Infinite Damage & Infinite Series: Exploding Dice in Dungeons & Dragons
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- čas přidán 5. 09. 2024
- Here's my submission for the SoME3 competition. This is really my first time making an "educational" math video and using Manim, so this video is certainly rough around the edges, but it did make for a fun and worthwhile project over the summer. If I did get anything wrong, then please say so in the comments. After this video, I do want to try making more videos focused on the probability and stats of dice in D&D and maybe other TTRPGs, but probably not as math heavy as this one and with much less Manim animation. I've actually wanted to make a video series discussing dice rules in D&D for a while and SoME3 gave me a great excuse to start one.
Also, I'd like to note that after I wrote the script for this video, I realized that WOTC had actually implemented Exploding Dice into a spell in a recent Unearthed Arcana called Sorcerous Burst (although, the spell does have a cap to how many times it can explode). So Exploding Dice may actually become an official part in D&D and not just neat homebrew.
Thanks to my friends who helped make this video possible!
Mari's Twitter: / ririichu_
Mimi's Commissions: comimissions.c...
Exploding D1 seems to be the best die
Time stops as the mobius die shoots an endless laser beam at the entity.
It destroys the universe once the DM terminates the process.
The only problem is that it doesn't terminate, and the entire D&D universe was oneshot.
So as long as you're not playing a monk, a race with the Natural Weapons feature, or take the Tavern Brawler feat - you can be One Punch Man (as the base punch is essentially 1d1+Str)
D&D doesn't go down to D1, the smallest actual dice size is d2, when it goes lower than that it just becomes a flat 1, no dice rolled.
11:00 It would probably be better to find the chance of dealing 676 or _more_ damage, since that would also kill it.
It happens that you only have to check if the 84th dice roll is a 6, 7, or 8, which triples your chances (to 3/(8^84)...)
15:20 This graph suggests a possible homebrew rule: When rolling (non-exploding) dice, _before_ the roll, players may _choose_ to declare their roll "exploding" and take either -1 to the roll per die (1d6 -> 1d6!-1, 2d8 -> 2d8!-2) or downgrade the die class by one rank (1d6 -> 1d4!, 2d8 -> 2d6!). This would represent taking a "risky"/"desperate" action, as the _average_ would go down slightly (for both options) in exchange for increasing the _maximum_ possible result. For example, in a situation where a character needs to roll at or above 16 (for a OHKO, (non-"d20") skill-check, or whatever) but they only have 2d6 to roll against that target...normally, that would be flatly impossible. But, if they chose to downgrade to an exploding _2d4_ instead, they'd have a _small_ chance.
...this sort of takes the idea of "automatic success on natural 20" and generalizes it to other dice (if/when a player wants to "push their luck" and take the penalty). Actually, in d20 based games, this could _replace_ the "nat-20" rule, and allow for success chances other than a flat 5% when the DC is higher than 20 + all modifiers. (You'd have to take the minus-1 option, or roll a "d18" by rolling a d20 and discarding-and-rerolling any 19s or 20s, to explode on 18s.)
I like this idea a lot. I can see it being used on a magic homebrew weapon of lower rarity or maybe a homebrew weapon property for that Weapon Mastery stuff that One D&D is trying to introduce. Totally keeping this suggestion in my back pocket.
@@CubingAdrian Just wondering, have you used a d120 in DND?
@@ValkyRiverI have! Kind of..
It was curse dice relic, which gave 120ish different effects when triggered. It was really succesful, but mostly just because of how big the dice was. A real event when rolled.
Altough I'm really curius about an idea how to use it in an actual way.
That's also really fun because it encourages players to make more use things like Savage Attacker, Empower Spell, Lucky or Portent by giving them more of an opportunity to explode than normal damage rolls.
@@CubingAdrian i wonder how the math works out if you apply exploding dice to the minimum instead of the maximum the dice can roll, to up the fun of accidently rolling poorly
I love the video, wonderfully explained and very informative, BUT WHAT IS UP WITH THOSE DICE WHY ARE THEY SO WONKY
They're called Skew Dice from The Dice Lab. Saw them in a Numberphile video once and had to buy them. They were also the only large-ish set of d6s I have, so I kinda had to use them for the video.
Like, at least they’re still fair, just mathematically more cursed
@@ianweckhorst3200 some might say that those skewbical dice skew ones expectations. And I wish they were around when I was in Skewl learning about probability.
