/sci/ - Science & Math

>>6056967
it depends on your crit nwb.

B

>>6056967
if we are assuming uniform distribution then they're both the same.

(50+60)/2=(20+90)/2=70

fugg i mean 55

>>6056967
Average damage is the same but A is better due to consistency.

Impossible to awnser without more data about the game and sword use. Higer damage might be lucky against an unbeatable opponent as opposed to a. A would be moree efficient to kill any enemy between 91 and 100 or under 50 but higher than 20

>>6056967
Let's have fun with this:
5% of the time you deal double damage.

Depends on hit, crit, procs, etc.

Depends on the distribution of enemies HP.

B for epeen dmg

>>6056967
blue

Depends on enemy HP

if (hp < 21)
it doesn't matter.

else if (20 < hp < 51)
Sword A is superior

else if (50 < hp < 61)
it doesn't matter

else if (60 < hp < 91)
Sword B is superior

else
it doesn't matter.

Blue. Less variance.

Going off the image alone it has to be A.

Chances of getting at least 50 dmg is 100%

For sword B, chances of getting below 50 dmg is about 43%

I'm sure this will sound extremely retarded, but this thread makes me wonder...

50-60. That's eleven numbers, even though 60 minus 50 is ten....In situations where you have to count EVERY number...is there an easy way to figure that out?

90 minus 20 is 70....But in this instance you would consider there are 71 damage possibilities

>50-60. That's eleven numbers, even though 60 minus 50 is ten....In situations where you have to count EVERY number...is there an easy way to figure that out?

I'm sorry, I'm not sure - an easy way to figure _what_ out?

>>6057057
but it does matter.

if enemy has 241hp, you can 3hko with B, but you need 5hits with A.
Keeping in mind that the more hits you take, the more life you lose... you could even die before having the chance to deal the last hit.

>>6057110

Your best-case is a 3-hit KO but you can also accidentally roll 20 on each attack and have to attack 13 times before it dies, whereas worst-case with the other sword is 5 attacks.

Now it IS true that that's not the same as "Doesn't matter" (Because e.g. it will kill you in 4 turns, so it is very important whether you can kill it in less than 4 turns) but now we're conditioning on more than enemy HP (We now also care about OUR HP and enemy damage. If we have 1000 HP and the enemy does 1 damage, it doesn't matter which sword you pick, you will win. If we have 1 HP and the enemy does 1 damage, it doesn't matter which sword we have, it will kill us).

>>6057110
That assumes you're dealing high damage with B. What if you get shitty rolls and do 20 per hit? You're boned.

>>6057110
Thats true only if you value the chance of early kill over the the chance of late kill. As in 241 case A will still guarantee a kill in 5 hits, while B might take as many as 13
Such as an important boss battle, where 3 lucky high hits would win the battle but you could consistently try again if you failed.
Meanwhile standard minion fight you might wanna take A instead as it guarantees kills and doesn't expose you to possible dying penalties if you had hit several times low with B.

I assume that every damage value has an equal chance of being chosen? That is, 51 damage and 54 damage have an equal chance of happening every attack?

Which sword gives a bonus to my fireball spell?

>>6057000
You mean lower variance.

A, it does more consistent damage so you can more easily create a strategy around doing ~55 damage per turn. The last thing you want is to do a "guaranteed crit this turn" and then land a 20.

>>6056967
sword A because variance is a bad thing for the player.

>>6057213
>>6057062
stfu

As a Dungeon Master: Definitely B - variance is a GOOD thing, the players are a lot more on the edge when I'm rolling 2d12+2 than when I'm rolling 2d6+8.

Under uniform distribution:

E(A)= 55
Median=55
Standard Deviation= 2.9

E(B)= 55
Median=55
Standard Deviation: 20.2

It's ultimately up to you but risk-averse individuals would choose A while risk takers choose B. After facing many enemies, there won't be any effective difference anyways assuming 1-to-1 damage.

This question should be simple to answer actually.

OP just give us a specific case with ALL the relevant data necessary to determine all the possible ways to win or lose and we can tell you which sword will win more often.

This question is only hard because we don't have more data.

>>6057000
That's dumb. What if the targets have 61 hp?

>>6057130
This actually matters sometimes.

http://www.garath.net/Sullla/FF/berserker1.html

With reference to which is of the best utility to the PC:

1.) blue is better because less variance is more reliable stats which in turn is easier to design a reliable strategy around.

2.) blue is a more popular color.

3.) When fighting a monster with relatively high HP, you will require relatively many hits so the damage will be about equal from either.
However, when fighting monsters with lower HP, red would either be more likely to do overkill (a neutral quality) or would sometimes require multiple hits to kill a single weakling (a negative quality).

blue wins on all counts.

