Using Mathhammer to Balance your Game
Use Mathhammer to balance your tabletop role playing games & wargames.
Mathhammer assists Game Design using the 216 System when designed around balanced games, not chasing flavor-of-the-month meta. Using The World That Was as an example, you can see how plateaus in stats ensures no single model dominates on the field.
DISCIPLINE/ACCURACY TABLE
Skill 1 2 3 4 5 6 7 8 9 10 11 12
To Hit 5 5 4 4 4 3 3 3 2 2 2 2
Average Attacks to Destroy Unit: # To Wound/% To Wound
To determine the number of Attacks to destroy a Unit, divided the number of Wounds you want to cause by the percentage chance of causing a Wound. To wipe out a Unit of 5 Dwarf Veterans (5 Wounds), the Orc Warriors (12.5% to cause a Wound) would divide 5 (number in Unit) by 0.125 (percentage to cause wound) for 40 Attacks to destroy the Dwarf Veterans. A Unit of 16 Orc Warriors with two hand weapons can bring 32 Attacks only if they surround the Dwarf Veterans entirely. Orc Warriors with double-hand weapons (20.8% to cause a Wound) would need an average of 24 Attacks (5/.208 = 24) to destroy 5 Dwarf Veterans. That’s almost 2 Rounds of Assault for a Unit of 13 Orc Warriors with double-hand weapons surrounding the Dwarf Veterans that strike last due to reduced Initiative. In both cases the Orcs would be suited to form in Skirmish Formation in order to surround the Dwarf Veterans and bring their numbers to bear. A Unit of Orcs in Ranked Formation can bring 7 Attacks total with corners touching on the sides of the front Orc rank, dropping their survival considerably.
ARMOR SAVE MODIFIER TABLE
Attack Strength
1 2 3 4 5 6 7 8 9 10 11 12
+1 0 0 -1 -2 -3 -4 -4 -4 -5 -5 -6
Roll Modifier
TO WOUND TABLE
Strength 1 2 3 4 5 6 7 8 9 10 11 12
To Wound 5 5 4 4 4 3 3 2 2 2 2 2
Average Damage Output: # Attacks x % To Wound
To determine a Unit’s average damage output, multiply the number of attacks with their equipped weapon (damage output = 1 Wound) by the chance of causing a Wound. The Unit of 16 Orc Warriors with two hand weapons (32 Attacks with 12.5% chance to cause a Wound) will kill 4 Dwarf Veterans on average (32x0.125 = 4) if they can surround the 5 Dwarf Veterans. But that’s not taking into account the Dwarf Veterans’ Rhino Hide saving them 20% of the time. The Unit of 13 Orc Warriors with double-hand weapons (13 Attacks with 20.8% chance to cause a Wound) have chance to slay 2.7 Dwarf Veterans on average (13x0.208), which increased by removing the Dwarf Veteran’s Rhino Hide Save.
CONSTITUTION SAVE “RHINO HIDE” TABLE
Constitution 1 2 3 4 5 6 7 8 9 10 11 12
Rhino Hide Save - -- -- 6 6 6 5 5 5 4 4 4
“RHINO HIDE” MODIFIER TABLE
Attack Strength
1 2 3 4 5 6 7 8 9 10 11 12
- 1 0 0 +1 +1 +1 +1 +2 +2 +2 +3 +3
Rhino Hide Modifier
How about the Dwarf Veterans when they attack the Orc Warriors?
1. Total number of roll results that result in a successful Hit (4+): 4, 5, or 6 = 3 roll results.
2. Total number of roll results that fail the Armor Save (No Save, with 5 Strength Modifier of -2 for Armor Save): 1, 2, 3, 4, 5, 6 = 6 results since no roll is required.
3. Total number of roll results that result in a successful Wound (4+): 4, 5, or 6 = 3 roll results.
4. Multiply results together: (To Hit & Failed Armor Save) 3x6 = 18. (Include Successful Wound) 16x3 = 48.
5. Divide the possible dice rolls (48) by 216 (total number of 3d6 rolls) to determine the percentage chance to cause a Wound: 22% chance of causing a Wound. AND the Orc Warriors lose their Rhino Hide Save (Constitution 4 = 6+ Rhino Hide Save) due to the Dwarf Veterans’ Strength of 4 (-1 Rhino Hide Save modifier).