@@CubingAdrian we love the skew dice haha
intentional or not, they make for a fun visual gag in the video
U can use the fact that E(X) = 1/s(1+2+…(s-1)+(s+E(X)) to solve for E(X) directly.
Edit: the interesting thing is that this shows that is doesnt matter for the expected value on what number you get to roll another time
Personally I homerule that healing dice explode. It makes being a healer more exciting. Attacks get crits, healing gets exploding. On average with this buff healing spells still don't outpace damage so it appears to work fine.
I played in a campaign during the D&D 3.0/3.5 era that had a variant of exploding dice. Instead of damage dice being able to explode, it was the attack roll using a d20. A natural 20 would always hit and you had roll the attack dice d20 again to confirm the bonus damage. This was a balancing mechanic that players always had a 1/20 chance of hitting an opponent regardless of how difficult it was to ordinarily hit. So a natural 20 would always hit and a natural 20 after that would always do double damage. So per our exploding dice rules, what happened if another natural 20 was rolled? Take the maximum damage and quadruple it. One more natural 20 would always insta kill your opponent regardless of their relative strength. A 1 in 160,000 to immediately slay an opponent, rare enough not to be game changing, or so we all thought. We played with a preverbal 'that guy' that embodied a chaotic character. So as 3rd level characters listening to the villainous speech of a 12th level duke oppressing the territory, that guy decided to simply throw his dagger at him from a 30 ft distance in a not so subtle means of shutting up the bad guy. Well he did got that 1/160000 luck to instakill him. Our DM had an immediate love/hate relationship with us from then on.
We also had an exploding series of failures for natural 1's as well with a similar number of consecutive failures resulting in immediate player death. Our DM insisted we keep this part in our game.
As someone who knows as much about D&D as a gopher, and who knows nothing about them fancy letters in maths, this video is very interesting, I like your fancy words magic man.
Hi, thanks for watching my SoME3 submission! I've never made an educational math video or have used Manim before, so this video is probably really amateurish. For all mathematicians and D&D rules lawyers, please comment on anything I might've gotten wrong in this video as I'm bound to have gotten something wrong. Thanks!
A small question: would exploding dice make the Greatsword (2d6) strictly better than the Greataxe (1d12)?
@@TheWackyWorkbench Good question. Debatably, you could say that the Greatsword is already better than the Greataxe, no exploding dice required, but mostly in the category of long-term damage. The average of a 2d6 is 7 while the average of a 1d12 is 6.5. Thus, over many, many attacks, the Greatsword will likely do more total damage. In the case of exploding dice, the average for an exploding 2d6 and 1d12 are like 8.4 and 7.09 respectively, so exploding dice give Greatswords more of an edge in terms of long-term damage, according to the averages alone.
I certainly wouldn't say that exploding dice would make Greatswords strictly better because there's a lot of other factors in the game that could boost Greataxes over Greatswords like racial features, class features, feats, etc.
Keep it up, you need the practice.
Not a mistake per se, but the mixing in the intro made it a little hard to hear what you were saying over the music - in future I'd make the music a bit quieter :)
Very interesting! So because the expected value of a non-exploded dice is s/2 + 1/2, we can get the the difference in damage per attack that exploding dice make by doing (s/2 + s/(s - 1)) - (s/2 + 1/2) = s/(s - 1) - 1/2. In the limit (for large s), this would mean that exploding dice do 1/2 point damage per attack more. For a d4, the difference is the largest, coming to 4/3 - 1/2 = 5/6 damage.
So actually a modest improvements, certainly less powerful than +1 weapons (even setting aside the +1 to the attack roll you get for a +1 weapon).
I dismissed exploding dice in D&D before, but now I think I may give my players the opportunity to gain some exploding-dice weapons at some point during my current campaign.
Fun fact: Technically exploding dice is canon to DnD! The first level spell chaos bolt states that if the two dice you roll, both roll the same you roll them again on another target, and that applies to those dice too, so on and so forth as lucky as you can get.
Not really exploding dice, as each target still gets the simple 2dX damage.
this is hard limited by the number of creatures within 30 feet of each other you can make a path between hitting each only once. that's usually only a few creatures so you can't go infinite
@@mo6555 and the amount of damage you can do with exploding dice is limited by the health pool of whatever youre targeting, unless you DM lets you keep rolling to destroy the world/universe/multi/omni/omegaverse
@@rjwaters3 it's not technically limited. the damage isn't applied until you're done rolling the damage dice for the attack. of course most DMs would stop when you'd kill them outright, but RAW it would just keep going
You can calculate the expected value a different way.
