges at you where you need a target number of 5-23, then you'll stay in "bonuses are good" territory and advantage will be equivalent to a lower bonus, between 3 and 4. If your GM has you roll for trivial and virtually impossible challenges and you stray further into "advantage is good" territory, then you may need a bonus of 4-ish to beat having advantage. (As I also stated in a reply to @pacattack2586, a bonus of 5 only beats advantage if you are equally likely to run into target numbers from -10 to 40.)

[@PedroViniciusRC]

I multiclass a monk with a barbarian to have a furious monk and I critically missed 4 attacks in a row (with advantage). This seems like a bug, as it's highly unlikely for this to happen.

[@TheChiptide]

Either a bug, or you just hit a 1 in 25 billion jackpot!

[@TheRealSteinloewe]

That’s what the Dice Jail is for…

[@tfallen9031]

Karmic Dice...

[@peterswanson3150]

This was so great and interesting although I don’t think he had to reiterate the super basic math parts as much for next time

[@vizzzyy190]

theres so many little probability things in dnd and bg3, hope you can do more!!

[@Essutos]

In the end you was talking about "triple (or quadruple) advantage", if we talk about rules as written, there's no such thing. Unless DM made a house rule, there's no benefit of having 7 advantages over 1 therefore your calculations should notched a little to the "flat bonus side"

[@TheChiptide]

True, but there are certain feats (like Elven Accuracy, I believe it’s called) that allows you to roll 3 dice and choose the highest, effectively granting you triple advantage, which changes the odds a lot!

[@Essutos]

@@TheChiptide yup, I forgot about this. It makes you admire how RELATIVELY balanced the game is witch such unique interactions. It must have been hell to calculate for the designers

[@xenon1416]

good 3am video

[@idonthavebones7086]

You can keep your fancy math, I’ll always choose advantage haha

[@DiamondzFinder_]

I think you should feel free to do more non "video" game stuff! I personally find it just as interesting :3

[@jeanlou3]

You don’t always know the DC you will need to hit beforehand. A useful metric is the expected roll, or the average result you would expect. Let’s find the average value of a d20 roll with advantage. Everyone knows the formula for a single dX: A=X/2+0.5. You can calculate it yourself by calculating the average of the d20 (so (20+19+18…+1)/20=10.5) With adv., the lowest dice does not matter. So for the 400 possible rolls of 2 d20, you have 39 results of 20 (1 [20,20]+19[20,X]+19[X,20]), 37 results of 19, etc. Since we don’t care about the lower dice, we just set it to the value of the higher one to calculate our average, and we will divide by 2 at the end. So the average can be calculated using sum(X from 1 to 20) (X*(2X-1)) / (2X^2). We get an average of 13.66… You may have noticed the two thirds seems like a weirdly significant number. Our original average was 10.5, now with two dice it’s 13.66, surely there is a way to generalize for the average with Y dX, take the best one… And there is. If you calculate the average for 3 and 4 dice, you quickly find this formulae for Y dX, take the best one: A=X*(Y/(Y+1)) - (Y/(Y+1))+1. If we plug in a single d20, we get A=20*(1/2)-(1/2)+1=10.5 Two d20 we get A=20*(2/3)-(2/3)+1=13.66 Three d20 for the accurate elves out there, we get: A=20(3/4)-(3/4)+1=15.25. So on average, advantage is worth +3.16, eleven accuracy is worth +1.59 on top of that.

[@robinblaine5385]

So Advantage is really only consistently better if you're "crit fishing" (looking for a specific roll or range of rolls on the die regardless of bonuses... usually a 20, but some abilities can improve this to 19 through 20 or even 18 through 20)

[@cyruscrompton8221]

Quick nerd thing: The auto fail 1 is only homebrew! It's in bg3, but its never mentioned anywhere in 5e books. Its pure homebrew. And if anyone wonders if it's a good thing to add to games, fuck nah LMAO quick edit: I forgot some rules, attack rolls will always miss on 1 and when you roll a 1 on a death save it counts as two fails instead of one fail, but you can still succeed a DC when you roll a 1

