Friday, January 4, 2013

Maintaining Uncertainty of Enemy Hit Points in Solo Gaming

One of the features of tabletop roleplaying games and some wargames, that I've played at least, is that, for those systems that have them, a player doesn't have foreknowledge of exactly how many hit points a given opponent has. 

They might know that a kobold gets1d4 or a stand of irregular infantry have 1-3 points, but that's the extent of it.

They don't know that this particular ogre has 20 HP while that one there has a full 33 HP.

In a fight with the two ogres I mentioned above, the GM might give clues that one is more capable of surviving than the other, but it isn't necessary. In the latter case, or the former for players not paying attention, which to attack is arbitrary, all other things being equal (distance to target, whether one is armored and one isn't, if one has a giant battle axe but the other has a club, etc.). 

The first question is, is this experience something worth replicating in a solo game? Obviously, I'm inclined to say yes or I've just wasted everyone's time.

This lack of omniscience helps generate tension and the right kind of tension can make a solo game more enjoyable (I say right kind, because there is the tension where one thinks, "This isn't fun and I'm wasting my time", which I am sure most people do not enjoy). 

Here is one way to reduce your omniscience in a solo game:

Instead of calculating hit points/strength points for your opponents before battle, check against the likelihood that they're still standing during the battle.

I am working with dungeon crawling type monsters where the hit points are multiples of the d8 (aka hit dice or HD) and so that's what I'll use for my examples but it works equally well in wargames where figures/units have strength points, such as in Bob Cordery's rules sets.

For 1 HD or less, it's just a straight percentage: divide the total damage dealt / max possible HP.

If you score the >= maximum HP in damage, you know you killed your opponent. If you score less though, you need to check to see if it's still standing.

So for example, in combat with a 1 HD monster, I roll a 1 for damage.
Total damage dealt: 1
Max: 8
Chance that monster is killed: 1/8 or 12.5%. I round down so it's harder to kill things, 12%.

I roll my d100 and try to roll 12% or less. If I fail, the fight continues, if I succeed, the monster is dead.

I rolled a 59%. Looks like the fight continues.

Next round  I hit and score 4 more points of damage
Total damage dealt: 4 this round + 1 last round = 5
Max: 8
Chance that monster is killed: 5/8 or 62.5%, rounded down to 62%.

I roll my d100 and get 21%. Down it goes!

For more than 1HD, it's a little trickier:

(total damage dealt - (max hp possible - number of possible hp values))/number of possible hp values

Eek! Math!

Don't fret.

In English:  subtract the difference between the max HP value and the total number of possible HP values from the total damage dealt and divide the result by the number of possible HP values

(hmm, I'm not sure that was any clearer)

Once you've got the gist, you can open up a spreadsheet application and pre-generate the percentages for the HD combinations you're likely to encounter. Then, you just refer to it during the game rather than calculating on the fly. If you do encounter something unexpected, it's a simple matter to copy and modify the formula without disrupting the game flow too much.

Let's go back to those ogres from above.

An ogre has 4HD +1 in Labyrinth Lord. That means roll a 4d8 and add 1 to the result to find an individual ogre's HP.

Thus, the lowest I can roll is 4 + 1, so 5. The highest I can roll is 32+1, so 33. The range of HP is 5-33. How many possible values is that?

Take the max - min and add 1 to the result. Adding the 1 back in has nothing at all to do with the +1 in our ogre's hit dice. We get 29 possible values.

Ok, so I attack the ogre:

My first hit does 2 points.

If the value is less than the min HP, I don't even check. It's just a scratch, make note of it, and the fight continues.

Next round, I hit for 6 more.

Total damage dealt: 8
Max HP Possible: 33
Number of possible HP values: 29

Once again, here's our formula: 
(total damage dealt - (max hp possible - number of possible hp values))/number of possible hp values

((8 - (33-29))/29
4/29 = 13%

I roll a 96% aka not bloody likely. The fight continues and hopefully goes in my favor.

By the way, for a 4+1 HD monster, I don't even have a 50% chance of killing it until I score 19 points of damage. For a low level or small party, a Sleep spell is really handy here.

