level 5 fireball + level 5 fireball does 5 damage turn 1 and

Charge can not miss.(A charged fireball can still miss)

>>7900937
1488420666

>>>/v/
>>>/tg/
>>>/trash/

>>7900946

This is a math question fuck you you autistic gentile.

>>7900937
lev 5 by 5 = 5 damage
charge + 5 = 10 damage
chance of garbage = sage

When your hit is above 50% you only want to check it once, when it is below 50% you want to check it twice.

fireball + fireball at hit below 50
charge + fireball at hit above 50

This is just me theory crafting and it could be the opposite.

>>7900961
faggot

You always want fireball + fireball
Charging is pointless

>>7900942
>>7900946
>>7900973

engineers please go and project your dick sucking complex elsewhere please.

>>7900975

Say that a charged fireball did 11 damage.

How low would your hit need to be for fireball+fireball to be better?

>>7900993
yes

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it would be 50% for both right because of the outcomes
2 fireballs has 4 outcomes, 1/2 chance to hit turn 1 1/2 chance to hi turn 2
charge fireball has 2 outcomes 1/2 chance to hit turn 2
in that sense they are statiscally the same, both will do the same amount of damage over a fight of about 100 turns. however, in situations where the enemy has 5 hp or lower then the fireball would be better.

in summary: they are the same to my knowledge

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>>7900937
It's always better to shoot 1 shot.

1-x is charge
(1-x)^2 is the chance of both shots hitting

>>7901110
Here x is the chance to miss

>>7901110
grossly incomplete. there's a chance for 1 shot to hit which you're ignoring completely. two shots give more stable damage. one shot has higher st.dv. (they both have the same expected damage)

>>7900946

FIREBALL Z!!!

>>7901118
1 shot can hit, and do 5 damage m8, whereas a charge shot has the same chance as a single shot and does 10, so the 5 shot doesnt matter

>>7901124
Retard, the average damage by no-charge in any number of turns is the same or higher than the average damage by charging. This is because despite charging having a higher chance of doing 10 damage every two turns it also has a higher chance of doing no damage every two turns.

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>>7901118
x is hit %

Have I satisfied your autism?

>>7901124
If the charged shot misses, that's 2 fire balls = 2 wasted turns
If I missed with one uncharged fireball, I would still have an extra 5 damage if I made my 1st shot; or have another (X) hit chance for my second fireball
Both fireballs charged or not have the same (X) hit chance

>>7901132
>the average damage by no-charge in any number of turns is the same or higher than the average damage by charging.
Lel retard 5+5=10
99% chance per shot is 0.99*0.99*10 for 2 singles, and 0.99 *10 for a charge
Charge > 2 uncharged

>it also has a higher chance of doing no damage every two turns.
1-(0.99*0.99) > 1-0.99
2 single miss chance > charge miss

Fucking kek
You must be trolling
Please kill yourself, you fragile x syndrome tier retard

>>7901133
>your autism
what the fuck does this even represent, you idiot? the probability distribution is really simple, they have the same mean and one has higher std.dv.
what the fuck do you even think you're graphing?

>>7901143
>99%
Yeah but you don't know that

>>7901142
>If I missed with one uncharged fireball, I would still have an extra 5 damage
[5x +5(0)] / 2 turns < 10x/2turns m8
Please an hero. I'm not wasting time on the last cause that you are any further :^)

Enjoy your shit tier job with those math "skills" (or lack of)

>>7901143
are you 12

two shots:
chance of doing 10: (1-x)^2
chance of doing 5: 2x(1-x)
chance of doing 0: x^2

one shot:
chance of doing 10: (1-x)
chance of doing 0: x

you see how they're different? how you can't just compare the chance of doing 10 dmg and call it a day? stupid fucking asshole, they have the same expected value of 5 but one shot has higher standard deviation

>>7901148
it's not 5x vs 10x you brainded fucker

it's 10*(1-x)^2 + 2*5x*(1-x) vs 10*(1-x), turns out they're exactly the same

THEY HAVE THE SAME EXPECTED VALUE

>>7901143
>99% chance per shot is 0.99*0.99*10 for 2 singles, and 0.99 *10 for a charge
Retard, you fail at basic probability. Again you ignore that you can get 1 miss and 1 hit if you do uncharged.

Average damage after two turns with 0.99 chance to hit for uncharged:

(0.99^2)(10)+2(0.99*0.01)(5) = 9.9

Average damage after two turns with 0.99 chance to hit for charged:

(0.99)(10) = 9.9

>>7901143
>1-(0.99*0.99) > 1-0.99
>2 single miss chance > charge miss
1-(0.99*0.99) is the chance of not getting two hits (i.e. the chance of getting only one hit or no hits), it's not the chance of missing two hits. What you should have done is

(1-0.99)^2 < 1-0.99

Dunning-Kruger in action.

the expected damage is the same you fucking maggots
x*5 + x*5
x*10
unless overkill is important theyre equally valuable

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>>7900937

>>7901331
While the expected damage on even turns is the same, on odd number of turns the uncharged shots have higher expected damage. If the enemy's health is between 10n and 10n+5 where n is a nonnegative integer then the expected number of turns to kill the enemy will be 1/x less than with charged shots.

>>7900937

They have the same expected value no matter what

But, fireball+fireball has lower variance

You always pick the lower variance in this case

>>7901412

What if a charged fireball did 11/12/13/X damage instead of 10.

Could you determine how much hit you need vs the dmg increased from charge fireball for it to be worth it.

>>7901585

If it did any more damage than 10, it would have a higher expected damage

Whether it would be ''worth it'' over the two fireballs depends on your own desires

If you want the most damage possible, then sure. but if you want lower variance, then it's up to you.

For example consider this:

You can pay $1 to flip a fair coin, if it goes heads, you win $5, if it's tails, you get nothing. Basically, you can either profit $4 or lose $1

Now imagine if you can pay all the money you have to flip a coin that is stacked so heads comes up 55% of the time. If it's heads, you win 5 times as much as you paid, if it's tails, you get nothing.

The 2nd game has a higher expected value, because you win 55% of the time rather than 50%. But, you would still choose to play the first game, because it has a much lower variance.

While these are rather extreme scenarios, the same principle applies to the fireballs. If you use the charged fireballs, it will do more damage on average, but it could leave you fucked if it misses (just like losing the 2nd game).

Right but say you had the original spells or the option of

charge + FB = 13

Say this is WoW and you have a 13% chance to miss without any gear, with gear you can get hitcapped and have 100% firebolts always hitting

Say that a charged fireball did 5/10/15/25 more damage than a fireball fireball.

However for each instance, wouldn't there be hit values in which one favors the other?

If we introduced crit and say that there was a 10/25/50% chance that a spell could deal double damage.

Because it's mirrored I assume it won't change any results and both methods would be the same overall DPS over 100 turns?

>>7901615

If you have a 100% hit chance and the charged does more damage, then you should always pick charged

Again, it depends on what you want. If you just want to do more damage, then pick the charged. If missing a charged would leave you way more fucked than missing one fireball and hitting another, then pick the 2 fireballs, otherwise pick charged.

Also, WoW is a fucking horrible game and you are autistic for playing it

>>7901618

Given the option of more spell power or more hit is more hit always going to be better than more spell power? Say that your at 99% hit and your average firebolt does 1kdamage.

Could you mathematically determine how much spellpower would be needed to take that instead of taking the final 1% hit to reach hitcap

>>7901625
Yes of course. But assuming that the key factor you want to conserve is the average number of turns it takes to kill an enemy, which method is better will depend on the amount of health the enemy has.