[@TanusMorken]

the auto fail on 1 is homebrew only on part. since roll a dice is used to see the probability if the action is a success, if the target numeber (Difficulty Class or DC) is 1 we have that you have 1-(1-1)/20 = 1-0/20 = 1. it means that with the DC at 1 tha player have 100% to succeed so why make the player roll the dice? If the DC is 2 we have 1-(2-1)/20 = 1-1/20 = 0.95. it means that with the DC at 2 the player have 95% to succeed and 5% to fail so if the player roll a dice it fails with the 1. Since the DC is always an positive integer number, we have: if the DC is 1 the game master don't ask to roll the dice. if the DC is from 2 to what the game master can came up, we have the rule of autofail on 1. What is homebrew is give who roll the 1 additional malus, like if you roll a 1 while swing a sword, the sword slips away from your hands. What happens with the 1 is up to the game master and usualy used, keeping in mind the tone at the table at the moment, to try to make people laugh if the tone is light, emphasize the dramma in a difficult situation.

[@cyruscrompton8221]

​@@TanusMorken Honestly dude I don't get the point you're making LMAO the grammar is a bit hard to read and we might be talking about different things because crit failures aren't in the book anywhere, at most attack rolls with 1 auto *miss* There are also negative modifiers, so getting below 1 on a DC is possible! (nobody would ever call for anything that low though) And with the malice thing, I still wouldn't recommend it unless it's JUST flavor, if your friends are cool with it that's a-ok but generally you shouldn't punish players that heavily for rolling a 1, missing is enough

[@iglerflexrex1276]

@@TanusMorken Sometimes the DM doesn't know the players bonus to a check. There are 18 skill checks, 6 pure ability checks as well as 6 saves plus many tools. No way your DM knows every number on your sheet. There is a possibility, that you have a -1 to a specific skill or ability check and you woudn't pass the Dc 1 check on a 1 on the die. There is also the case that a character can have a +17 and automaticly pass any Dc 18 or lower check but you as a DM don't know about this, because the character just leveled up and gained expertise or proficiency bonus increased. Besides the math a critical failure on a nat 1 discourages players from trying things where they need to roll a d20 because it can fail regardless of modifiers and something bad happens. A bard sliding down a stair railing with a +12 to acrobatics results in falling of and taking damage is something I would avoid, so I just don't do that. Then most DM cry about the players why they don't interact with the world and surroundings anymore.

[@alexandrep830]

how can i add disadvantages on the calculator???

[@travishartzler9155]

Excellent video, thanks!

[@BeaglzRok1]

Statistics: advantage is a +5 to your roll Real Life: advantage is a 1/20 chance of rolling the same number twice, and the better your first roll is, the worse the mechanic becomes. That's why I go with flat bonuses, every time. Even if it's pretending not to be, Bless adding 1d4 to a roll, that's still anywhere between a +1 to a +4 raising the floor for failure is plenty.

[@AttacMage]

advantage provides greater odds of avoiding a nat 1, so it's quite nice to have if you're not worried about rolling a 2 or 3-20. And in BG3 especially, it's easy to get a 4 or so to be your minimum roll to pass, and I'd rather have advantage for most things.

[@DarthCasus]

What is the average distance between numbers that are rolled with advantage/disadvantage? I always heard that rolling with advantage is the equivalent of giving yourself +4.5 to any roll

[@ABCWarrior]

Fun and interesting video!

[@solalabell9674]

Fastest I’ve clicked on clicktide and I love chiptide as is

[@erpedro1630]

Finally, DnD!

[@CakeDayZ]

If you like bonuses more, play Pathfinder2e. It really rewards every +1, as crits happen on anytime you exceed the TN by 10. So fighters can have a 25%+ crit chance if they can get the right circumstances!

[@tobiasflohr3417]

i just say every roll is a 50/50. either i beat it or i dont. and i have failed many, many 50/50's

[@shadylizard3115]

loved it

[@Jiffjeff7314]

efficient gambling lets go

[@robertdemarco5209]

Thought this was a good video, maybe you could do a video on the math of card games like Magic.