Let's summarize:

  • If total damage dealt  >= maximum HP, you know you killed your opponent.
  • If total damage dealt  <= minimum HP, make a note of the total damage and the fight continues.
  • For 1 HD or less, divide the total damage dealt / max possible HP to get the % likelihood that your opponent has been killed.
  • For more than 1 HD, subtract the difference between the max HP value and the total number of possible HP values from the total damage dealt and divide the result by the number of possible HP values to get the % likelihood that your opponent has been killed
  • Roll a d100 against the % likelihood, if you roll equal or lower, it's dead. If you roll higher, continue the fight.
  • Set up a spreadsheet covering the common HD combinations you'll encounter to save you time during a battle


  1. How about this one using the number of dice and dice type.

    HP = whatever you score.

    HD = whatever's hit dice. We are assuming contiguous values from 1 to the number os sides on the dice.

    Adds = HD adds, as in 4HD + 2, the 2 is the Adds.

    T1 = HP - (# of dice - 1)

    T1 = T1 - Adds

    T2 = (# of dice) X (# of sides on dice)

    T2 = T2 - (# of dice - 1)

    Percentage to kill whatever = (HP - T1) / T2

    Seems to work for all dice.

    Is it simpler to implement? I don't know. Probably since one formula covers all dice.

    Percentage = (HP - ((# of dice - 1) + Adds)) / ((# of dice) X (# of sides on dice)) - (# of dice - 1)


    1. Jim,

      Thanks for the comment. I may be missing something, but I get the same results with your formula as the one I'm using, even with non-d8s.

      The benefit of your approach though is that you don't have to do any pre-calculating (i.e max values, number of possible values). Certainly easier to use on the fly, I would think, although both formulas benefit from pre-generating the possibilities prior to game play.

  2. Interesting and cool idea, especially for solo games.

    I may be missing something, but does the number of hit die rally matter? (or does it make enough difference?) It seems to me what matters is the possible range of values. If the damage so far is below the minimum, you keep going, If it's equal to or above they're dead. If it's in between then figure out the percentage based on the number of hits vs. the maximum possible hit points. Or maybe I'm over-simplifying in an attempt to make it simple?

    To make a simple example - let's say your hit die is 5-sided, 1-5 and the monster gets 2 hit die. The minimum is 2 and the maximum is 10. If you have 1 damage on them they're still alive. If you have 2 damage roll 1 or 2 on 1d10 to get a kill. (ah, maybe that's where I'm missing the idea of multiple die...?).

    Another idea - can you do something with the same hit die? In other words, if your ogre has 4d8 +1 hit die you roll 4d8 +1 and if that is lower than the damage you've got on him he's dead?

    (thinking off the top of my head - I'm sure I'm still missing something)

    Still, I think your idea is a promising one for solo rpgs and battles where you want the amount of damage an opponent can take to be not a known predetermined quantity.

    1. Hi Fitz-Badger,

      I think this whole thing started out with me over-complicating something that was pretty straight-forward!

      With respect to using max HP vs possible values, at the low end of the HP range, the differences are significant (in my ogre example, 5 points of damage is but 3% likely to kill the ogre using my method, but 15% using the max HP). They become less so the closer you get to the max HP (same example, at 17 points in damage, 44% vs 51%).

      I really like your suggestion of rolling 4d8+1 (as in the ogre example) and comparing to the total damage. It would prevent the need to pre-generate the percentages, and eliminates the need to have one more file open/one more printout on the table.It's also easier to explain!

      I'll have to give that a try the next session.

      Thanks for commenting!

  3. You are correct your formula and my formula give the same answer. That was my point.

    The Difference is that for mine all you need to know for any creature is the Hit Dice, the 4D8+1 or 3D6 or 10d12+23. One simple formula for them all.

    Oh, I just had a thought...

    One Formula to rule them all, One Formula to find them,
    One Formula to bring them all and in the darkness bind them.

    Nah. Never mind. It'd never catch on.

    Just trying to make a more generic calculation, even for those with Excel.

