Sycarion Diversions

Avalon Hill produced statistics based versions of the major sports. Baseball was the most enjoyable, especially because the rules for making your own players were included. The big, index-card-sized FAC cards that determined what happened were chock full of encoded information for any situation.

And then there was the dreaded, “Z”.

Some of the same things carried over to the football game, which I dearly loved, too. The one thing I did not like, though, was that it was almost impossible to figure out how to add your own players. This became a bigger issue when updated player rosters ended in 1991.

A few hobby sites have some ideas on card creation, but none of them seem compatible with original card sets. In other words, using their rules on the 1991 teams would not create something close to the ‘official’ cards from Avalon Hill. Not even close in some cases.

So I decided to attempt to reverse engineer a set of 1991 official cards. Turns out that almost every card is arbitrary in some way. Two statistically identical players can have different results. Art Monk’s card is wrong and only they know how they came up with Andre Rison’s card.

So, I’m in mid-process of refining a consistent and universal set of rules to generate cards. This, of course, will mean refactoring official sets. With all the football stats around, that’s not too hard.

More later.

Thinking about a board game based on this machine. Just jotting down a few ideas:

Move proceeds around a board as player assemble pieces to construct their machine. The first to make it to the patent office with a working analytical engine wins. Players first make a difference engine and either patent it or build one by commission. Pieces from difference engine funds analytical engine.

If a player builds one for patent and not commission, he or she can use all the pieces of the difference machine to build analytical machine. Everyone else can only reuse their original (before being commissioned) pieces.

There are three pieces – spacer, cog, and rack.

The rack is a piece that allows the machine to be built ‘up’ a level. Presumably, the more racks, the more variables that can be calculated at once, but also the longer it takes to finish the machine.

The spacer allows the machine to be built ‘out’ a level. Presumably, the more spacers, the more decimal places that can be calculated for each variable. Once a spacer is added, it is added to every level.

Cog is a bit of machinery that fits on the grid created by racks and spacers. For example, a machine with 5 racks and 8 spacers would require 40 cogs to complete.

There would need to be a funding source, so I guess each player is a hobbyist until if and when a company commissions a machine to be built. Each would have different specifications and different advantages (more cogs per turn, alternate build rules, etc.)

Upon completion, they would get paid and then start to build the analytical engine.

Need to add in bonus or random elements like:

Ada helps your project (build at twice the rate)
Building trouble (destroys rack or spacer)
Lose funding. Keep your pieces, lose those purchased by company commissioning the machine.
Cogs go bad and must be replaced. or only red cogs go bad.
An entire rack goes bad and must be replaced.
A green rack goes bad or a red rack goes bad.

Piece would be two different colors to distinguish pieces built by you, the inventor, and those purchased by company commissioning you. Say Green are built by you and red built by company. When difference machine is finished, you can use only the green pieces to start analytical engine. (Thus if you built it entirely yourself, you could reuse all the pieces.)

Analytical Engine would need fourth piece, don’t know what to name it. Maybe replace cogs or modify cogs. Maybe analytical cogs cost more, but difference cogs can be modified very faster. For example in one turn you may get an analytical cog or convert three difference cogs to an analytical cog.

Building rules:

Rack pieces can only be removed from the top down, not the bottom up.
Removing a spacer affects every rack. The cogs lost cannot be reused. (Someone may remove a spacer in order to finish their machine faster.)
When you start on your analytical engine, you must add at least one rack and one spacer.
A difference machine must be at least 6 racks by 6 spacers.

Unless directed by card or company paying you (difference engine only), you can only add the piece you land on while moving your token around the board. If you are being paid to build, it must be a red piece. If you are going it alone, it must be a green piece.

Yehuda at Jerusalem Gaming blog has an idea to spice up Rummy with Action Cards.

The article is here

Enjoy!

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Heads up English Majors and other mathematically challenged folks! D6 MOD7 Dice Sheets are now available on the Downloads page and at the links below. (I have an English Literature Degree by the way.)

The frequencies of each roll are given at the bottom of the page. They are generated completely at random, but you may decide to use a different sheet based on the frequencies given.

As noted on the sheet, it only works well if you start on the upper left corner and move down the columns. Remember to cross out numbers already used.

3D6 MOD7 Rolls | 2D6 MOD7 Rolls

As always, there may be a name change as I discovered a company named MOD7 and I do not want to harm their business (though I don’t think I really could. I have four readers.) So, I’m looking at D6 MOD 7 for now. Nothing shows up on Google when I search for it (except me).