5 Dwarf Veterans have an average damage output of 1.1 Orcs. (5 Attacks x 22% chance to Wound.) The 5 Dwarf Veterans kill 1 Orc Warrior on average, but will require an average of 72 Attacks to destroy 16 Orc Warriors with two hand weapons. (16 Wounds to cause divided by 22% to cause a Wound or 16/.22 = 72.72) That’s 5 Rounds of Assault to wipe out 16 Orcs. The 5 Dwarf Veterans would require an average of 36 Attacks to destroy 13 Orcs with double-hand weapons (13/.22 = 36) for 4 Rounds of Assault.
Points per Wound: Damage Output/Unit Cost
To determine Unit effectiveness, divide cost of the Unit by average damage output.
5 Dwarf Veterans (80 points) with hand weapons (average damage 1.1) cost 72 points per unsaved Wound against the Orc Warriors.
16 Orc Warriors with two hand weapons (80 points) with an average damage output of 4 shows each Wound cost 20 points per unsaved Wound. (80/4 = 20).
13 Orc Warriors with double-hand weapons (78 points with average damage 2.7) cost 28.8 points per unsaved Wound.
Divide these numbers by the cost of a Wound of the Unit being Assaulted.
A Dwarf Veteran costs 16 points.
16 Orc Warriors with two hand weapons cost 1.25 points per unsaved Wound against Dwarf Veterans.
13 Orc Warriors with double-hand weapons cost 1.8 points per unsaved Wound against Dwarf Veterans.
16 Dwarf Veterans cost 14 points per unsaved Wound against Orcs with two hand weapons.
16 Dwarf Veterans cost 12 points per unsaved Wound against Orcs with double-hand weapons.
Dwarf Veterans are highly effective until they are overwhelmed in numbers. The Dwarf have survivability on their side – being able to take a hit – while the Orcs have the weight of numbers that can be brought to bear against their opponent. A Unit of 5 Dwarf Veterans can stand toe-to-toe against a Unit of 13 to 16 Orc Warriors and survive for a couple of rounds, if not hold the line until reinforcements arrive.
10 Dwarf Veterans can take out a Unit of 10 Orcs before the Orc reinforcements arrive.
No Plan Survives the Battlefield
Using the 216 System assists in ensuring Game Balance for the players who choose your Game to invest time and money. This System also provides Game Developers the tools needed to balance their Game and determine which Units need tweaking before release. Just remember this does not take into consideration the unexpected events or circumstances that occur on the battlefield. We cannot plan for every outcome, no matter how hard we try. However, a balanced System will ensure flexibility and fairness for every participant in your Game.
Alternative 216 Systems
Numerous games in Historical, Fantasy, and Science Fiction wargames exist using the 216 System. Below are examples of these systems
Alternative Ranged To Hit Chart using 216 System
For example, a Discipline of 6 when rolling against a Discipline of 3 would need to roll a 2+ to Hit. A Discipline of 3 when rolling against a Discipline of 6 would need a 6+ to Hit. A Discipline of 4 when rolling against a Discipline of 3 would need a 3+ to Hit. A Discipline of 5 when rolling against a Discipline of 6 would need a 5+ to Hit.
For example, a Discipline of 6 when rolling against a Discipline of 3 would need to roll a 3+ to Hit. A Discipline of 3 when rolling against a Discipline of 6 would need a 5+ to Hit. A Discipline of 4 when rolling against a Discipline of 3 would need a 3+ to Hit. A Discipline of 5 when rolling against a Discipline of 6 would need a 4+ to Hit.
For example, Strength 6 rolling against Constitution of 3 would need to roll a 2+ to Wound. Strength 3 when rolling against Constitution 6 would need a 6+ to Wound. Strength 4 when rolling against Constitution 5 would need a 5+ to Wound. Strength 5 when rolling against Constitution 4 would need a 3+ to Wound.
Note: these systems in low point costs Armies allow an Avatar to dominate the battlefield while the Rank-and-File are relegated to watching the heroics. Unless that is the goal of the game, be cautious of imbalance when using these 216 System alternatives.
Game Design - 216 System
Using the 216 System for game balance.
Game Designers struggle to create games that are balanced to ensure game play is enjoyable for everyone involved. The Game of Kings Game Engine uses the 216 System to ensure game balance.