E(Dn) = (1/n)*1 + (1/n)*2 + .... (1/n)*[n + E(Dn)]
this way you get a calculation that solves down to
(n-1)*E(Dn) = (1 + n)*n / 2
or
E(Dn) = (1+n)*n/[2*(n-1)]
I checked it against your solution and the result is the same
It would however be interesting to see the dispersion of the different dice (by how much on average they deviate from the average value that they roll)
E([Dn-E(Dn)]^2)
It's a nice video, thanks !
My complaint is that the music is quite too loud at the beginning and end.
Also, it made me wonder how the variance behaves under the exploding dice rule.
I don't know how common these are in 5E, but this does change the balance of 2d4 vs 1d8 and 2d6 vs 1d12.
Under normal rules the average of 2d4 is 5, but the chance for 8 damage is only 6.25%, while the average for 1d8 is only 4.5, but the chance for 8 damage is 12.5%, so twice as high.
If we introduce exploding dice, the average of 2d4 becomes 6.56 (rounded to 2 decimals) and the chance to deal 8 or more damage is 34.38%! The average of an exploding 1d8 is 5.13, barely above the non-exploding 2d4, and the chance to get 8 or higher is still 12.5%. Thus the only advantage the 1d8 had over 2d4 is eliminated.
Though, to avoid this, one could rule that (1+n)dx only explodes when ALL dice land on the maximum. That would bring the average for 2d4 to 5.33 and the chance for 8 or more damage to 6.25%, restoring the balance with 2d4 having the higher average damage, but 1d8 having the greater chance for massive damage.
this is a great video! i hope you hit the algorithm soon
Cool video! Your weird D6 are killing me though 😂 either way, good math and a cool concept that I had never heard of.
Another interesting fact: Exploding dice improves lower dice more than higher ones.
The formula for the improvement exploding gives is 1/2 + 1/(s - 1)
Thus, exploding increases the average of a 1d4 by around 0.83, while 1d12 only gets an increase by around 0.59.
***stares at the 6th level version of Shatter being presented as equivalent to the 3rd level casting of Fireball, and struggles to contain my laughter***
Really solid video, well edited. Thought this was from a much bigger channel!
Loved the video. Cheers from Brazil.
I used lots of graphs to decide how many dice my players would get for hit points and such, because the average of 3d6 is better than 1d18, since the minimum is 3.
I play my own simplified version of D&D (15-pages long document), where very powerful characters have 30 HP (because lethality), so exploding dice are too much, but I house-ruled that exploding dice add +1 for every exploded dice. So a string of (6,6,4) actually results in 8 damage (6+2) rather than 16 (6+6+4). Considering player characters themselves start with maximum 10 HP, doing 8 damage is already a lot.
1d18 makes it much easier to get an 18 though
It's all fun and games until my tiny creature throws punches with d1s, and always rolls max damage for infinite damage.
punching is just 1 + str mod tho
@@BahamutEx nonono, 1+strMod; max so add a d1, max so add a d1....
@@itchykami but there is no d1 involved it's a flat 1 - a fixed number/amount
@@BahamutEx hmm... so maybe you need to roll a d3 where you reroll 1s and 2s
> I personally think it's a very interesting and exciting way to reward players by boosting their damage.
That holds only true, as long as it is a player-only mechanic.
If you do allow enemies to have exploding dice as well - then they no longer provide an advantage to players.
I'd even argue that the increased damage variability creates a disadvantage for players, since players are typically supposed to be the winning party in any confrontation, and an increase in randomness always increases the chances of the underdogs to win against expectations.
Suggestion: each die explodes into s dice instead of just one die, but they retain their original values. For instance, if you roll a 6 on a d6, you then roll six more d6s and add them up. Those dice can also explode, etc.
Let X be the value of a full chain for an s-sided die. E[X] = [1/s][s(s-1)/2] + [1/s][s+sE[X]], where the first term is the sum of the first s-1 numbers, each with probability 1/s, and the second term is the case where it explodes. So E[X] =(s+1)/2 + E[X]. But since s > -1, (s+1)/2 > 0, so E[X] = E[X] + k for some positive k. Therefore E[X] is not a real number.
It's not hard to show that E[X] = +∞. Using the definition of expected value gives E[X] = Σ (s-1)/2 with no reference to n, in other words just the sum of a positive constant.
