Comparing a couple ways to do hit points.

[0-hr]

1) When I DM, I have characters gain hit points equal to the average (for their die type)rounded up. So wizards get 3 hp each level (before CON), clerics get 5, barbarians 7, etc..

2) In another game, the DM and the player both roll a die and the character uses the better roll for their hit points.

Intuitively, I believe that the two-dice method yeilds better results in the long run - especially for d10 and d12 classes. I'm not so sure about the d4's. If someone with a knowledgge of statistics is really bored, could you enlighten me as to the actual numbers involved? Is method 2 always better, for every die type? Does it favor the big dice more than the little dice? If so, by how much?



Note that in either system, 1st level is maximum hit points as normal.

 

[Thanee]

The chance to roll HD/2+1 or higher (i.e. 3+ on a d4) with two dice, picking the highest one, is 75%, regardless of the die type.

It's precisely 50% to roll one of those numbers (top half of the possible results) on one die.
It's also 50% to not roll one of those numbers on one die.
It's 50% x 50% = 25% to not roll one of those numbers on both dice.
Therefore it's 100% - 25% = 75% to roll one of those numbers on at least one die.

Bye
Thanee

 

[Darklone]

Thanee is soo right ... just one example to add.

For the d4 if you want a better result than just taking the 3, you need to roll a 4 with two attempts.

The chance not to roll a 4 is 75%. Twice it's 75%^2. So the chance to roll at least one 4 is (1-(75%^2)) = 43.75%.

I'd say that's a pretty high chance to be better than the three. Might be interesting to look what's better on average in the long run... I'll do that later if noone else is faster.

 

[chriton227]

Here are the full numbers. The bigger the die, the better the benefit compared to (HD/2)+1. But then again, (HD/2)+1 benefits smaller dice more than larger. It looks to me like rolling twice has a more even benefit than (HD/2)+1 (+25% to +30.30% instead of +7.69% to +20%).

D4
1 = 1 in 16 (6.25%)
2 = 3 in 16 (18.75%)
3 = 5 in 16 (31.25%)
4 = 7 in 16 (43.75%)
Average: 3.125
Compared to (HD/2)+1: +4.12%
Compared to single roll: +25%
(HD/2)+1 compared to single roll: +20%

D6
1 = 1 in 36 (2.78%)
2 = 3 in 36 (8.33%)
3 = 5 in 36 (13.89%)
4 = 7 in 36 (19.44%)
5 = 9 in 36 (25%)
6 = 11 in 36 (30.56%)
Average: 4.47
Compared to (HD/2)+1: +11.75%
Compared to single roll: +27.71%
(HD/2)+1 compared to single roll: +14.29%

D8
1 = 1 in 64 (1.56%)
2 = 3 in 64 (4.69%)
3 = 5 in 64 (7.81%)
4 = 7 in 64 (10.94%)
5 = 9 in 64 (14.06%)
6 = 11 in 64 (17.19%)
7 = 13 in 64 (20.31%)
8 = 15 in 64 (23.44%)
Average: 5.81
Compared to (HD/2)+1: +16.2%
Compared to single roll: +29.11%
(HD/2)+1 compared to single roll: +11.11%

D10
1 = 1 in 100 (1%)
2 = 3 in 100 (3%)
3 = 5 in 100 (5%)
4 = 7 in 100 (7%)
5 = 9 in 100 (9%)
6 = 11 in 100 (11%)
7 = 13 in 100 (13%)
8 = 15 in 100 (15%)
9 = 17 in 100 (17%)
10 = 19 in 100 (19%)
Average: 7.15
Compared to (HD/2)+1: +19.17%
Compared to single roll: +30%
(HD/2)+1 compared to single roll: 9.09%

D12
1 = 1 in 144 (0.69%)
2 = 3 in 144 (2.08%)
3 = 5 in 144 (3.47%)
4 = 7 in 144 (4.86%)
5 = 9 in 144 (6.25%)
6 = 11 in 144 (7.64%)
7 = 13 in 144 (9.03%)
8 = 15 in 144 (10.42%)
9 = 17 in 144 (11.81%)
10 = 19 in 144 (13.19%)
11 = 21 in 144 (14.58%)
12 = 23 in 144 (15.97%)
Average: 8.47
Compared to (HD/2)+1: +21%
Compared to single roll: +30.30%
(HD/2)+1 compared to single roll: 7.69%

 

[IanB]

My system:

d4 classes still roll d4 (2.5 avg)
d6 classes roll d4+2 (4.5 avg)
d8 classes roll d4+4 (6.5 avg)
d10 classes roll d4+6 (8.5 avg)
d12 classes roll d6+6 (9.5 avg)

So far it has not actually reduced the player death count, but AoW is a tough campaign (which is why I added this rule in the first place.)

One thing to note is it changes the average distance between die types from 1 to 2, except for the difference between d10 and d12. d10 rolling classes see the biggest benefit from this system, as they get relatively better compared to everyone below them without losing any ground to the d12 people, which is a decent little boost for fighters. And arcane casters and commoners have to be careful, like always.

 

[0-hr]

Thank you very much for the thorough (and fast!) answers!

 

[frankthedm]

Remember every single HP characters have above average hurts the evocation school.

 

[Darklone]

Remember every single HP characters have above average hurts the evocation school.

... and allows me to use more villains with wands of fireballs ...

 

[Thanee]

If you are looking for a good hp system, that does not leave the PCs to the fate of lucky dice rolls, but also does not give them too high average hit points, I can only recommend this one...

Roll one die as normal.

If you rolled equal to or above HD/2 then you keep your result.
If you rolled below HD/2 you get HD/2 instead.

IMHO by far and wide the best method available.

Bye
Thanee

 

[Kurashu]

One house rule I've seen, and plan on implementing next I DM, is you roll for HP. But if you roll below average (rounded down), you get the average HP for your hit die rounded down.$

Edit: Sometimes, I get distracted and get severly ninja'd. Like, what Thanee did.