Frostgrave - Alternative Probability Approaches and Results (Or, "Don't Let Me Design Games!")

As I previously mentioned in my Frostgrave first impressions post, Mike and I decided to try the system out with a 2d10 approach versus the official d20 system.  For me, this idea was introduced by the Meeples and Miniatures podcast (I think) having mentioned using 3d6 instead of a d20.  I assume their reasoning, like ours, was the appeal of a Gaussian distribution that multiple dice give versus a straight uniform distribution.  See below for what I mean (being lazy, I didn't feel like doing probability math so I just simulated results instead):

From left to right, the probability of dice roll:  1d20, 2d10, 3d6

As you can see from the 1d20 graph, it results in an equal probability of any potential result, whereas the 2d10 and 3d6 methods are weighted toward the middle.  Seemed like a great idea to me and it works very well for Warmachine.  Now, if you are smarter than me you already know I was pretty much wrong (or at least not very right).  If you don't know why then keep reading but the key is the fact that attack rolls are "opposed" rolls in Frostgrave (attacker and defender both roll, as opposed to Warmachine where the attacker rolls against a Target Number).

Assumptions/Definitions:

• For the simulation, I used 100,000 "random" rolls for each attack and defense roll, for each of the proposed distributions to to calculate the statistics for:  1d20, 2d10 and 3d6.  From above you can see it was more than enough to guarantee a good sample size by how uniform the graphs are.  
• To provide the absolute most clarity in the interpretation of the results I assumed the attacker and defender had the same pertinent stat lines with:  Fight +0, Armor 10, Health 10.  
• %HIT:  In order for a attack to "hit" the attackers roll + fight must be greater than the defenders roll + fight.  
• %DMG:  To inflict damage, you must score a "hit" and using the original attacker's roll + fight + modifier (some weapons grant extra damage or reduce damage, 0 in this exercise) - defender's armor must be greater than 0.  
• %H&D:  The combined chance to not only hit the defender but to damage the defender (%HIT * %DMG).
• AVG DMG:  The average amount of damage per hit.
• HITS2KILL:  Given the average damage how many hits to kill the defender
• SWINGS2KILL:  Given the %H&D, how many swings (attacks) to kill the defender

As you can see from the table above, the alternative approaches only have a marginal impact on the chance to hit (%HIT) but interestingly lowers the chance.  The follow on chance to damage, if you do hit (%DMG) is a little more interesting for a couple of reason.  Firstly, I expected this number to be more along the lines of 50% since (with armor 10) the attack roll would have to be greater than that, but I "think" the fact that it is an opposed roll is pushing %HIT rolls higher in the distribution (I ran this a couple of different ways with the same result, but I need to go back and look at the distributions to make sure).  The second is that the 2d10 method results in almost a 5% gain in chance to damage - I think this is because you've maintained the same top end range of possible results (a roll of 20) while reducing the lower end range (ie, you can't roll a 1).  Despite the 5% advantage in %DMG though, everything evens out much more closely if you look at the combined chance to hit and damage (%H&D).  Anyway, given how close all these numbers are it is a bit of a push which method to use until you get to looking at average damage and the related hits to kill and swings to kill.  Pretty significant impacts here based on the different distributions, 3d6 looks like it would really draw the game out.

Now, in the case of casting spells things are a little different and end up more as intended (since they are compared to a Target Number).  There is definitely a non-marginal impact and in retrospect, looking at the data, a possible good reason to stick with the as published 1d20 system.  Below is a graphs showing the probability curves for each method vs the spell casting Target Number.

Probability vs Target Number

You can see at the lower end of the TN, the alternative approaches give a better likelihood of success but the higher TNs successes are less likely.  

In both the case of fighting and spell casting, an argument could be made to utilize an alternative approach to tailor the game to the players desire.  Want your solider's to live longer, use 2d10 or even 3d6.  Maybe you want out of school casting to be harder, use an alternate.  I initially thought that the alternatives could be used to make your game more like "low" magic but they actually make a portion of your spells even easier to cast, so can't really do that.