>>6057324

This. If you add up all the permutations for each interval (11 for 50-60, 71 for 20-90) and divide that number by the number of permutations for each respective sword, you get 55. If each sword does, let's say, one swing per second, then over time the average damage per second for each sword is 55. This is assuming that each of the permutations within the interval have the exact same chance of occurring.

>>6057069
this is not a discrete problem dont try and make it one

It's a game of luck.

red wins if opponent has high damage resistance

Depends on what you're doing with it.

Prolonged battle? Sword A is better. One-hit kills? Sword B.

>>6056967
Not enough information. Are the damages uniformly distributed? What's situations are you using the swords in?

Consider the following example. You're fighting a mob with 61 hp, it kills you in 1 hit guaranteed, but only hits after you have. Sword B is the only sword that offers you the possibility of defeating the mob.

Now consider the example where you're fighting a mob with 100 hp, it kills you in 2 hits. Sword A guarantees victory, sword B does not.

Now consider the space of all possible encounters and realise that there is no way to determine which is the better sword.

>>6057570
however, if a monster has 65 HP sword A will always take 2 hits to kill it, while sword B will one-hit it one third of the time, which can be quite valuable against suicide bombers or other enemies who have a dangerous attack with high cooldown.
In the extreme case where they can instakill you, with the second sword at least you have a chance (0.35^N_monsters) to survive, while with A you will hit only once and then die for sure

>Is the distribution normal?
Actually, in most RPGs, the distribution is flat. Let's roll with that from now on, guys.

>>6057062
>implying low variance is desirable
There's no reason to believe this to be true based on the information the OP has given us. Both swords are equivalent with extremely low confidence.

>>6058828

>forgot pic

>>6058832

Let's calculate the odds that, given that the distribution is uniform, and we have a repeating set of attacks (disregard the attacker's defenses and any other RPG conventions)...

What are the odds that using Sword B would do more damage than Sword A in... say 10 attacks?
>Useful question for a Boss Battle.

There is a 3% probability that if Sword B is chosen, you will inflict damage greater than the maximum damage of sword A.

>>6058845

Under what conditions?

>>6058847
Consider sword B damage range is 70 numbers in difference. Only 30 of these numbers will be greater than 60. Therefore we stack the odds. 1/70 [for any number between 20-90] + 1/30 [for any number greater than 60 but less than 90]. We find the LCD of 210. 3/210 + 7/210 = 10/210. This evaluates to 4.7% chance that Sword B damage will be greater than Sword A. My mistake for my previous miscalculation of 3%. Anyways thats how i came to my conclusion.

Get this cancerous shit out of here.
>>>/v/

>>6058824
Why the fuck would you attack a monster when there's a ~50% chance you won't survive the battle?

>>6058861
Those examples of his appear to be examples, not fully worked scenarios.

>>6058851
Bullshit it is 50% (49.2958 if you don't count equal).

Assuming independence, approximate both to be continuous.
A ~ U(50,60), B ~ U(20,90)
fA(a)=1/10, fB(b)=1/70
fA,B(a,b)=1/700
now double integral from 50,60 dB on the outside and from B,90 dA on the inside.
ie.
<span class="math">\[ \int_50^60 \int_B^90,dA,dB}[/spoiler]
equates to 0.5

But either way, less variance is better in most cases. In most games, it is about being consistent. Sword B will allow you to take mobs that A cannot, however that also means that you will die to mobs that sword A never dies to. Since the reward for killing a mob is usually much lower than the penalty for dying, sword A is better. (note in things like PvP, you may want to use high variance swords for fun)

>>6058868
failed latex
<span class="math">\int_50^60 \int_B^90,dA,dB}[/spoiler]

>>6058868
fail LateX
<span class="math">\int_50^60 \int_B^90,dA,dB[/spoiler]

>>6058868
<span class="math">\int_{50}^{60} \int_{B}^{90}1/700,dA,dB[/spoiler]
LaTeX fail

A for pve(consistency of dmg and produced threat, no overnuke)

B for pvp (burst dmg, surprise anus rape with crit combos)

>Why the fuck would you attack a monster when there's a ~50% chance you won't survive the battle?

Everybody dies some day and this way I might have glory first for having defeated the Lion of Arrash.

The monster is threatening my spouse/child/parent/insert.

I'm in a gladiatorial battle and it's kill or be killed.

Or in other words

>There ARE stupid questions.