Ah, Exploding dice. Closest game I have seen that uses them as standard is Savage Worlds, making use of the same dice, trying to meet or beat 4, with each level of 4 above that adding extra to the result.
That said, my favorite exploding dice story comes from Deathwatch (40k Space Marine RPG, uses d10's and d%(d100). My technology specialist stayed behind to help an Imperial Guard (regular human space army guys) regiment prepare to besiege a Tau (Alien) fortress while the rest of the Marines snuck in. So while they were getting into combats and so on, I was sitting around and blessing tank turrets and ammo (standard techno-religious stuff). When I finally got the chance to shine, I rolled to hit the fortress walls, and succeeded. Then I rolled for damage...the die exploded, then again, then again, then again, then again, then again...about that time the game master told me to just stop, then described my shot hitting an ammo bunker and operating most of the outer wall of the fortress.
That's the thing you have to keep in mind when describing crazy damage like that. It's less disintigrating a dragon with a dagger and more shooting the Giant in the eye with such force it penetrates through to their brain.
Right before this video, I watched a video explaining the difference between infinite and arbitrarily large. In this case, the infinite series results in a potential for arbitrarily large damage, not infinite damage.
Hi there!
loved the video (maybe your music was a bit too loud, great explainer nonetheless)
Mathematician, DM and DnD optimizer here :P
couple of things i wanted to add:
i would probably write the additional damage as: (s+1)/2 + 1/2 + 1/(s-1), since (s+1)/2 is the normal damage a dice would deal,
you can then see that exploding dice give an average increase of 1/2 + 1/(s-1) which averaged over a d4,d6,d8,d10 and d12 is around 2/3 additional damage.
from that we can conclude... exploding dice are a really bad upgrade, worse than a straight up +1 weapon. The problem here is, that WotC seems to horribly overvalue this.
If a dice has n sides, then its expected value is (n+1)/2. Let E(X) be the EV of the corresponding exploding dice. Then we have E(X) = (n+1)/2 + 1/n * E(X), because there's a 1/n chance that we get to roll again. Solving this gives E(X) = n(n+1)/2(n-1) which is the same as your result. We can rewrite this as (n+1)/2 * (1 + 1/(n-1)), which shows that the extra contribution of making a dice exploding is 100/(n-1) percent.
Part of the issue with this balance comes from weapons and spells that don’t simply roll one die. A weapon dealing a D12 is slightly worse than one dealing 2d6. With this change the 2d6 weapon becomes much better. A spell like magic missile deals 4d4 + 4 but cannot miss and is comparable to other level 1 spells that deal something like 3d8 with a chance of missing. D&d isn’t a perfectly balanced game by any means but if you adopt these rules then some classes and features are going to get much more benefit than others.
Some abilities let you reroll any 1’s that you roll. That’s already a big deal in that 2d6 vs 1d12 example but when that also comes with an increase to your odds of exploding things get wild. I’d be interested in seeing the math on exploding dice when you get the option to reroll though. You’d only be able to reroll once, so if you get a 1 twice you’re stuck with it. Otherwise you’d just be rolling a 5 sided die that went from 2-6.
Call an exploding dice with s sides eds, and a normal dice ds. when you roll and eds, 1/s of the time you get another eds added to the roll, so if E is expected value E(eds) = E(ds) + E(eds)/s. Rearranging, and using E(ds) = (s+1)/2, you get your formula. This assumes the mean exists, but it does in this case, so no harm done. I think things get interesting when comparing say 3ed4 vs 2ed6 => E(3ed4) = 10 vs E(2ed6) = 8.4. This exacerbates the non exploding E(3d4) = 7.5 vs E(2d6) = 7 which is maybe already a bit surprising.
Now I'm wondering about double exploding dice (so roll two more dice for every max roll you get). Does that still converge? How many more dice per max roll do we need until the expected value diverges?
for double exploding dice, the Expected value is 3*(5/6)+(6+2*E)/6, which can be solved for with algebra:
E=5/2+1+E/3
2/3*E=7/2
E=7/2*3/2=21/4.
You can continue solving until the number of new dice is equal to the size of the number of dice.
This leads to E=3*(5/6)+(6+6*E)/6=5/2+1+E=7/2+E, which would imply that it couldn't be finite.
The probability of having to roll infinitely, or Xplode (E was used already) can be solved for as follows:
X=1-(1-1/6*X)^2, where the 6 is the dice sides, and the 2 is the number of scale.
Now to solve.