Anyway, the reality is if you really wanted these things you could do it an easier way (IMO).  Want your solider's to live longer, bump the base armor stats for everyone up by +2 (or whatever you desire).  Bump the armor down if you want them to die quicker.  Want "low magic", bump all school TN modifiers up by +2.  "High" magic, bump them down.  Want just the out of school magic to be harder, bump those specific modifies up.

Well, I think I will keep my toes out of game design (or modification) from here on out.  To a degree.  Maybe.  At least for awhile...

Frostgrave

Last Saturday, my regular opponent, Mike and I met up at the local gaming store prepared for some miscellaneous gaming of:  Malifaux, Guildball and/or Frostgrave.  Malifaux was really only on the agenda in case some of the local Malifaux people showed up, which ended up not being the case.  So, Mike and I decided to give Frostgrave a run through.

Events conspired that morning to keep from putting a list together, so I headed over a little early to work on a Frostgrave list in case we got the opportunity.  For simplicity, and speed, I just hired a very basic list of apprentice and 6x infantrymen and everyone with standard equipment.  Interestingly enough, Mike showed up having taken a similar approach except with x3 infantrymen and x3 archers.

Semi-randomly, I chose enchanter for my wizard and hastily grabbed spells.  I thought enchanter would be great for giving out +1 weapons and armor to everyone, which I only did once.  Some of the "cool" spells I ended up taking were also near useless, because the neutral school difficulty rating put them out of reasonable reach.  Of note it is really not awesome when you cast heal on yourself and fail the roll causing yourself damage, LOL.  Mike's spell list seemed better thought out and afforded him some nice strategies during the game.

So it was my fishmen warband (Wrath of Kings Hadross models) against Mike's goblins lead by a witch in the standard scenario.  Mike won with only 2 goblin archers remaining and having fully frustrated every last one of the fishmen before their ultimate demise:  He employed a very solid tactic of casting telekinesis on the treasure tokens to bring them closer to his guys and then casting mud in front of his troops.  With no range attacks (except via spells), this left me at a bit of disadvantage.

Things I liked about the game played:

1. Fairly concise set of rules (later in this post you will see that I think this is a bit of a double edge sword though).
2. The spell schools, alignments and choices provide a nice depth to an otherwise heavy amount of parity.
3. Group activation with a "cost" such that you have to sometimes make difficult choices in whether or not to do it.
4. Use any models!  I see a future for some Confrontation and Alkemy models...

Things I think I will like about the game in the future:

1. While I really haven't digested the campaign system yet, I already see the potential for it forcing interesting choices/decisions.  For example, there are several spells that are out of game spells that might be very worthy of taking but then reducing you in game spell pool quite a bit.  Also, of course, there is question of how much risk to take with your wizard during campaign games.
2. Random creatures (we choose not to play with them for our first game).
3. The other scenarios, again I really haven't dug into them but I hope they are good because IMO the base scenario stinks (see below).

Things I am concerned about:

1. I am concerned about the scenarios.  As I just mentioned I really haven't dug into the scenarios yet but the base scenario (each person puts out 3 treasure tokens 9 inches from their table edge) stinks.  In the base scenario ultimately you "should" just place them exactly 9 inches from your table edge, rush them and the get them off the table forcing a draw.  There are only a few low probability ways for your opponent to stop this IF you put your treasure in clear line of sight.  Hopefully the other scenarios are more tactically challenging.
2. Archers seem a bit over powered.  They have the exact same cost as infantrymen but the infantrymen will get shot up crossing the board to get to them (wait for my next point before you scream terrain).  Additionally, the way melee is structured there is a risk as the "attacker" that you could loose and take damage but you don't have to worry about that if you are shooting a bow.  Unlike the infantrymen, the archer can always melee if you want to or if they get trapped, not quite as well as an infantrymen but decent enough.
3. I think the game was envisioned to be played on a terrain heavy board.  This would potentially offset the range combat advantage.  I actually prefer games that use lots of terrain but there are 3 main issues I have seen with terrain heavy games:  a) logistics of having that much terrain, b) understanding by both players of what all the terrain represents (rough ground, climbable, etc etc) and c) exactly how much to have such that range attack profiles are not now over costed.
4. As hinted at above, I sometimes find the rules to be a little to vague.  Without a clear definition of LoS, I was left unsure as to whether to use a true LoS interpretation or a more abstract one.  Also, combat is described as being in "contact" with the other figure.  Caveat, I may have missed some of the finer points that clarify some of these things, it was after all my first time through the rules and game.
5. Some specific rules are buried away in text (an example is that spellcasters can not cast if they are in combat).  Luckily the rules are short enough that this does not seem to be a major issue but I still feel a bit uncertain at times and finding that exact sentence to confirm consumes time.  I think this will be a non-factor after reading over the rules a second/third time but stands now as a concern.
6. As always with campaign systems, there is the fear of "run away."  A really good way to mitigate this is to keep campaigns short but balancing that with allowing a rewarding amount of character growth is difficult.  Perhaps the fact that only your wizard and apprentice level up helps manage this, but I can't say for sure without having played through a campaign.
7. I may not have all my facts straight here, but wizards get experience points for treasure removed from the board and from kills.  So buffing/non-combatant casters will suffer some in the campaign system compared to direct damage casters.  

