D&D 5E On Die Averages and Hit Points in 5e

[NotAYakk]

Without a doubt mistakes can happen, but this is just you floating in to act intellectual and insult people. So please drop the Math Paladin mantle.

This is about "The GWF post used simulated rolls over a mathematical model specifically to keep from arguing about the model."

Which is harmful nonsense.

Then add in your dismissal of using math to understand things.

I included concrete problems in your simulation, as revealed by your post.

Look, I get that throwing together a simulation is often easier than making a model. But pretending it is better is nonsense. They tend to have different kinds of errors, so cross validating them is good.

Mathematical models describe their assumptions and are usually simple enough for people to understand. Simulations tend not to be, which is why arguing about their assumptions happens less. Does not men0an their assumptions are more valid.

It is the bikeshed problem. Law of triviality - Wikipedia

And I agree that GWF takes up too much time for its impact. I just think your model isn't convincing.

--

Anyhow, reroll 1s has definite psychological impact. It does make a detectible difference in results.

And yes, it should be "reroll 1s until you donpt get a 1". That adds 0.5 points to every die.

(1d8 becomes 1d7+1, as the result is still uniform. 1d8 average is (8+1)/2; 1d7+1 is (8+2)/2. This holds for every die size, a half point.)

Rolling dice is something people enjoy. Making it the mechanically inferior choice sucks for them.

It would be interesting to wok

 

[Umbran]

Or a ***load of work

Mod Note: Language. Keep it clean, please and thanks.

 

[Charlaquin]

Because it depends on what you're trying to fix.

I thought I made it clear I was trying to fix the discrepancy between the average result of rolling for HP and the fixed value.

If your fix is that you want rolled HP to be as good as average HP, then I have to question why you're rollling?

Because I want rolling and taking the fixed value to both be valid options. If rolling produces a worse result than taking the fixed value on average, it’s just a trap option. Rerolling 1s fixes that.

To me, the fix to make something like the other thing is to use the other thing. In this case, if what you want is Average Hit Points, then use Average Hit Points.

What I want is not to have average HP. What I want is for players who want to roll for their HP not to be at a disadvantage compared to players who take fixed HP.

 

[Umbran]

So know what is equivalent to a mathematical proof? A computer program.

As a physicist who did his thesis with computer simulations - no, a computer program is not a proof. You get very weird in here, with some distinctions between proofs, simulations, and models that are not well-defined (and, if I get what you intend, are incorrect).

Simulations are computer programs (I mean, technically, you can do on on an abacus, but... why?), and simulations are expressions of mathematical models. You cannot make a simulation without a model of some sort.

 

[OptionalRule]

I thought I made it clear I was trying to fix the discrepancy between the average result of rolling for HP and the fixed value.

Because I want rolling and taking the fixed value to both be valid options. If rolling produces a worse result than taking the fixed value on average, it’s just a trap option. Rerolling 1s fixes that.

What I want is not to have average HP. What I want is for players who want to roll for their HP not to be at a disadvantage compared to players who take fixed HP.

All fair, all good. I'm using the infinite 1s reroll in my own house rules buy more to give the player party something to debate and decide early on than any actual outcome on HP. (They have to decide which method to use as a group). My point of what fix someone is using is important for people to realize on a case by case basis. Again, the utility of this to me is just to try to understand the underlying assumptions to discuss if a rule is worth it.

 

[Ruin Explorer]

Because it depends on what you're trying to fix. If your fix is that you want rolled HP to be as good as average HP, then I have to question why you're rollling?

Um buddy? Did you read the article you wrote?

You said:

"However, it’s not so simple from a players point of view. Perceptions of agency, risk vs reward, and the gamblers fallacy all combine to make an interesting party debate. They feel a sense of tension about this choice, and as if something good was given them, which I think is generally good for a game. The metagame benefit I get as a DM is that this gives the players something to debate right out of the gate in a new campaign. Which means they start working out how to negotiate as a party immediately."

By your own logic, re-rolling 1s infinitely offers the same benefit you're describing for re-rolling ones once, and it has the superior characteristic of getting a closer result.

Unless you're thinking that players are going to do a mathematical analysis on on your approach and that's a good thing, which seems, hmmm, unlikely. I think you need to explain what you're "trying to fix" because apparently it's not what you said in the article. Unless you're just trying to trick people into accepting a very slightly inferior (on average) result and are deriving some questionable pleasure from that manipulation. Which I'm guessing isn't the case?

 

[NotAYakk]

As a physicist who did his thesis with computer simulations - no, a computer program is not a proof. You get very weird in here, with some distinctions between proofs, simulations, and models that are not well-defined (and, if I get what you intend, are incorrect).

Simulations are computer programs (I mean, technically, you can do on on an abacus, but... why?), and simulations are expressions of mathematical models. You cannot make a simulation without a model of some sort.

Curry–Howard correspondence - Wikipedia

en.wikipedia.org

 

[clearstream]

Oh my god, I can’t believe I never thought of this before! It’s always bugged the crap out of me that the fixed value rounds up from the average for rolling, making it the clear better choice. But this totally fixes that problem! And it removes the feel-bad moment of deciding to roll HP and getting a 1. I’m totally adopting this.

I have used that method for the last three and a half years. First during my OOTA campaign and now in ToA. What I have observed is that low rolls hurt more than high rolls feel good, so players revert to using rounded-up averages. My sample was about a dozen individual players (two parties of six, with little crossover and some rotation). Mathematically reroll-1s makes sense. Roll below average a few times and you renew your love for rounded-up averages.

For my next campaign I will be using the method in Worlds Without Number, where at each level gained above 1st, you roll all your hit dice. If the total is higher than current HP max, it becomes your HP max, otherwise your HP max increases by 1.


EDIT based on my experience I would certainly recommend offering reroll-1s infinitely - any 1 feels horrible, even on your second roll of the die - and I might even offer reroll-2s on the first die.

 

[Charlaquin]

I have used that method for the last three and a half years. First during my OOTA campaign and now in ToA. What I have observed is that low rolls hurt more than high rolls feel good, so players revert to using rounded-up averages. My sample was about a dozen individual players (two parties of six, with little crossover and some rotation). Mathematically reroll-1s makes sense. Roll below average a few times and you renew your love for rounded-up averages.

2 of my 5 regular players prefer to roll for HP even knowing the average is less than the fixed value - they both tend to take the fixed value their first few level ups so they have a decent base of HP and then start rolling at 4th or 5th level. A third would prefer to roll for HP but doesn’t because she knows the average is lower than the fixed value. One never likes to roll for things if there’s an option to take a fixed number instead, and would continue always taking the fixed value if I implemented this house rule. And the fifth is pretty indifferent to rolling vs fixed value. So, I’m pretty sure this house rule would be nothing but a positive for my players.

 

[clearstream]

Not true. If you roll every time and don’t re-roll 1s, a 20th level character with, say, a d8 hit die, has an average of 90 hp. If you do reroll 1s, that character has an average of 100 hp. The same average as a character who takes the average-rounded-up value of 5 hp every time. That’s the point of the house rule. To eliminate the slight advantage of choosing to take the rounded-up average instead of rolling.

I might not read too much into the 20th-level case. Assume most characters top out and 9th, and some make it to 15th. We didn't roll at 1st, so we are going to roll 8-14 times per character. More is better. For the low value - which is the most common case - a bad early streak will feel horrible and will not correct (there will not be sufficient additional rolls to reinforce the average.)