[@defmod3397]

Like the video concept, but you the way you present this has quite a lot of problems to it. At the start you present this video by only mentioning D&D 5e and BG3, but proceed to do the math in the video assuming a general ttrpg ruleset. This matters because you do not make a distinction between attack rolls, saving throws, and skill checks when it comes to natural 20s or 1s. You mention in the video that getting either would result in an automatic success or failure respectively. This is only true for attack rolls in D&D 5e. In BG3 what you say present is true (at least to my knowledge). This is very misleading because people in the comments are talking about this math for the importance of concentration saves, or how the DMG mentions a quick calculation of +5 to represent the value of advantage for passive perception, but those types of things don't follow this formula. When you do complicated and long math videos like this, especially on topics that are hard to grasp like probability, people tend to take the presenters word as fact and will think about it later if it matters to them. As a presenter it is your job to make it as easy as possible for everyone, regardless of how much effort they put into understanding what you are saying, to understand the point. When you don't include calculations that make natural 1s and 20s automatic failures and successes the math is very different. On average advantage is a 3.325 bonus to a d20 roll, so the average roll with advantage is 13.825 (the average normally is 10.5 for a d20). You overcomplicate this math by a ton, by trying to take into account when a specific bonus would be better than advantage against a certain target number. By doing this you are opening the viewer to question why you stopped the target number at 25. This entire process feels extremely arbitrary. You also take way too long to get to the point of this video and take time explaining terminology that does not really matter for the understanding of the viewer. You take time to explain the basic concepts of probability, something that everyone learns in school, and if they are a ttrpg fan are very likely somewhat familiar with how it works. It feels like you are trying to fish for a specific audience (nerds, more specifically math nerds) and then being patronizing to the targeted viewer. Overall, this video has a neat idea, but you do not execute well. The video title, and intro are in agreement (specifically talking about D&D 5e and BG3), while the bulk of the video tries to be broad to apply to ttrpgs of all shapes and sizes. You are talking about an inherently nerdy, somewhat hard to grasp concept, as if the viewer has very little experience with probability to people who likely are already well versed in the topic. This entire piece feels like a rough draft of an idea, not cohesive with itself, and does not have a clear idea of what it wants. P.S. I fell as though you have the capability to make good content, as you personally explain things well, you just need to organize the video idea and script better. 6/10.

[@drachirx3323]

THAC0 lol

[@pacattack2586]

Advantage is about a +3 or so, disadvantage is roughly -3. So the thing that you are missing here is we try to go overall benefit where we add up the percentages we get 1332 total for advantage and 1345 total for +3. This is assuming you are playing with nat 1 autofail nat 20 autosucceed, without which the difference is more pronounced. This being said: There are a lot more ways of gaining advantage in 5e then there are of gaining a +3 bonus, and considering you can only apply advantage once, I would actually argue the +3 is more valuable.

[@TheChiptide]

Not necessarily! While the average roll with advantage is a 13, it’s not really the same as rolling once and adding 3. When rolling with one die, every roll is equally likely to get every number, so with a plus 3 getting a 4 is just as common as a 23. It’s a 5% chance across the board. With advantage, though, since you’re always choosing the highest number, you only have a 0.25% chance to get a 1, since they both need to be a 1, while rolling a 20 is technically the most likely outcome at a 9.75%! (And the opposite is true for disadvantage)

[@Pystro]

So your main point "we add up the percentages we get 1332 total for advantage and 1345 total for +3" seems to make sense. The video claims that if there are 10 difficulties where it would be better to have a bonus, and 10 where it would be better to have advantage, then that cancels out. But if most of the cases where advantage is better it's by 16%, but most of the cases where a bonus is better it's by 25%, then the bonus would clearly help you more overall. [edit: As I also stated in a stand-alone comment, a bonus of 5 only beats advantage if you are _equally_ likely to run into target numbers from -10 to 40.]

[@pacattack2586]

@@TheChiptide That's why I said 'about' a +3 bonus... I'm aware that they aren't exactly the same and there are pros and cons to both (especially if a nat 20 doesn't guarentee success)

[@angeloid_]

first 12 minutes are absolute yapping that could be condensed. rest of the video is really interesting though

[@quan7umjack]

You claimed that advantage helps you avoid low rolls, but does not make you roll higher numbers. This is definitely false. With advantage a 20 becomes the most likely outcome (39/400) and a 19 the 2nd (37/400) and so on.

[@forsackean4123]

What he was more so talking about was that advantage in it of itself doesn’t guarantee a higher roll, more so that it nearly guarantees avoidance of a low roll because of the statistics you mentioned. At least that was my interpretation of the statement. As I haven’t taken stats yet I could 100% be wrong though and if I am could you please explain how.

[@mrosskne]

there are so many better ways to resolve actions than d20 plus numbers