Don't get the wrong impression because of my concerns.  I think Frostgrave is a good, solid game and I love the support it is getting:  A new campaign book, sellsword/captains, etc.  Plus it seems to have generated a lot of traction.  These concerns are not anything that will keep me from jumping in on a campaign if one gets going.  Is it better than some of the alternatives such as Otherworld, Mordheim, Song of Blades, Heroes, Regiments of Renown, etc - I don't know.  Don't really care since it seems to be a decent enough system that people around here might want to play.  Basically if the game system is decent enough and there is not an alternative I LOVE, then I am not going to fight an uphill battle to convert people.

Also of note.  Mike and I played our game utilizing 2d10 rather than the standard d20.  The reasoning was that 2d10 would provide a Gaussian distribution (like Warmachine) rather than a uniform distribution of a d20.  I am actually interested in quantifying the effect of this change along with the 3d6 approach.  Hmm, I wonder how exactly to approach that analysis.  I do know I will be lazy and do it via Monte Carlo's rather than figure out the probabilities with math.  lol

January Recap

Been a little quiet on the blog, so I thought I would post a quick update recapping January.  I'm not sure a monthly recap is going to be a regular thing or not, I had actually planned to post most of this as more individual updates but never got around to it.  We will see...

On the "hobbying" front I have managed to get in a little bit of modelling every week.  No actual painting though.  Surprisingly time consuming, I did get my Malifaux and MERCS models transitioned from foam storage/transport to magnetic tray storage/transport (btw, I believe MERCS second edition comes up in Feb/Mar and includes rules to use a standard tape measure instead of the card based movement - should be interesting to see).  I also got 4 new guys for my Hadross Wrath of Kings assembled and based:  I wasn't really satisfy by (game play wise) one of the specialist from the starter set, so I wanted to either try a different specialist or add another taxi crab.

(The loner off to the side of the group was actually assembled last year)

I have also gotten 4 games of Guild Ball in over the month with Mike over at Mini Mayhem.  I continue to be impressed with the game.  So far Mike and I have only gotten 1 game in at the full team and table size (without terrain).  I'm holding off a post with more thoughts on the game until I get a few more under my belt.

I've gotten a little more connected into the Kings of War and (separate) Malifaux communities.  It has been a little hard but I think I'm starting to unravel the fractured gaming community here.  We will see.  I would really like to get out to one of the weekly Malifaux nights that has been re-established to show support but so far I just haven't been able to juggle it into the mix.  Hopefully soon.  There have been some rumblings about Frostgrave too, so I picked up the rules for that but haven't digested them yet.  It really looks like I am going to have to bite the bullet and get into Facebook though to help integrate into the gaming community down here.  *sigh*

The only other thing to note for January is I started and finished reading Caliban's War.  The second book in the Expanse series  Again, I can not believe that such frantic pacing can be maintained for the entire length of a book.  It manages to introduced some really great new characters that I hope to see again.  Hopefully this puts me far enough ahead that I can now watch the first season of the SyFy series.  For reading though, I think I am going to take a little break from this series and read something lighter, probably one of the new Star Wars books.  But then again Lois McMaster Bujold has a new book out:

This month (/next) we appear to be on course for closing and moving into a new house.  That should see the establishment of my new man cave, the return of all my tiny soldiers and my airbrush!  The harsh reality of this is that I probably wont have much actual time for hobbying for the rest of February and maybe part of March.

