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Old 11-02-2021, 03:47 PM   #1
phiwum
 
Join Date: Jun 2008
Location: Boston area
Default Missile spells and minimum damage

I don't really have any questions here, but I was messing around with a spreadsheet and calculated the expected value of each of the missile spells at each of their strengths (ST 1, 2 or 3, ignoring rods with unlimited ST castings). I hope this is at least modestly interesting.

I was curious how much good the guaranteed minimum damage produced -- how much of a consolation prize is it, anyway? If I cast a 3 point Magic Fist or Fireball, I know that I'll cause at least 3 points of damage. That's better than nothing, right?

Now, notably, the rules say "with minimum damage equal to that ST", not that the minimum of each die rolled will be 1. That means if I roll a 1 and a 4 when casting Magic Fist, I only get two damage since it is calculated as

max{2, d_0 - 2 + d_1 - 2}

and NOT

max{1, d_0 - 2} + max{1, d_1 - 2}.

The latter is, of course, always greater than or equal to the former.

So, anyway, here are my results.
Code:
                  1       2       3
Magic fist	2.00	3.56	5.08
Fireball	2.67	5.11	7.57
Lightning	3.50	7.00	10.50
Now, of course, the minimum guarantee matters more for Magic Fist than for Fireball, since it comes up more often. But it also comes up more often for a 1 ST casting than a 2 ST casting, due to the bell curve for multiple dice. All of this was obvious without any calculations.

I was surprised how little the minimum damage guarantee matters for a 3 ST fireball. It just barely affects the expected outcome (since, for Fireball, say, it only comes up when you roll a 3, 4 or 5 on three dice, so not bloody often).

Without that minimum damage guarantee, the expected outcomes are
Code:
                  1       2       3
Magic fist	1.67	3.11    4.57
Fireball	2.50	5.00	7.50
Lightning	3.50	7.00	10.50
(The numbers for Magic Fist reflect the fact that 0 is definitely the minimum damage one can do -- no accidental healing by casting Magic Fist!)

And were the rule "minimum one damage for each die" -- which it totally and obviously is not, but I'm playing with numbers so don't stop me -- the expected values would be:
Code:
                  1       2       3
Magic fist	2.00	4.00	6.00
Fireball	2.67	5.33	8.00
Lightning	3.50	7.00	10.50

Last edited by phiwum; 11-02-2021 at 06:19 PM.
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Old 11-02-2021, 05:59 PM   #2
Axly Suregrip
 
Join Date: Jun 2018
Location: Durham, NC
Default Re: Missile spells and minimum damage

Yes.

BTW, you wrote, "(since, for Fireball, say, it only comes up when you roll a 3 or 4 on three dice, so not bloody often)"

But really it is a roll of 3, 4 or 5 that gets affected by this rule. Minor correction.
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Old 11-02-2021, 06:21 PM   #3
phiwum
 
Join Date: Jun 2008
Location: Boston area
Default Re: Missile spells and minimum damage

Quote:
Originally Posted by Axly Suregrip View Post
Yes.

BTW, you wrote, "(since, for Fireball, say, it only comes up when you roll a 3 or 4 on three dice, so not bloody often)"

But really it is a roll of 3, 4 or 5 that gets affected by this rule. Minor correction.
That minor correction pointed me to a small error in my spreadsheet. On three dice, the expected damage for a fireball is 7.57, not 7.52 as I had it.

My apologies to anyone who made critical decisions based on that error.
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Old 11-11-2021, 04:17 AM   #4
JustAnotherJarhead
 
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Default Re: Missile spells and minimum damage

For me it was always less about the "average damage" you could plan for, but more about the Epic high roll, or disappointing low roll that those 3 dice might yield.

Magic Fist is less about damage to foe, as it is special attack possibilities via it's telekinetic blow.

I mean dice roll result of a 1, 2, or 3 results in a single point for each die by the ST guarantee, and If I roll three 3s (considered close to avg.) I STILL only get 3 points total regardless.

But the knockdown potential, or knock off a narrow pathway etc... has value.

Knockdown in TFT can be the kiss of death, nobody wants to be prone in combat.

The Beauty of Magic Fist is a single point of ST can achieve a knockdown result.
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Old 11-12-2021, 07:55 PM   #5
Axly Suregrip
 
Join Date: Jun 2018
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Default Re: Missile spells and minimum damage

Quote:
Originally Posted by JustAnotherJarhead View Post
The Beauty of Magic Fist is a single point of ST can achieve a knockdown result.
The most damage a single point of ST can achieve with Magic Fist is 4. That is not enough to achieve a knockdown. You need to score 6+ damage (before armor, so that will help but it still will not change the one die of 4 damage to 6) in order to achieve knock down. And they still get a save.

But yes, I agree with your point that MF's knock down is the best part of this spell.
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Old 11-12-2021, 08:09 PM   #6
phiwum
 
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Location: Boston area
Default Re: Missile spells and minimum damage

Quote:
Originally Posted by Axly Suregrip View Post
The most damage a single point of ST can achieve with Magic Fist is 4. That is not enough to achieve a knockdown. You need to score 6+ damage (before armor, so that will help but it still will not change the one die of 4 damage to 6) in order to achieve knock down. And they still get a save.

But yes, I agree with your point that MF's knock down is the best part of this spell.
There's always double or triple damage to get that 6+ points, isn't there? Sure, a lot lower probability than 1 in 6, but still could happen.
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Old 11-12-2021, 09:51 PM   #7
Axly Suregrip
 
Join Date: Jun 2018
Location: Durham, NC
Default Re: Missile spells and minimum damage

Quote:
Originally Posted by phiwum View Post
There's always double or triple damage to get that 6+ points, isn't there? Sure, a lot lower probability than 1 in 6, but still could happen.
good point. always a chance
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Old 11-13-2021, 06:54 AM   #8
phiwum
 
Join Date: Jun 2008
Location: Boston area
Default Re: Missile spells and minimum damage

Well, I suppose that I was overestimating the odds of a 1 ST Magic Fist knockdown.

You need to roll a 4 on three dice and then a 5 or 6 for damage OR a 3 on four dice and a 4, 5 or 6 for damage. So, if I'm not mistaken, that's

3/216 * 2/6 + 1/216 * 3/6

and hence about 0.7% chance. That's rare enough not to worry about. So I guess I was just being a pedantic pain in the butt.
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Old 11-13-2021, 08:51 AM   #9
hcobb
 
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Default Re: Missile spells and minimum damage

Either that or get a starting character with Wizards Wrath and Missile Weapons III.
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Old 11-13-2021, 10:42 AM   #10
phiwum
 
Join Date: Jun 2008
Location: Boston area
Default Re: Missile spells and minimum damage

Well, the first step is to find a GM who regards missile spells as a kind of missile weapon. I don't, so Missile Weapons skill doesn't help a wizard in my games.

In general, I find wizards powerful enough. They don't need extra bonuses.
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