Changes in DEF Ability

Because D6 MOD7 uses a smaller range of numbers to determine success (0-6 instead of 3-18), changes have to be made in DEF and in many Traits. DEF is changed to 3+REF from 10+DEF. Without this change, an average person (Stats and skills of 3) could never successfully attack successfully.

For example, Joe, an average guy is in a fistfight at a bar with Andy another average guy.

Old Rules: Joe uses STR + Unarmed Combat Skill + Roll. Andy uses DEF + REF. Since both are average guys, Joe is trying to meet or beat a TN 16. (DEF = 10 + REF or 10+3. REF = 3) He had a STR of 3 and a skill of 3, meaning he has to roll a 10 or better to strike Andy. Using 3D6, Joe had a 0.625 chance to hit Andy.

Because a MOD7 roll cannot go higher than 6, Joe could never hit Andy, even if he surprised him.

New Rules: Joe uses STR + Unarmed Combat Skill + Roll. Andy uses DEF + REF. Since both are average guys, Joe is trying to meet or beat a TN 9. (DEF = 3 + REF or 3+3. REF = 3) He had a STR of 3 and a skill of 3, meaning he has to roll a 3 or better to strike Andy. Using a MOD7 roll, Joe has a 0.574074074 chance to hit Andy.

Changes in Traits and Modifiers

Needless to say, traits that give +3, +6, +9 modifiers to skills or attributes would present a similar problem. Rather than list the specifics, here is the general guideline:

Traits that affect skills are +1 (Convenience) +2 (Edge) +3 (Gift)
Traits that affect initiative are +2 +4 +6
Traits that affect health or damage remain unchanged

For example: Hard to Kill remains unchanged +2 TGH, +4 TGH, +6 TGH applied to piercing damage. However, Athletic is changed to +1, +2, +3 to all Athletic Group skills.

Fast Reflexes is partly the same and partly changed. Convenience is still +2 INI, but +1 to Awareness Skill Rolls. Edge is +4 INI and +2 Awareness rolls, Gift is +6 INI and +3 Awareness rolls.

Fast Healer is also only partially changed: progression on the Time Chart remains the same, but skill bonuses at the Edge and Gift levels are +1 and +2 respectively.

Full list comes later.

As far as modifiers are concerned, modifiers to Initiative are the same, modifiers for attacking or any other skill roll are reduced by 2/3 rds rounding up. The numbers aren’t easy rounded, so a full chart will be created at some point in the future. Below are examples:

Combat modifiers for size:
Target Size ………………………………………………. Modifier
Gargantuan, 32m or more (ship, bridge) ………………. +4
Huge, 16m or more (whale, house) …………………….. +3
Very large, 8m or more (city bus, big mecha) ………….. +2
Large, 4m or more (horse, car, tree, sm. mecha) ……… +1
Medium, 2m (human) ………………………………………. 0
Small, 1m or less (dog, barrel) …………………………… -1
Very small, 1/2m or less (cat, head, limb) ………………. -2
Tiny, 1/4m or less (mouse, bullseye) ……………………. -3

Damage rolls are still the same

If a greatsword does 4D6 damage, it still does 4D6 damage. Theoretically, it would be four Major MOD7 rolls added together, but that would be impractical. Roll (add together 3d6, divide by 7, find the remainder) 3 + roll (add together another 3d6, divide by 7, find the remainder) 2 + roll (add together another 3d6, divide by 7, find the remainder) 0 + roll (add together another 3d6, divide by 7, find the remainder) 4 for umm, err. 12 points of P/L damage. Hah! Take that thou varlet!

It slows down play and besides, it’s a whole lot of trouble. It’s one thing to do that for one roll (Skill roll, initiative, etc.) it’s another to have to add a series of Mod7 rolls together.

However, if you do want to still use D6 MOD7 rolls for damage or any other rolls, Dice Sheets will be provided with pregenerated Major and Minor D6 MOD7 rolls. Simply add up as many as you need down the column to get your total and then cross them off the sheet. The numbers are created by a True Random Number Generator to provide dice rolls. Then three dice rolls are added together and modulus 7 is taken from the total, just like any other D6 MOD7 roll. In short, it saves you from the math. Using a TRNG prevents the biases to low number that occurs in many spreadsheet programs with Psuedo-Random Number Generators in them.