You can’t steal my whimsy!
Combat in the Game of Kings is built around the 216 System of 3 successive rolls (To Hit, Armor Save, To Wound) on 1d6 to cause a Wound; (6x6x6 = 216). This System is efficient in determining percentage probability of causing a Wound by totaling up the chances of getting a desired result then dividing them by the number of results that can occur.
MathHammer
For example, an Orc Warrior (4 points) with a Discipline of 3 and Strength of 3 is making one (1) Attack against a Dwarf Veteran (16 points) with an Armor Save of 4+ (Chain Armor & Shield).
1. Total number of roll results that result in a successful Hit (4+): 4, 5, or 6 = 3 roll results.
2. Total number of roll results that fail the Armor Save (4+, with no Strength modifier): 1, 2, or 3 = 3 roll results.
3. Total number of roll results that result in a successful Wound (4+): 4, 5, or 6 = 3 roll results.
4. Multiply results together: (To Hit & Failed Armor Save) 3x3 = 9. (Include Successful Wound) 9x3 = 27. This shows there are 27 possible dice rolls on 3d6 for the Orc Warrior to cause a Wound on the Dwarf Veteran with one (1) Attack.
5. Divide the possible dice rolls (27) by 216 (total number of 3d6 rolls) to determine the percentage chance to cause a Wound: 12.5% chance of causing a Wound.
This shows the Orc Warrior’s one (1) attack has a 1 in 8 chance of causing a Wound on the Dwarf Veteran. Yet if the Orc Warrior is equipped with an extra hand weapon (+1 Attack = +1 point), then the Orc Warrior fighting with two hand weapons (5 points x2 = 10 points) has a 25% (12.5 x2 Attacks) chance of causing a Wound. Fight smarter, not harder.
Unmodified Saves
By incorporating Unmodified Saves into the 216 System by making models take an either/or approach to Saves (Quantum/Unmodified Saves if Armor Save reduced to zero (0)) this reduces the complexity and durability of all models on the board: everything can and will die if you throw enough Attacks at it.
Constitution “Rhino Hide” Saves
Constitution Saves are an Exception That Proves the Norm yet is easily gamed away by increasing Strength of the attacking model/unit by 1 point. This demonstrates that fragility of the common soldier in comparison to a hardened warrior with years of training under their belt, and being able to take a beating without giving up. Until this is gamed out, there is still a small chance (6+ to ignore Wound) for the Dwarf Veteran with 4 Constitution to be able to shrug off the Wound from the Orc Warrior with Strength 3.
To determine survivability due to Rhino Hide, divide the number 6 (the number of rolls on the six-sided die) by the number of roll results that cause a failed Constitution Save (5, 4, 3, 2, 1 = 5 roll results). 6/5 = 1.2. With the Orc Warrior’s damage output causing one (1) Wound, the Constitution Save of the Dwarf Veteran increases survivability by 20% (1.2 – 1 = .2 or 20%).
Bound Bonus
By keeping bonus modifiers bound to a +2 maximum, with Legendary Tech being the ETPN, the player must work to get past the natural plateaus ingrained into The Game of Kings 216 System. Players can get past these plateaus so their Avatars and Units are Hitting on 3+, but they must pay the point cost to get past that limitation. When compounded with the number of models required to meet minimum standards (5 models or 3 Large models), the points add up quickly. Players must choose between Quality or Quantity depending on the model/unit placed on the field. What their Units are equipped with matters.
Using the examples above a Unit of 5 Orc Warriors with two hand weapons is 25 points. A Unit of 5 Dwarf Veterans is 80 points. It would take 16 Orc Warriors with two hand weapons and no armor (80 points) to match 5 Dwarf Veterans in points.
Equip the Orc Warriors with a double-hand weapon (+2 Strength, -1 Initiative for 2 points), a unit of 13 Orc Warriors with double-hand weapons (6 points) is 78 points total. Let’s MathHammer this out.
1. Total number of roll results that result in a successful Hit (4+): 4, 5, or 6 = 3 roll results.
2. Total number of roll results that fail the Armor Save (6+, with 5 Strength Modifier of -2 for Armor Save): 1, 2, 3, 4, 5 = 5 roll results.