X=1-(1-2/6*X+1/36*X^2)=2/6*X-1/36*X^2
X=2/6*X-1/36*X^2
36X=12X-X^2
36X-12X+X^2=0
24X+X^2=0
X=0 or -24.
Since there cannot be a -2400% chance of explosion, the explosion chance for two dice rolls is 0.
Similar logic applies until the number of new dice is one more than the number of dice sides.
In the case of d6s with septuple explosions, the chance of a full explosion is around 31%. For octuple explosions, it's 50.5%.
There's a spell that sorta does explodeing dice choas bolt where the target takes 2d8 + 1d6 damage. Choose one of the d8s. The number rolled on that die determines the attack's damage type but if the d8s match no matter the number then it jumps to a new target. It's not quite exploding dice but it's always fun when jumps to another target
I think a recursion argument would be much better for explaining. It would take advantage of the fact that when you roll the maximum, you're in the same spot you were, just plus more
In my country (Czechia), most people would associate the exploding dice rule with the children's game Ludo ("Člověče, nezlob se" in Czech) where you have to roll again after roling a six, I wonder if people know that game in America
We have a Game called 'Mensch ärgere dich nicht' (Dude, dont be mad), where you have to go around the Board and If you Roll a 6 you can move and Roll again...
Edit: i looked Up the Ludo Board and they Look very similiar, i guess they are the Same Game, Just different names for it.
We have ludo in the UK, at least
ohh thats what that game is called
Check up the Wiki Ludo page, there are lots of related games, all derived from the India game Pachisi: en.wikipedia.org/wiki/Ludo
In the US, I'm familiar with "Ludo", the closely related game "Parcheesi", and the related commercial/trademarked game "Trouble".
Roll and keep systems be wild with its exploding dice
The only problem with implementing this house rule is that a clever (or powerbuilding) player could make use of the mechanic and some feats, races and class features to manipulate damage rolls to exploit exploding dices. It's all fun and games untill the boss fight you carefully prepared for months gets obliterated by a single guy using a calculator...
Then again, it's still up to chance, so it may not be as bad as I made it out to be.
I remember the first time my DM tried introducing this rule into the game I was a player in. Due to another (Admittedly overpowered) Homebrew rule that allows for every weapon in 5E to have special abilities, I had a longbow that that as long as I could hit with disadvantage I would auto crit any target. We rolled stats and at level 1 I had a 20 in Dex. We had one combat with the rule. I crit his boss and insta killed it turn one. We were like level 5.
40 seconds in and all i can hear is the DOOOT DOOOT DOOOT from the music
Exploding dice is more fun when you also explode crit fails. It's not a math problem sadly, but it adds some mechanical backing to having interesting consequences for a crit fail.
"Dice" is plural. If you only have one, you don't have "a dice," you have "a die."
Dice can also mean singular, and most of the time, people use dice when referring to a single item. Unclear but correct.
I don’t think infinite series is really needed. If x is the expected value of an exploding die with n sides, then x is equal to the average roll of a regular n sided die plus a 1/n chance to roll another x. This results in x=(n+1)/2+x/n. Solving for x gives x=n(n+1)/(2(n-1)), and thus we have our expected value. For n=6 we get the expected value of 21/5, or 4.2.
You could have just considered that every subsequent explosion is s times less likely than the previous one, thus you could have used the sum as n goes from 1 to infinity of [(s²+s)/2s]/(s^n). This way you could have solved for n to get [(s²+s)/2s]*(s/s-1)=(s²+s)/2(s-1) wich is equal to your result, but with less calculations. Still a very interesting video, happy to see I'm not the only fool who uses math when trying to optimize dnd.
D&D doesn't have exploading dice, but savage worlds does.
I once got 47 total damage with an exploading 2d4
The GM, of course, has the final say in all of this.
The GM's job is to prevent mechanics from running away to absurd outcomes, like potential infinities, which would result in destroying the integrity of the game setting / game experience and leading to the campaign's story becoming unsatisfying. If I'm GMing, I don't actually care what the dice say; your level 1 character is not going to somehow off the main antagonist with an impossible one-shot in the 1st or 2nd session of what should be a year-long campaign. It's just not fun. It's a novelty and maybe a noteworthy story for one player to tell later, but everyone else is cheated out of the whole campaign when infinities break something that shouldn't be broken (yet) in that game world because it's an important story-driver.
banger video
The music is a bit loud compared to the voice over
I'm gonna throw exploding 1d1
wish me luck
the D&D equivalent of dividing by 0
Actual infinite damage
Isn't there a value for smaller dice, at which they are more likely to roll that or higher compared to larger ones? Like, if i wanted to do x damage, and rolled a small exploding dice, wouldn't no matter the x there be a point at which the smaller dice are more likely to arrive at that damage x, compared to the larger ones?
alright so it does still have a higher average with larger dice
BUT!
what about great weapon master
if you re-roll 1's and 2's and combo that along side exploding dice, does THIS change the averages in the smaller dices favor?