I’ve done quite a bit of work in exploring dice mechanics in various games. Here, I’m writing down a different mechanic for a role-playing game that is different from what I’ve seen. If someone has already developed this idea, then please let me know. The MOD7 part of the name comes from the mathematical operation called modulus. The modulus is the remainder after you divide two numbers. For example, 16 divided by 5 is 3 with a remainder of 1. Another way of saying it is the remainder of 16 divided by 5 is 1. Still further, the modulus 5 of 16 is 1. All three are different ways of saying the same thing. Modulus is a term used when you only care about finding the remainder.

So the MOD7 part of the name means we are looking for the remainder of something after dividing it by 7.

The D6 part of the name means that we are going to roll six-sided dice.

Put them together and you have rolling a number of six-sided dice, and taking the modulus 7 of the result.

Basic Mechanic:

If Attribute + Skill + D6 MOD7 roll is equal to or above a target number, the action has been performed successfully.

D6 MOD7 Roll:

There are two kinds of D6 MOD7 roll, a major and a minor roll. A Major roll is the modulus 7 of the total of rolling three regular six-sided dice. In other words, roll three regular dice, find the total, and figure the remainder after dividing that total by 7. A Minor roll uses two regular dice instead of three. Most players will only use a major D6 MOD7 roll.

Too Much Math?:

At first, it seems like a lot of work to get a number. It becomes automatic after a few rolls. However, if you want a table to make things easier at first, here it is:

3 — 3
4 — 4
5 — 5
6 — 6
7 — 0
8 — 1
9 — 2
10 – 3
11 – 4
12 – 5
13 – 6
14 – 0
15 – 1
16 – 2
17 – 3
18 – 4

Why bother?

The reasons behind this mechanic are:

1. the chance to roll a zero
2. a way to give players a small advantage that is fairly invisible
3. a more equal chance of rolling any number

Rolling Zero
The chance to roll a zero is to add some variety. Rolling a zero is not an automatic failure. It merely represents those times that ‘luck’ isn’t on your side. The good news is that players have a better chance of rolling anything rather than a zero. Folks that use a minor roll (usually controlled by the game master) have a better chance to roll a zero.

Invisible Advantage
The major roll has more chance of success than a minor roll, but it isn’t apparent from anything other than the number of dice thrown. The advantage isn’t huge, but it’s enough to make a difference. In the math section, you can see the breakdown of exactly how much of an advantage the major roll provides.

Even Distribution of Rolls
Rolling three dice and using the total alone tends to give you average rolls. In other words, you’ll roll average rolls more often than small or large rolls. This is seen by many experienced rpg players as giving an advantage to players with powerful characters. Although the distribution isn’t as even as just rolling one die, the distribution of rolling 1 through 6 is the same, only rolling a zero is different. For a major roll, roll tend to be something other than zero. For minor rolls, they tend to be zero.

Target Numbers:

Setting a target number for an action is up to the Game Master, though some guidelines are provided later on. To give some meaning to the numbers, descriptive adjectives are provided in order to give a sense of scale.

TN 09 — Average/Easy
TN 10 — Tricky
TN 11 — Challenging
TN 12 — Difficult
TN 13 — Demanding
TN 14 — Extreme
TN 15 — Legendary

Those familiar with the Action! System should recognize the adjectives. The D6 MOD7 system uses some terminology from the Action! System game as provided by the OGL.

THE MATH:
Nothing extremely technical here, just the percentages of rolling certain things.

Major roll
Roll — Chance to Roll — Chance to = or exceed
0 ——- 0.138888889 ——- 1.000000000
1 ——- 0.143518519 ——- 0.861111111
2 ——- 0.143518519 ——- 0.717592593
3 ——- 0.143518519 ——- 0.574074074
4 ——- 0.143518519 ——- 0.430555556
5 ——- 0.143518519 ——- 0.287037037
6 ——- 0.143518519 ——- 0.143518519

Minor roll
Roll — Chance to Roll — Chance to = or exceed
0 ——- 0.166666667 ——- 1.000000000
1 ——- 0.138888889 ——- 0.833333333
2 ——- 0.138888889 ——- 0.694444444
3 ——- 0.138888889 ——- 0.555555556
4 ——- 0.138888889 ——- 0.416666667
5 ——- 0.138888889 ——- 0.277777778
6 ——- 0.138888889 ——- 0.138888889

I have been fascinated lately with variations on chess. The one played by many in Europe, including current Grandmasters, is Janus Chess. The board has two extra spaces (10 x 8 board) and each side has a Janus, a combination of a knight and bishop.