NOVA Open Registration Tonight

***Caveat, full disclosure:  I used to be a volunteer for the NOVA Open.

So, this is perhaps the (al)most useless post in the history of blogging.  Why?  Because I think the only people that are aware of this blog, are people I met through the NOVA Open.  But, on the off chance someone else stumbles across this or that there is a future of having further reaches I thought I would share that registration for the 2016 NOVA Open goes live tonight.  Follow the link to learn more:  NOVA Open.

To give some weight and purpose to this entire post I guess I will tell a little story about how I stumbled across the NOVA Open, became a volunteer and have watched it evolve.  Before I do that it is important to provide a particular bit of background.  I do not, in general, partake of anything Games Workshop (40k, Fantasy, purchasing of product, etc).  The details and reasons are not important for this particular post and the reality is there is nothing wrong with you liking 40k and me not liking it.  I don't think any different of someone because they like what Games Workshop offers and I hope they provide me (and the rest of the non-GW world) the same courtesy.  People like what they like in this hobby, there really does not have to be reasons, excuses or justifications.

I don't really feel like looking up the dates to get this 100% right, but about 4-5 years ago I was living in the Northern Virginia area outside of Washington DC.  I had been there for a little while and still had not really found a gaming community to become integrated into.  Actually, I had not really even found a single one.  Then one day, on the way to work, I was listening to a miniature gaming podcast (who shall not be named because frankly I don't care for that person).  He mentioned he was going to the NOVA Open.  Wow, in spite of my internet searches, I had not uncovered that this podcast host lived in the area or that there was a miniature gaming convention locally!  As soon as I got to work, I looked it up.  Due to the delay in from when the podcast was recorded and when I actually listened to it, the NOVA Open was that very weekend!  Without paying much attention to anything about it, I quickly signed up and got back to my day job responsibilities.

***Please note, I do not mean anything that follows to come across as a criticism.  I "plan" to make a point.

The weekend rolls around and I head out to the NOVA Open excited to check out this miniature gaming convention!  I do so without having done one lick of further investigation into it.  I arrive and proceed to registration and are wonderfully greeted and welcomed.  As they process my registration, one of the ladies asks for my army list.  My what?  "Your army list for the 40k tournament."  Yeah, that was pretty much all that was NOVA Open was.  I can't recall if WFB, Warmachine were there.  I don't think there were any hobby seminars either.  There was another game system, shoved away in a back corner.  And there were about 3 vendors.  I will be honest, it was disappointing for me as a non-GW person.  Despite this, a few months later I received an email asking (since I was local) would I be interested in helping out building terrain for the convention.  Thankfully I said yes despite having no experience in terrain making and continued to be exposed to the NOVA Open.

I provide the above paragraph to illustrate a point.  Follow the link to the NOVA Open and check out the events now (well 2016 at least):  40k, 30k, WarmaHordes, AoS, Malifaux, SW X-Wing, SW Armada, SW Imperial Assault, Infinity, LotR, Blood Bowl, Dark Age, WoK, DZC, Magic.  Check out the sponsors and vendors, too many to list here.  Check out all the seminars and painting competition, and who is involved in them!  Let's not forget to mention, last year major manufactures had a presence at the convention:  Wyrd, Hawk Wargames, CMON, Corvus Belli.  In the past few years, I have done all the things the NOVA Open has to offer:  gaming (non-40k), seminars, hanging out in the charity lounge (you need to check that out!), etc.  It is a great and evolving miniature gaming convention.  It is unbelievable how it has grown since I first blindly stumbled upon it.  Most importantly to me, the NOVA Open is:  fun, relaxed, welcoming, friendly.

Having relocated some 600 miles away, I am no longer associated with the NOVA Open.  I'm just a fanboy and wish them the best.  Check it out.  And, if you want to bring the family along it is an unbeatable price for a hotel that is very accessible to the DC metro system (just a short hotel shuttle ride to the metro station).  Maybe if you are lucky, you can get the significant other approval rating.