What's the chance to survive a day in a dungeon?

It turns out that the players are overpowered since the change I made to monster damage. Read all about how I found out, tested it, and and came up with a solution.





During out last playtest it became obvious that since the fighter put on a suit of leather armour she was, in effect, invincible when fighting one level 1,3 or even 5 goblin, even though these also had leather armour.

It started as a feeling I had, a sense of hopelessness, futility. Every battle went the same way, or rather it had, had I not improvised to make it work. I later did some napkin maths which indicated that I was right, sort of.

So my next step was to do mass testing of the system, using a PHP script that simulates 10000 battles in a row, just basically displaying the outcome as a percentage.

It quickly became evident that the armour was not the problem as I had first through, but rather the fact that the fighter had 2D10 attack, and the goblins only had 1D6, meaning it was very unlikely that they would hit, and if they did hit they would only do one (1) point of damage.

Now, for a level 1 creature one point of damage is sufficient, but the problem with the armour was that higher level goblins, such as Veterans (level 3) or even the chieftan (level 5) only did D4 damage, and the armour reduced that to one again.

So, to summarise so far, for level 1 opponents the armour is fine, for higher level creatures it may still be too powerful. In addition, the bigger issue is the high level of skill available to a level one character, if they optimise.
 

What to do about it?

There are several solutions to the issue: Make monsters stronger in some way, for instance by giving them more hit points, better armour, more damage, or more skill. After running the simulation for all of the above, and for combinations of this, it's evident that the only thing that really helps is to fix the skill ratio, and that means one of two things: make monsters more skilled, or player characters less skilled.

The easiest solution is then to reduce the maximum ability score for a level 1 character to D8 rather than D10. This makes a warrior have a survival rating against two normal level 1 Goblins of around 88%, as opposed to 93%, and while that doesn't seem the biggest deal in the world, it is actually quite significant, especially when adding in the below fixes as well. Also, the beneficial side effect of this is that it will get more exciting to level up, as characters now will gain three ability increases instead of two during their career.

As can be seen above fighters have a good survival chance against two goblins. What about other classes? Well clerics and rogues survive in 75% of the fights, wizards in 50%. Bear in mind though that wizards are ranged, and will probably kill one of the goblins before they are in melee, and against one goblin wizards survive in 90% of the fights. Cleric's healing is not factored in, and increase their survivability, and rogues can of course use ranged just as wizards, and also has a higher than average chance to surprise the two goblins by using their superior sneak.

So when these things are factored in, every class has at least 90% chance to survive alone against two goblins.

Long term planning is good

One of the things I've not yet implemented in Solum is limitations on spells, and to be frank I don't much want to. I think, however, that I have to.

As it stands the player characters are basically reset after every survived battle, because the cleric can just cast his healing spell repeatedly until all hit points are healed.

Similarly a wizard could lob fireballs all day without tiring. But also similarly, a fighter can swing his sword all day without tiring, and that's the reason I don't really wish to impose restrictions on spell casters, it seems unfair that some classes have restrictions that others don't have.

However, magic is potentially more powerful than a sword, and I guess that's the rationale for it.

So, with some sort of restriction in place characters wouldn't necessarily be able to heal up to maximum hit points after each fight,  so the 90% survival rate against the first two goblins would be slightly reduced against the next pair and so on.

In the case of the fighter, it would start out at 88%, then (assuming half of the lost hitpoints were regained before the next battle) it would go down to 75%, and then in the third fight down to 50%. And now it's suddenly very dangerous again. In reality, the restriction would not apply like this because it's likely that clerics use their resource early rather than late, because it will have effect for longer if they do. So in practice we might have survival series like this:

88%, 88%, 88%, 75%, 50%, 15%.

A system like this does one thing: it makes the party plan long term, and gives the game master an excellent tool for applying pressure on the characters - make places to rest scarce and you don't have to pit the players against difficult fights in order to erode their survivability.

A spell limitation system

Here, then, is what I want: A system which limits spell use so that powerful spells are more restricted than less powerful, and in fact spells that are comparable to normal weapons should be unrestricted. It needs to be very easy to manage and light weight.

My current thought is this: Divide spells into levels, from 0 (cantrips) and up. The level equals the cost. Zero cost spells are free to use at any time, just like swords and other things. A spell caster has the following amount of spellpoints:

[primary attribute's die type] / 2 +[level]

So a level three Wizard with D8 Logic would have 4+3 = 7 spell points. She can cast 7 one-cost spells or any other combination amounting to seven before needing a full nights rest to recouperate. 

Clerics has a small healing spell (it heals 1D4 hit points per application), so at level 1 a cleric could be able to cast this spell five times (assuming D8 in Spirit), for an average total heal of 12.5 hit points. 

The average level 1 character has three hit points, so the cleric can restore this characters survivability four or five times each day (of course if several characters are hurt, the cleric will have to choose who to heal).

It's possible this system is too restrictive, or it may be too lax still, but on paper it looks all right.

The chance to survive a day in a dungeon

Looking at the series above it seems wise to avoid more than four battles a day. Assuming this is possible, a warrior would then have (on average of course) roughly 50% chance to survive the day (0.88*0.88*0.88*0.75). If he skips the fourth battle he has almost 70% chance, and if it's just two battles the chance is almost 80%.