Having a combination piece means that a player can be checkmated with a Janus alone.

Reading about it, though, I stumbled upon a website with many, many different chess variants. People have combined pieces of all kinds, including ones from Shogi (chinese chess) and Tamerlane. Folks come up with some wild variations, including some rather unplayable ones. There’s a rabbit that can make as many knight moves in a counterclockwise fashion as it can. (Am I in check from your rabbit? Let me check.) There’s variations of the knight that make the “L” longer, wider, or both. There’s a checker piece that captures by jumping. The list is really large at chessvariants.org.

My favorite, however, is Chess with Different Armies. Four different armies have been playtested by the inventor and it is fascinating to see a game being played. Both sides are pretty much equal, but the tactics of each of definitely not the same. I imagine a tournament where players can switch armies between matches. I imagine two variant armies squaring off will be the most exciting matches.

If I ever live out my fantasy of opening a store, I’d like to create and sell Chess with Multiple Armies. It could be like the release of Deadwood with new armies every year. Heck, I may do that anyway.

Of course, I also like Arimaa, designed to confound computers. Enjoy the wikipedia reading.

It has come to my attention that another role paying game used the term ‘Hesperian’ to refer to a Roman-based society in an alternate future. Although I came up with Hesberian independent of them, the folks at Steve Jackson Games came up with it quite a bit earlier than I did. I do not want to infringe on their trademarks at all. It’s obvious to me that as they have prior art (I know it’s not a copyright thing) I need to change.

So, the Hesberian Empire material I came up with will have its name changed again. I am making certain that there are no duplication of specific people mentioned in other products. Awrelius will have a name change to Cutelium, but others with different names should be okay.

Henceforth, the empire that dominated Dira and influences Lenga is known as the Bedrian Empire.

NKQB

Nabrolus Kenuraque Bedrianus

For the Senate and Ken of Bedriana

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In finalizing Takteek, mrtool and I had an idea to use dice to determine the outcome. Basically, there would be one die for each rank. If a 3 attacks a 2, 3 six-sided would be rolled by the attacker and 2 six-sided dice would be rolled by the defender.

The idea is a sound one that I hope we get to test tonight.

However, I thought that it made sense to give the defending piece a small advantage. The reason being that in many pre-modern battles, a weaker force could defend against a much stronger force. One extreme example comes from Rome’s conquest of Britain. In one battle, the Romans were outnumbered 10 to 1, yet emerged victorious.

One idea was giving the defender an additional die. Another idea was giving the defender eight-sided dice to use. I compared these two scenarios with the default rules using an attack by a 2 piece on another 2 piece.

Under normal rules, the attacking piece will win outright 44.3673 % of the time, tie 11.2654% of the time and lose outright 44.3673% of the time. In English, both pieces have an equal chance of winning or losing (where a tie is considered losing because both pieces are demoted).

Adding a die to the defender, the attacking piece will win outright 15.2006 % of the time, tie 6.9444 % of the time and lose outright 77.8549 % of the time. In English, the defending piece has a huge advantage.

Allowing the defender to use eight-sided dice, the attacking piece will win outright 27.5608 % of the time, tie 8.5069 % of the time and lose outright 63.9323 % of the time. In English, the defending piece has a big advantage.

Thinking about this, I would lean more towards the eight-sided dice option, but the advantage still seems pretty large. It makes attacking with pieces with a rank of two almost useless. If you have a piece that has little more than a 1 in 4 chance of winning, presuming it attacks a piece with a rank of 2 is pretty dismal. Then again, they would serve as useful scouts, finding out the rank of the opposing piece.

Adding another die to the defender is definitely out. That’s just too much of an advantage.

In a perfect world, I think the defender should use seven-sided dice. The advantages are smaller, but still significant enough. However, I don’t have the money to purchase seven-sided dice at 5$ each. Besides, the goal is commonly available materials. Eight-sided dice are not as common as regular dice, but not very hard to get (and they tend to be inexpensive if you forgo the 733t dice used by role playing gamers).

Anywho, just a post to let everyone know that Takteek is not dead.

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I think I need to redo some of the Lenga traits. I originally had the power trait adding to the amount of Mana. That doesn’t work well. Instead, I propose this:

Tahares suffers penalities to TN and increase to mana ceiling. They cannot purchase the trait that provides bonuses to TN.

Paucalus suffers penalities to mana cieling and bonuses to TN. They cannot buy trait that increases mana ceiling.

The power trait will not increase the multiplier to compute mana for a spellcaster.

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