>>6058826
i see what you're saying, but I don't think it would be unfounded to make the assumption that mosters with lower HP are more common than higher HP; and unique monsters (one that can instakill you) are relatively uncommon.
I still think blue is better just because the monsters it is superior against are more common enough to outweigh any benefit from the red sword.

>>6058828

You already know it's not normal because there is a min and max.

>>6056967
EXPERT RPG PLAYER GOSU PRO COMING IN

THE ONLY REAL ANSWER IS: DEPENDS ON YOUR ACTUAL CLASS-CHARACTER. MAXIMIZING DPS WILL YIELD STATISTICALLY EQUAL RESULTS, BUT IF YOUR ROLE IS DAMAGE AND YOU HAVEE SUPPORT, THEN B. IF YOU ROL SOLO OR ARE A SUPPORTING CLASS (THINK "TANKS") THEN IT DOESN'T ACTUALLY MATTER AT ALL UNLESS THE SWORD HAS EXTRA BONUSES RELATED TO OTHER FEATURES OF THE GAME.

CRIT % IS ALSO IMPORTANT, ASSUMING THERE IS NONE, SEE ABOVE.

ID LOVE TO STAY AND DISCUSS BUT I CANT.

TRUST ME, I WAS A RAGNAROK ONLINE PRO ONCE.

>>6056967
PDF for Sword A : f(x) = x/550, 50 < x < 60
(because F(60) - F(50) = 1)

PDF for Sword B: g(x) = x/3850, 20 < x < 90
(because G(90) - G(20) = 1)

Expected value for Sword A = integral[50, 60](x*f(x))
= x^3/1650, evaluated from 50 to 60
= 216000/1650 - 125000/1650
= 55.1515152

Expected value for Sword B = integral[20, 90](x * g(x))
= x^3/11550, evaluated from 20 to 90
= 729000/11550 - 8000/11550
= 62.4242424

Assuming a uniform probability distribution, Sword B has a higher expected value and is thus the better choice.

>2013
>still doing rpg
>not glorious chess master
>check your fedora

captcha
>calamity oodurex

>>6059328
>PDF

The distribution is discontinuous so you can't do that, you want to do a probability mass function instead, which gets you 55 for both swords.

>>6059581

And I will say: That is a very subtle error because your math seems to works out, so it took me quite a while to find - I didn't remember that a PDF had to be continous until I looked it up. The only reason I persisted rather than go "Welp guess I'm wrong" is because I've played a lot of roleplaying game and have gotten quite a feel for how dice work.

>>6059581
>>6059586

Who told you you can't integrate a discontinuous function?

These threads are hilarious because you can tell who is a scientist and who is an engineer here and where the disconnect is.

Definitely Sword A. Like someone said earlier, assuming even distribution, they're pretty much the same. So we have to examine practical aspects rather than theoretical ones.

That being said, it really comes down to consistency, and which one you'd prefer. I'm sure there tons of ways you could combo sword B with certain game mechanics in whatever, but in general, Sword A, both due to consistency in damage, and the consistency in strategy that can provide when factoring your damage output into your strategy, as well as making the data itself easier to think about when shits going down.

Its hard to argue something like "but 61 hp" because yes, you might one hit with sword B and you will never with sword A, but you will always 2 hit with sword A and it could take up to 4 Hits with sword B! This being said, in the case of 61 hp, assuming even distribution, Sword B would only be better a fourth of the time. Worse half the time.

Theoretically, Sword B can never be more than equal(pretty sure, might be wrong about this part) but will usually be worse, if you are taking hp and damage into account solely.

>>6057069
if you mean what I think you mean, you figured it out yourself. Numbers from a to b are b-a+1.

>Who told you you can't integrate a discontinuous function?

That's not what I said; I said you cannot do a Probability Density Function over a discontinuous probability mass and get a correct result.

>>6059328
You're assuming that the damage takes all values in the given range, rather than integer values. Pretty sure the intent is integer values.

>These threads are hilarious because you can tell who is a scientist and who is an engineer here and where the disconnect is.

This is me:

>>6057057
>>6057103
>>6057128
>>6057323
>>6059088
>>6059581
>>6059586
>>6060032

Am I Scientist or Engineer? (Bonus points if you can guess what kind of Scientist/Engineer)

>>6060041
Not that guy but clearly you're a computer scientist.

>>6060041
If that's the case, let me just say that B allows for more chances of new, useful adaptations to appear. Damage variance is good for survival.

>Not that guy but clearly you're a computer scientist.

Nope

I'll give a hint: I don't actually use statistics in my work

>>6057535
>Guaranteed two-hits with sword A
>Max 4 hits with sword B