    Fitz-Badger's idea might let something like this happen.

    In the first combat round your party gets 6 hits on the Ogre. For the Orge you roll 4D8+1 and score a total of 5. The Ogre dies. Not likely, I agree, but would you like something like to happen? Maybe it's a lucky thrust to the Orge's gizzard, whatever. It allows even poor fighters to get lucky, maybe that's a good thing. Actually, it is about the same effect and much simpler which is always the right direction to be going.

    Cumulative hits on opponent > opponents hit dice total = dead opponent. Otherwise continue fight.

    I like the whole idea, seems more straight forward than a lot combat mechanisms I run across. I vote for Fitz-Badger's method.

    Will this work damage to your party? Can you use it for all combat?

    Just ideas to get your creative juices following.


    1. I like both Fitz-Badger's and JF's ideas. They reduce the need to prepare before hand and the elimination of the need to check yet another table during combat, I think they both offer an incentive the formulas do not, with or without spreadsheets.Although the formulas are fun to derive and test!

      The combat narration has the opportunity for more drama (or maybe humor, perhaps the fighter is only successful in combat because of dumb luck) too - a one hit kill by a 1st level character for a 4HD monster is pretty uncommon.

      I rather like the idea of applying it to the party as well - rather than giving them hit points, just give them HD. At first level, most characters can only take a hit or two as it is, so I suspect there would be little noticeable effect. I'd have to look further into the effect at higher level, but I'm intrigued enough to try this out next session.It turns combat into an opposed roll situation, something I happen to like.


  4. Brilliant write-up!

    This subject crossed my mind years ago, but I quickly dismissed it when I considered how I played in groups: as a GM, I may not have stated how many hit points an enemy had remaining, but I described its wound status so vividly that the players could easily tell how much life was left in it. Thus, when going solo, I didn't think it was worth the effort to obscure enemy hit points.

    Now, you've got me thinking otherwise.

    I'd keep it simple for myself, though. If enemies are in battle to the death and my PCs take them to 0 hp, I'll immediately make some sort of a roll to see if, in fact, the enemy has a few more hp left in him that I didn't know about.

    Great stuff! This is going into my 2013 solo campaign! Thanks!

    1. Hey JF, thanks for the compliment.

      I like your idea for testing for additional HP, especially when soloing published modules where HP are pre-determined by the author. And it seems to apply whether running them as the GM with Mythic(or whatever) controlling the PCs or treating the module as a document in the PC's possession as well (I think I first encountered that idea on your blog, although I've yet to give it a test myself - I really like running the module as GM with Mythic as the PCs). I'll give this a try when I run through one of the many modules I picked up during 2012.

      If you didn't get a chance to read Fitz-Badger's comment,and then Jim Wright's taking it to it's logical conclusion, please do - it's an idea that sounds like it'll work well for on the fly created adventures (or published modules where the author doesn't specify HP) with far less interruption than the formula method.

  5. John,

    Give everyone and everything a number Hit Dice.

    Use the discussed Cumulative Hits versus HD roll mechanism for all combat.

    When PCs or non-Pc's "level up" give them more Hit Dice. Now all one needs to track is a characters HD. And cumulative wounds during an encounter. I think this simplifies a lot of stuff I find excessively fiddly.

    We all look forward to you next solo dungeon exploration.

    I swore of playing RPGs years ago in the era of Disco and the DnD white books in the box thing. Actually, I was playing more Tunnels and Trolls than DnD. But reading your blog has started me thinking again. I really had not considered playing an RPG solo until I came across your blog. I'm debating whether I should say thanks. Or not. :-)


  6. I like the way this discussion is going. I think I will have to try this idea, as elucidated by Jim in his latest reply, when I try some solo rpg'ing. This could even be used for things like bashing down doors and other opposed roll actions, even non-combat non-physical actions and events...

    I used to play T&T many years ago, using the solo dungeons by Ken St. Andre, et al. A while back I downloaded and printed the old Fantasy Trip rules, based on the Melee and Wizard minigames. I had used TFT a little back in the day and am going to give them another read through to see if they still hold up for my tastes.