I wonder what happens to the expected value if you "explode" on a 1
Now I get divergent vs convergent… amazing what framing can do
Great premise, great video, great didactics.
Pls dial down the music and dial up your voice on the intro for future videos, it was hardly intelligible.
Not explodey enough. Instead of adding up all those dice, multiply them.
So if you roll 6,6,2 on a d6, that scores 72.
Nice video, but I'm still unconvinced of the balance of exploding dice in general. Seems like it'd be safer to roll a die of one size smaller on an explosion, that might help balance out your high-result oddity.
Crunching the numbers, you get basically the same result by splitting a large die into two whose maximums sum to the original, i.e. splitting a d10 into a d6 and a d4 is a tenth of a percent off the expected of an exploding d10 where every explosion brings it a size smaller, to a minimum of a d4.
But what if the dice explode higher or always to the same die. Like x on Dx always explode to D6 and then goes with D6.
The music wasn't loud enough in the beginning. i could almost hear what you were saying
🥳❤️👍🏿
13:51 I need help getting this step. How can you change the series in that way?
2:53 inanimate singular they?! you use the word it to refer to bows, but dice are animate to you? Is it because the dice are the subject of "rolling" and thus are viewed as taking an active role making them take 'they' in stead of 'it'? This is very cool to me, I hope this wasn't just a one time mistake but an actual variant use :)
It's because dice is plural. This would be more obvious if he was using the correct singular, 'die', for the rest of the video, however
@@Starwort , "the dice resulting from the initial explosion can *also* explode, if they role their highest possible value", ok, after reading this over a few times I now understand that they could be talking generally with the plural 'dice'. I think it is a wierd way of saying it tho, considering that the dice only ever explode one more dice each time.
Just give me an exploding 1d1 that will always throw the highest number.
i though for the tarrasque it said 1/884 not 1/8^84
Me showing up with a one sided die and some weird rules.
you didn't need to use infinite series
good video but you should work on the audio mixing, the music in the intro was way louder than your mic audio for example
yay math rocks!
Does this mechanic only work when rolling ONE die? What if you're rolling an exploding 2d6?
I believe it applies to each die
exploding dice are kinda used in rolemaster
the singular is DIE
You sir need to get a d676 instead, after all on average with a d676 you can expect to twoshot a Tarrasque. But with a nat676 you'll oneshot it.
This is just Acing in dead lands
Woo hackmaster!
just rolling again isn't much of an explosion. Would be more satisfying to me if a dice exploding meant you reroll using the next smallest dice but rolling more dice. So D20 becomes 2D12 becomes 3D10 becomes 4D8 becomes 5D6 becomes 6D4. offering a higher max outcome each time from a larger explosion of dice but it caps out and the smaller the start the smaller the finnish. If you rolled 2D6 and they both rolled 6s then you now roll 3D4s... which has the same max roll of 12. This idea can't work can it? Well damnit I've already dug my grave on this hill so I'm dying on it.
Exploding dice doesn't belong in D&D. Just play Shadowrun like a normal human being. They have those there.
whys the music so loud lmao
2:34 hey um. i think there's something wrong with your dice. i think something's wrong
They're Skew Dice from The Dice Lab. They do function as fair dice if you disregard the pips. They were also the only matching set of dice I had, so they had to do for this video.
In the 1st minute, the music is too loud, and tends to drown out your voice.
For what it's worth, exploding dice mechanics go back to the 80s, and D&D is a late-comer to using them.
Also, the singular of 'dice' is 'die'.
I don't like the standard exploding dice, because of those gaps.. Rather, it should be that rolling max means you get max-1/die plus another roll.
Please don't put a doorbell thing again. It's really annoying especially since it does sound like my doorbell. I'll try to watch this video, but this is very hard.
EDIT: Ok. It was cool video. I kind of expected it to not make much difference except for cases when it explodes once - where I thought it might be an edge case, but it's nice to see it calculated.