All chances are quite high, but bear in mind the following: Every battle doesn't pit the warrior against two goblins (and it may well be the warriors primary objective to manoeuvre into a position where he only faces one opponent at a time). Sometimes it's one, sometimes the wizard of the group manages to take out the goblins without melee, and so on. Two things here then: The group mitigates more than a single character and fights are varyingly hard. A third factor is other sources of healing and buffs, such as potions and scrolls. 

What stat is most effective?

The short answer is: Attack chance (the same is true of all versions of DnD that I know of btw). 

The slightly longer answer is that if you have to choose one thing at level 1 to improve, Ability score or Skill is best. But for your second choice, don't choose the same thing. Armour is good, as is more hit points. The one thing that is less than optimal really on lower levels is damage, but I suspect that will change on higher levels (because monsters will have more HP).

This prompts another question, which I will not go into now: Should monster creation take this into account? Well, maybe. But it will make an elegantly simple system much less so.

Finally, for the so inclined, please find part of the table that my PHP script produced for me:

Diff	P1				P2				% P1 wins
	HP	AT	DM	AC	HP	AT	DM	AC
None	4	1D4	D4	0	4	1D4	D4	0	50%
DM	4	1D4	D6	0	4	1D4	D4	0	58%
DM	4	1D4	D8	0	4	1D4	D4	0	62%
HP	6	1D4	D4	0	4	1D4	D4	0	65%
SK	4	1D6	D4	0	4	1D4	D4	0	68%
HP	8	1D4	D4	0	4	1D4	D4	0	75%
SK	4	2D4	D4	0	4	1D4	D4	0	78%
SK	4	1D8	D4	0	4	1D4	D4	0	78%
AC	4	1D4	D4	-1	4	1D4	D4	0	80%
SK+DM	4	2D4	D6	0	4	1D4	D4	0	81%
HP+DM	8	1D4	D6	0	4	1D4	D4	0	81%
SK	4	1D10	D4	0	4	1D4	D4	0	83%
HP+DM	8	1D4	D8	0	4	1D4	D4	0	84%
AC+DM	4	1D4	D6	-1	4	1D4	D4	0	86%
SK	4	3D4	D4	0	4	1D4	D4	0	88%
AC+DM	4	1D4	D8	-1	4	1D4	D4	0	88%
SK+DM	4	3D4	D6	0	4	1D4	D4	0	89%
SK	4	2D6	D4	0	4	1D4	D4	0	90%
HP+SK	8	1D6	D4	0	4	1D4	D4	0	90%
SK+DM	4	2D6	D6	0	4	1D4	D4	0	91%
SK	4	4D4	D4	0	4	1D4	D4	0	92%
AC+HP	6	1D4	D4	-1	4	1D4	D4	0	93%
SK+DM	4	4D4	D6	0	4	1D4	D4	0	93%
SK	4	3D6	D4	0	4	1D4	D4	0	94%
SK	4	2D8	D4	0	4	1D4	D4	0	94%
SK+DM	4	2D8	D6	0	4	1D4	D4	0	94%
AC+SK	4	1D6	D4	-1	4	1D4	D4	0	94%
HP+SK	8	1D8	D4	0	4	1D4	D4	0	95%
SK+DM	4	3D6	D6	0	4	1D4	D4	0	95%
SK	4	4D6	D4	0	4	1D4	D4	0	96%
SK	4	2D10	D4	0	4	1D4	D4	0	96%
SK+DM	4	4D6	D6	0	4	1D4	D4	0	96%
SK+DM	4	2D10	D6	0	4	1D4	D4	0	96%
SK	4	3D8	D4	0	4	1D4	D4	0	97%
SK	4	2D12	D4	0	4	1D4	D4	0	97%
AC+HP	8	1D4	D4	-1	4	1D4	D4	0	97%
HP+SK	8	1D10	D4	0	4	1D4	D4	0	97%
SK+DM	4	3D8	D6	0	4	1D4	D4	0	97%
SK+DM	4	2D12	D6	0	4	1D4	D4	0	97%
SK	4	4D8	D4	0	4	1D4	D4	0	98%
SK	4	3D10	D4	0	4	1D4	D4	0	98%
SK	4	3D12	D4	0	4	1D4	D4	0	98%
HP+SK	8	2D6	D4	0	4	1D4	D4	0	98%
SK+DM	4	4D8	D6	0	4	1D4	D4	0	98%
SK+DM	4	3D10	D6	0	4	1D4	D4	0	98%
SK+DM	4	4D10	D6	0	4	1D4	D4	0	98%
SK+DM	4	3D12	D6	0	4	1D4	D4	0	98%
AC+SK	4	1D8	D4	-1	4	1D4	D4	0	98%
SK	4	4D10	D4	0	4	1D4	D4	0	99%
SK	4	4D12	D4	0	4	1D4	D4	0	99%
HP+SK	8	2D8	D4	0	4	1D4	D4	0	99%
SK+DM	4	4D12	D6	0	4	1D4	D4	0	99%
AC+SK	4	1D10	D4	-1	4	1D4	D4	0	99%
AC+SK	4	2D6	D4	-1	4	1D4	D4	0	99%
AC+SK	4	2D8	D4	-1	4	1D4	D4	0	99%
HP+SK	8	2D10	D4	0	4	1D4	D4	0	100%
HP+SK	8	2D12	D4	0	4	1D4	D4	0	100%
AC+SK	4	2D10	D4	-1	4	1D4	D4	0	100%
AC+SK	4	2D12	D4	-1	4	1D4	D4	0	100%