How to calculate the chances of reaching a certain success level prior to failed channeling?

In Warhammer 4e casters can use channeling in order to gain success level prior to casting a spell. Success levels are essentially for every 10 you exceed the skill number you gain a success level and they keep piling up till you make a failed roll.

As a wizard I am trying to figure out how to calculate the probability of piling up enough SL’s before failing channeling and suffering a miscast.

What I wish to ask if how can I calculate my odds of reaching a certain SL prior to suffering a miscast (Making a failed roll) and losing all of my SL? (Note that the system uses a d100 and you try to roll below your skill.)

How to calculate the delivery of a touch spell using the familiar?

Familiar Conduit text reads

Under your tutelage, your familiar has grown attuned to the hidden currents of the world and can serve as a conduit for your magic. If the next action you use is to Cast a Spell that has a range, the spell uses the familiar as its origin point.

Touch is a range, but familiars do not have the required stats to make an attack. How does one calculate the success or failure?

D&D 3.5e: How exactly do you calculate changing a Line into a Cone?

Exactly as the title is asking. But to be more specific, I am asking for the purposes of the Shape Breath Metabreath feat. As the feat says:

If you have a line-shaped breath weapon, you can opt to shape it into a cone. Likewise, if you have a cone-shaped breath weapon, you can shape it into a line. When you use this feat, add +1 to the number of rounds you must wait before using your breath weapon again.

Comparing this to the breath weapon of a Dragonborn of Bahamut, which is a Line with a range of 5ft per hit die, how would you calculate converting the breath weapon into a cone? Would a 6th-level Dragonborn of Bahamut breath out a 30ft cone? Or would the length of the cone be reduced?

How can I calculate the optimal amount of attack bonus to give up when using Power Attack?

The Power Attack feat lets you sacrifice attack bonus (AB) to increase your damage.

It’s easy to see that you don’t always want to give up the same amount of AB, and that the optimal amount (assuming you’re trying to maximize your expected damage output) depends on multiple factors. Consider the following two degenerate cases where it’s easy to see that the optimal choice differs:

  1. If your opponent’s AC is so much higher than your AB that you will only ever hit them by rolling a natural 20, then you clearly want to sacrifice the maximum possible amount of AB, since it won’t affect your chance to hit at all (5% in any case), and maximizing your Power Attack damage will result in more damage if you do roll the natural 20.
  2. If your foolish DM has granted you the legendary +Graham’s Number Sword of Munchkinry at level 1, then you clearly don’t want to use Power Attack at all (unless you’ll only miss on a natural 1), because your base damage is so high that even a 5% decrease in your chance to hit will utterly dwarf any piddly damage you get from sacrificing your 1 BAB.

In between these silly cases, though, I’m not sure how to determine the best amount of AB to sacrifice when using Power Attack. It’s not even clear to me what information I need to do so, though I think it includes some or all of the following:

  • The attacker’s AB
  • The defender’s AC
  • The attacker’s BAB (because it’s the maximum amount of AB they can subtract)
  • The number of attacks the attacker is making (if they’re making a full attack)
  • The amount of damage the attack(s) will do on hit
  • How much damage the attacker gains per point of sacrificed AB (e.g., 2 points when using a 2-handed weapon instead of 1 point for a 1-handed weapon)
  • Whether the attack could crit, and its crit stats (range/multiplier) if so

Given this sort of info, how can I calculate the amount of AB to sacrifice to Power Attack that maximizes my expected damage output for the round?

A couple notes:

  • I will happily upvote partial solutions (e.g., ones that only apply to a single attack without considering iteratives, or ones that ignore crits for simplicity’s sake)
  • Ignore considerations that require you to know how close to death the defender is. I’m happy with answers that naively maximize the expected value of my damage output against an idealized combat dummy with infinite HP. Accounting for the desire to maximize the probability of dealing lethal damage against low-HP opponents is, I think, too complicated, and beyond the scope of this question.
  • Ignore the Shock Trooper feat for purposes of this question; obviously if you’re giving up AC for damage instead of AB, it’s a risk/reward judgment call, not a case where there’s an objectively optimal value.

Calculate CR of creatures that share spells (like a hag conven)

I recently got inspired by this stat block, that shows that witches can get more powerful when together.

I want to make a similar creature that gets access to some spells when 3 or more of them are within 5 feet of each other. On their own they are CR 1/2, but together they can suddenly pack a punch. I guesstimated them as CR 1 now, but I wonder if that is correct?

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How to calculate Attack Bonus as a 5th Level Monk

Starting out at 5th level, and I am not sure how to calculate attack bonus. The reason I have this question is because with the Martial Arts feat(?) it says that I would use DEX instead of STR for attack and damage rolls, so do I use DEX when calculating my attack bonus? Or do I still use STR for calculating my attack bonus (for an unarmed strike).

Strength is 11, so the STR modifier is 0 whereas Dexterity is 18, so the DEX modifier is 4. Proficiency bonus is 3.

So would my unarmed attack bonus be 3 or 7? Or am I missing something completely?

How do you calculate your character’s Maximum Hit Points?

I am very new to tabletop games. I have recently started playing D&D 5th Edition with a good group of people and we have a great DM. I have also purchased the 5th edition Player’s Handbook. Half the fun of D&D is creating these amazing player characters. But for the life of me, I cannot seem to find anything on establishing a player character’s Maximum Hit Points. Can anyone tell me what figures or formulas are used to calculate maximum hit points?