3. Total number of roll results that result in a successful Wound (4+): 4, 5, or 6 = 3 roll results.
4. Multiply results together: (To Hit & Failed Armor Save) 3x5 = 15. (Include Successful Wound) 15x3 = 45. This increased to 45 possible dice rolls on 3d6 for the Orc Warrior to cause a Wound on the Dwarf Veteran with one (1) Attack from a double-hand weapon!
5. Divide the possible dice rolls (45) by 216 (total number of 3d6 rolls) to determine the percentage chance to cause a Wound: 20.8% chance of causing a Wound with a double-hand weapon. AND the Dwarf Veteran loses their Rhino Hide Save (Constitution 4 = 6+ Rhino Hide Save) due to the double-hand weapon Strength modifier.
A Unit of 13 Orc Warriors with double-hand weapons (78 points) is almost a match for 5 Dwarf Veterans.
With the 216 System we can see how an equal amount of points for Orcs and Dwarves are evenly matched. This balance lays a stable foundation for all games based on the 216 system using points costs for balanced stats. There are additional ways to use Mathhammer to forecast how well your Army will fare against opponents. But let’s save that for another post.
Never stop gaming!
~CJ
#TheWorldThatWas #TW2 #GameBalance #GameDev #GameDevelopment #216System #Mathhammer
A Carnie’s Life
It’s a Carnie Life for us!
A peek behind the scenes of a traveling Toy & Game Store.
Here we are at the Lane County Fair, my home town. The morning of set up for the Amazing Tinkers booth. There’s a silent calm before the buzz of crowds are let in to roam the park, before you here the screams of delight from ride fanatics and see families together for a festive event.
CJ is working on setting up the foot print for our booth while I photograph some of the outdoor vendors as they set up.
I’m walking around the grounds enjoying early morning moisture in the air, unlike the desert, appreciating the simplicity of lush green GRASS under my feet. The kind of grass you’ll never find in the desert. A simple pleasure.
Touch grass!
Jumbo Dumbo Rides for the entire family.
I see Carnie families, crews that have traveled together for years setting up rides and booths. These are the rides and booths that caught my eye.
The Fun Houses with wacky mirrors and mazes are still exciting!
The colorful artwork pops in the morning sun. It’s quite lovely really.
Different Themes for different Fun House experiences.
Did you hear the music change?
Here are giant Plushies laid out to be hung for prizes. It is a kind living, a sense of freedom to go where you like and roam freely as you make a living in this crazy world.
Everyone carries their weight on the road.
We meet so many incredibly talented and interesting individuals, the amount of effort that goes into making and displaying their wares. We love our carnie neighbors; always positive and uplifting happy faces.
Rootin’ tootin’ family pictures!
Yoinks!
Thank you to all who came to see us this year and returning super fans from previous years, it was a fabulous fair!
All set up and ready for the Show!
The Amazing Worldy Tinkers at the Lane County Fair in Eugene, Oregon!
See you next year!
~Tammy
Check out more fun Booth pics from this Show on the Shows Page!
#Life #Travelers #Carnies #Tammy #CJ #LaneCountyFair #Eugene #Oregon
What are the Karma Dolls Carnies?
The origin story of the Karma Doll Carnies.
Growing up, I always felt like I was on the outside looking in. I was an observer of the cliques of happy people around me. I was the middle child with my twin sisters being at the top, 3 years older then me and my little sister 6 years younger then me. As I think back, I imagine my twin sisters to be the evil Siamese cats from the story “Lady and Tramp.”
It was never simple to play with my sisters as it should have been. I was the outsider, they required me to accomplish various tasks before I would earn the right to be allowed to join in play with them. These tasks were often impossible to accomplish. The sheer fact that there were 2 of them meant that they really didn’t need to include me. They had each other.
It was so much easier to simply create my own rag doll friends who where always happy to see me. “They” unconditionally loved me just as I was, a misfit toy, just like they were. I lovingly hand sewed each character from readily available materials such as discarded clothing, mismatched button eyes that often fell off from my haphazard stitching, leaving an X in the place of where the button had been. Then I would fill them with dried rice or beans for filling. This created a fantastic weight in the bottom so they were like weighted sack, floppy rag dolls. I took them out for picnics, posed them and took pictures with my Polaroid camera, and tucked them in at night making sure to kiss each one goodnight. I imagined we would run off and join a carnival that would accept us flaws and all.
