# Context

So, at my Session 0, one of my players (which will be playing a Barbarian) asked about gaining HP on leveling up. I intended to use the options on PHB - you either roll it or you get the average rounded up. I see concerns that I myself would like to change on this, that I'll comment later on. He stated that rolling a 1 on a 1d12 that only happens when he levels up (opposed to a damage 1d12 that happens every time he hits something) is frustrating.

He proposed that the players could roll it, and if it was below average, they could take the average rounded up. The problem is that the new distribution $x = \text{max}(x, \bar{x})$, where $\bar{x}$ is the average from the hit dice would be increased by around $20-22\%$. That's significant. He said that it was used in another table he played, but the DM would rebalance the encounters.

By this point I should note that we are not in an optimization-heavy table, pretty much the opposite, but we are not playing Walk on the Park either and PC death is a thing.

# Concerns

I agree with him - being a 2nd level barbarian that rolls a 1 on his Hit Dice is frustrating. Taking the concept of Goblin Dice, I don't think a roll that only happens 19 times in an entire full-leveled campaign should have high variance. It is not as game-changing as TPK on fail, but it is still significant, mainly early on.

The problem I mentioned about the PHB system is that rolling against taking the ceiled (rounded up) is not really a trade-off from a optimization point of view. It is less consistent and has a lower average [(d+1)/2 against (d+2)/2]. Specifically, rolling only makes sense for the suspense and gambling - but it is one of the rolls with least creative ways to use its outcome in my opinion. However I want some degree of randomness, not just "gain 7 HP".

Finally, the reason I instantly refused my player's method is because it would require me to rebalance every creature in the game in ways I don't even know how to (increasing their average damage by $20\%$ maybe? lol). Note: This question is not about this balancing. So, I don't want something that increases the average HP too much.

# The question

I would like alternative ways to increase max HP when leveling up, consdering my concerns, summarized as follows:

• The mean average HP doesn't change by too much (I'd say about $5\%$) compared to the (1+d)/2 average.
• There is randomness. (i.e. it involves rolling 1 or more dice)
• The probability of low rolls ($\leq d/4$) is low.

If you have any experience with another method that works fine with my restrictions, I don't mind not having any statistics backing up, but please clarify the system used and any other house rules or DM concerns (like rebalancing encounters) that could interact with this change.

As always, frame challenging answers are welcome.

• While I think this is an interesting question, I voted to close because it's written as an idea generation question, which is primarily opinion-based – Icyfire Apr 22 '18 at 0:14
• @Icyfire I agree and mentioned in chat that I feel it might still be opinion-based or even broad. If there is any way I can make it either narrower or more experience-based, I'd edit it happifully. Mostly the problem seems to be that there is no objective way to define if an answer is better than another, right? – HellSaint Apr 22 '18 at 1:09
• @Icyfire This looks like the rare exception where the asker's circumstance is so very clear --the problem, the constraints, how to tell if a solution works-- that experience-based answers will be easily identifiable as useful or not. – BESW Apr 22 '18 at 1:23
• @HellSaint, since it looks like you already have a potential solution to your problem, you might want to reframe the question as a "is my homebrew balanced?" question, which are generally well-accepted. This also lets people suggest tweaks and improvements but generally has a much narrower scope. – Icyfire Apr 22 '18 at 1:42
• This is essentially a maths question, how can that be opinion based? – SeriousBri Apr 23 '18 at 8:52

The simplest method I've thought is

# Roll 2, take mean, round it up.

Statistically:

• The average increases only from 4 to 6 percent. (Still lower than the rounded up average from PHB).
• The probability of a 1 is $\frac{1}{d^2}$, opposed to the usual $\frac{1}{d}$. While yes, it might still happen, it is MUCH more unlikely.
• The probability of low rolls ($\leq d/4$) is less than $10 \%$, opposed to the usual $15 \%$.
• The probability of getting 9+ or 4- ($\pm 2.5$ from average) using d12 is still $45\%$, so there is still randomness involved.

From my experience with the Advantage system, the worst case scenario (rolling 1 on both dice) ends up being seen as a funny moment rather than a frustrating one in almost every case, even in scenarios the failure is disastrous for the party. That's why I think even when the guy still gets a 1 on both dice, he might not feel so frustrated as before, although it might seem counter-intuitive (rolling two 1s should be more frustrating than rolling one 1).

• As I had mentioned in a comment, I've waited to playtest it before doing any change to either reopen it or let it closed. I've been using this method for the last couple weeks, many PCs leveled and players rolled. Specifically the Barbarian actually rolled a 1 and 8 for his 2nd level - and the 1 was the first roll, so I would say he has been thanking me for the chance of rerolling it for days. Everyone else got consistent HP increases, but were still thrilling for the rolls. I would say it is working for now. I will update when we get more level ups. – HellSaint Jun 7 '18 at 7:16
• Yeap, this works/worked fine for my table. :) – HellSaint Jan 3 '19 at 22:00
• I've seen the 'd-down' method result in interesting results. You downgrade your main hit die to d4s and d2s that add up to your hit die. d6 classes get 1d4 and flip a coin (d2) . So a barbarian would get 3d4, a fighter would get 2d4 and a d2,, and rogues, warlocks etc would get 2d4 instead of 1d8. I haven't seen the stats on the roll spread, but it seems swingier in the middle with a floor of at least 2hp increase (3 for barbars) – user47897 Feb 14 '19 at 22:49

He stated that rolling a 1 on a 1d12 that only happens when he levels up (opposed to a damage 1d12 that happens every time he hits something) is frustrating.

## So don't f&^%ing roll! If you can't stand the heat ...

This is not an issue of goblin dice: this is an issue of a player not liking the consequences of exercising their agency. When the player levels up they are given a choice to take the mean + $1 \over 2$ or roll the dice each and every time.

A 2nd level Barbarian who chooses to roll is foolish and should wear the consequences of their foolish actions.

Not every level is equal - the higher the level the less consequence the roll for hp has and so, at latter levels, it may be wise/fun to roll. Similarly, the smaller the HD there is both less variance and less consequence - a Wizard may choose to roll starting at lower levels than a Barbarian.

Choosing to roll or not is every bit as significant as choosing your archetype or proficiencies - why would you take that away from the players?

• This reads very didacticly, perhaps just calm the tone a bit. Also, the original question asked that some level of randomness be maintained; this is why they didn't want to simply take the rounded up average. – Medix2 Apr 22 '18 at 15:00
• @Medix2 If you read it that way then I got the tone perfect. The OP also asked for a frame challenge. – Dale M Apr 22 '18 at 21:08

I have three suggestions:

# Roll 1dX and replace 1s with the average rounded up.

This method removes the sad 1s, and it makes rolling for HP equivalent (on average) to taking the default hit dice value.

# Roll the 3dX and take the middle value.

This method does not change the average of rolling for HP, but it reduces the variance.

# Roll the 3dX, replace 1s with the average rounded up, and take the middle value.

Like method #1, this method removes the sad 1s and is also equivalent (on average) to taking the default hit dice value. Moreover, like method #2 it reduces the variance.

You can find a graphical comparison of the two default methods and my three suggested methods here. It's a great website to fuss around with dice.

The best simple replacement solution:
Max(roll, 4) for d8-12 and Max(roll,3) for d6's

These are the minimum values equal to or greater than taking the flat value every time.

d6 -> 4hp / level (0% increase)
d8 -> 5.25hp / level (5% increase)
d10 -> 6.1hp / level (1.7% increase)
d12 -> 7hp / level (0% increase)