Math question for roll xD dice and keep highest

[jaz0nj4ckal]

In a new idea, I am making all weapons do static damage of 1d6; however, larger weapons can roll 2d6 or 3d6 (depending on weapon) and keep the largest single dice roll. So, for example: Two-Handed sword would use 2d6, and you keep the highest roll.

Due to the latter, what does the math look like? What are my chances of scoring a single roll of 6 if I roll 2d6 and keep highest roll?

Thank you
JJ

 

[JonnyP71]

Almost 1 in 3.

There are 11 combinations of 2d6 which give at least 1 6.

 

[Nagol]

Here is a chart comparing 1d6 to keep highest from 2d6 to 5d6. Use the "Graph" and "At Least" buttons for the clearest display of the results.

As you can see, the biggest gain is when you add a single die. Each extra die adds progressively less effect which make intuitive sense.

 

[jaz0nj4ckal]

Here is a chart comparing 1d6 to keep highest from 2d6 to 5d6. Use the "Graph" and "At Least" buttons for the clearest display of the results.

As you can see, the biggest gain is when you add a single die. Each extra die adds progressively less effect which make intuitive sense.

So does that mean my idea is bad? Confused at what the graph is trying to show.

Thank you

 

[Nagol]

So does that mean my idea is bad? Confused at what the graph is trying to show.

Thank you

The idea is neither good nor bad in and of itself. An implementation is bad if the implications/consequences of adopting the idea don't mesh with the expectations.

What the math shows is the expected results rising from 3.5 for 1d6 to ~4.5 for 2d6, ~5 for 3d6, ~5.25 for 4d6, and a bit less than 5.5 for 5d6.

Let's assume you expect a human to be capable of wielding 3 classes of weapon: Light (dagger sized): 1d6, Medium (typical sword) best 1 of 2d6, and Heavy (two-handed sword) best 1 of 3d6. A heavy weapon will score, on average, a half point more damage than a medium weapon and a medium weapon will score, on average, 1 point more than a light weapon.

So, the question becomes is that form of damage variance in line with your expectations? If there are other possible advantages of using a medium weapon (such as being able to dual-wield or use a shield), will the expected damage increase comparably compete for player attention?

 

[jaz0nj4ckal]

The idea is neither good nor bad in and of itself. An implementation is bad if the implications/consequences of adopting the idea don't mesh with the expectations.

What the math shows is the expected results rising from 3.5 for 1d6 to ~4.5 for 2d6, ~5 for 3d6, ~5.25 for 4d6, and a bit less than 5.5 for 5d6.

Let's assume you expect a human to be capable of wielding 3 classes of weapon: Light (dagger sized): 1d6, Medium (typical sword) best 1 of 2d6, and Heavy (two-handed sword) best 1 of 3d6. A heavy weapon will score, on average, a half point more damage than a medium weapon and a medium weapon will score, on average, 1 point more than a light weapon.

So, the question becomes is that form of damage variance in line with your expectations? If there are other possible advantages of using a medium weapon (such as being able to dual-wield or use a shield), will the expected damage increase comparably compete for player attention?

Yes... you have touch on all methods/concepts I am trying to factor. Players are no longer just running to get the best dealing damage weapon and I am able to make quick calls on how weapons should be used, or if the weapon is to large to use in a cave for example.

Either way, I believe from what you point about damage - the model works for what I am trying to achieve with my simple dice system.

thank you for the help, and taking the time to explain it differently.

Much appreciated.

 

[GMMichael]

So does that mean my idea is bad? Confused at what the graph is trying to show.

Your idea seems to say "all weapons deal 1d6 because the size/type of weapon doesn't change the damage expectation." So, a d12 is unneeded.

However, by introducing a new rule that allows larger weapons to deal more damage on average, you're backtracking on the previous concept, saying "the size/type of weapon changes the damage expectation."

If this is the case, I would limit the additional d6s to be used on critical hits or weapon specialization - not bigger/deadlier weapons.

 

[jaz0nj4ckal]

Your idea seems to say "all weapons deal 1d6 because the size/type of weapon doesn't change the damage expectation." So, a d12 is unneeded.

However, by introducing a new rule that allows larger weapons to deal more damage on average, you're backtracking on the previous concept, saying "the size/type of weapon changes the damage expectation."

If this is the case, I would limit the additional d6s to be used on critical hits or weapon specialization - not bigger/deadlier weapons.

Hmmm you make an interesting point. I was looking at it in the following manner: All weapons do 1d6; however, some weapons will get a chance to roll additional dice, to pick the largest amount. But damage is still 1-6 points. Due to the latter

A) Two-handed sword, Two-handed axe, two-handed spear, two-handed Maul/mace would do 2d6 keep and keep the highest die.
B) All other weapons: short/long sword, one-handed axe, etc would do 1d6.
C) Magical weapons would range from 3d6 or 2d6. For example: Group (a) from above would use 3d6 in magical form. While Group (b) would get 2d6 in magical form. But that might not be the only benefit.. weight, other items... etc. For example: Two-handed sword of Lizard Men slaying would be 3d6 vs Lizard Men but 2d6 against anything else.


However, maybe I am looking at it wrong. Yet... I do like your idea because that would introduce mechanics on specialization.

 

[Lanefan]

Your idea seems to say "all weapons deal 1d6 because the size/type of weapon doesn't change the damage expectation." So, a d12 is unneeded.

However, by introducing a new rule that allows larger weapons to deal more damage on average, you're backtracking on the previous concept, saying "the size/type of weapon changes the damage expectation."

If this is the case, I would limit the additional d6s to be used on critical hits or weapon specialization - not bigger/deadlier weapons.

I think (s?)he is trying to do something just a bit different here with some possibly interesting ramifications: allow for varying damage by weapon while at the same time keeping a hard cap of 6 on the upper end of the range.

So, instead of a dagger doing d4 and a longsword doing d8, the dagger does d6* and the longsword does (in 5e terms) d6 with advantage. In either case the highest possible is still 6, but the larger weapon still gives out a bit more pain on average, which makes sense enough of the time that it might as well be baked in.

* - side suggestion: maybe have small weapons e.g. dagger do d6 with disadvantage (roll 2d6, take the lower) to further reflect the difference?

Hard-capping the top end is a brilliant way of reefing in numbers bloat, provided other bonuses from strength, spec., blessing, magic, etc. don't then make the original die roll moot. (if your damage roll is d6+13 the roll becomes almost irrelevant)

Lanefan

 

[TBeholder]

Here is a chart comparing 1d6 to keep highest from 2d6 to 5d6. Use the "Graph" and "At Least" buttons for the clearest display of the results.

Since those links are not very persistent, here's what you enter into the input field:

output 1d6
output [highest 1 of 2d6]
output [highest 1 of 3d6]
output [highest 1 of 4d6]
output [highest 1 of 5d6]

Damage rerolls are used in d10 RPG system (Warhammer 40k RPGs) for Tearing weapon property (d10 is rolled 1 more time, and 2 more if it's a chain weapon used with Chain Weapon Expertise; also, there's critical hit chance if any "10" is rolled).
With larger dice rerolls squeeze the range less.
Chainsword:

output 1d10+2
output [highest 1 of 2d10]+2
output [highest 1 of 3d10]+2

Eviscerator:

output 2d10
output [highest 2 of 3d10]
output [highest 2 of 4d10]