My Dad left, my Mom worked 2 jobs to support us, other then us kids doing all the house chores, we pretty much had no structure and had no supervision. The twins would boss me, and I would boss my little sister. Someone forgot to send me to preschool, I was the forgotten one out of the 4 of us who had no education before kindergarten.
My Pre-K learning came from Sesame street and PBS since we did not have cable TV. I enjoyed the art in my collection of Dr. Seuss storybooks, which I know influenced my art later in life, well before Tim Burton films came along. As a result, I wasn’t particularly good in school unless it was something creative. I was and remain terrible at spelling no matter how much effort I put in to improving over the years. I wasn’t good at sports, we were poor so I wasn’t popular for brand name clothing, I didn’t particularly fit into any clique in school any more then I fit into my family. I was a misfit through and through. I spent the majority of my time daydreaming, writing, sketching, doing photography, creating things with my hands and selling my creations on the sly from my locker at school. I grew up on the West Coast then ran off to New York to find myself, ended up traveling and embracing that I am a Gypsy though and through.
The Karma Dolls are a product of my childhood. By being pushed out, I have become a strong independent individual who always thinks outside the box. This has helped me in life. I accept everyone. The Creator inspired me to create a world about the Karma Dolls Carnies to be a place where all are welcome. A place of imagination with no limitations. A place for all the misfit toys to gather and feel accepted just as they are. A place for people of all ages, shapes, sizes, colors and walks of life. A place to learn while having fun. A place to remember that it’s never to late to have a happy childhood.
Welcome to the Karma Doll Carnies.
YOU are perfect, just as you are.
~ Tammy
#Tammy #KarmaDolls #KarmaDollCarnies #PillowFight
Be The Change You Want To See
You can’t stop an American who never gives up.
Many of you are probably wondering what happened after 2020 when we disappeared off the Internet. However, before I go into details, I want you to take a look at the pictures on our Site and know that this Story has a Happy Ending. Like The Empire Strikes Back: we survived, we got back up and dusted ourselves off, then got stuck back in after the Mean Guys won. We didn’t give up and in return began to fulfill what is truly the American Dream.
Between 2018 to 2020, during the Time of Troubles, The Amazing Worldy Tinkers were censored across the entire Internet. We were deplatformed and removed from Twitter, Facebook, Instagram, YouTube, & Reddit. We moved to platforms that said they were open and free, but found ourselves shadowbanned and blacklisted from sites such as Truth Social, Rumble, Bitchute, & Parler. And our own Wix website deplatformed our business and payment processors. This censorship crossed over into the Game and Comic Industries as well as sites blocked our attempts at communication and businesses kept us from making a living on the Internet.
But we didn’t give up.
We knew we were kept from the water, so we brought our Art and Toys directly into the hands of our Superfans by participating in Craft Shows. Those in charge of the Internet and their domains cannot stop word-of-mouth, and over the years we kept traveling while creating the Art, Stories, and Games we wanted to see in the world. Now, we travel to Conventions, Faires, and Events bringing our handmade Toys and self-published Games & Books to our Superfans.
5 years later, the world is still shifting and it’s time for me to update our website, showing what we’ve built and what we’ve learned along the way. Tammy and I hope that what we share inspires you to not give up and to chase your dreams to become the person you want to be. Don’t think we didn’t make mistakes along the way - that is the nature of knowledge! We don’t learn if we do everything right & proper the first time. So be gentle with yourself and be forgiving. But never give up. Never ever.
Meanwhile, enjoy the adventures of the Karma Doll Carnies as they journey along and discover other Misfit Toys along the way. Enjoy walloping each other at a Slumber Party in the Karma Doll Pillow Fight game, or shoot lasers and blasters with your Toys in the Mr. Mustache Red Rover game of space battles. Enjoy the Comics and stories we create in the Mr. Mustache Milky Way Galaxy, along with the adventures in The World That Was. And learn how we did it as we share our knowledge here so you can achieve your own goals.
Be AmeriCANS, not AmeriCANT’S.
The praise is to The God, LORD of the nations, who fed us and protected us then and now. May HE pour down blessings upon you, dear Reader, and your House now and in the years to come.
~ Tammy & CJ
#Life #Travelers