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The Invisible CRT

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Desprez
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Joined: 12/01/2008

EDIT: There is a second version a few posts down, that I personally prefer.

I had a flash of inspiration last night, and came up with an interesting twist involving multiple attack modes and a CRT embedded into dice.

The Invisible Combat Results Table.
Ok, this is still a work in progress, but I'd though I'd show you an interesting little system that takes a whole bunch of complexity and hides it inside of a set of custom dice.

Features:
1) Each attack is resolved by a single d10 die roll. Results are printed on the die.
2) As a result of this roll, either or both units can be hit or eliminated. (You could redefine a hit to make a unit retreat)
3) During a players turn, he gets three options on how to conduct his attack.
• All Costs: Tries to damage the target at all costs, even at the expense of his own unit.
• Cautious: Tries to damage the target, but with the safety of your own unit paramount.
• Balanced Attack: Simply balanced between damage and safety.

One of the nice things about having different attack modes is to better control risk depending on the tactical situation. For instance, if the risk is in an opposing unit surviving, if you need to kill it NOW no matter what, than an all costs attack may be called for. You trade a better chance to hit for the health of your unit.
If the risk lies in one of your strong units getting an unlucky roll against a weak unit, then use a cautious attack. It will probably take longer to score a hit, but you are less likely to take damage. You trade time for survival.

Components and Procedure:
• Military units. Only necessary to use 1 number to represent overall combat power. It should be noted that this is a relative system, and it is the difference between the the units' scores that is important. The battle results are the same for a 2 vs. 4 as a 10 vs. 12, (both difference of 2) so your values need to be designed accordingly.

• 8 Custom 10-sided die. (See below for the info on the die faces) The labeling refers to the difference in combat scores. So a 4 vs. 7 would use die #2.

One balanced attack set:
1) Yellow, labeled 0-1
2) Orange, labeled 2-3
3) Red, labeled 4-5
4) Purple, labeled 6+

Special attack mode set:
5) Dark Yellow, 0-1
6) Dark Orange, 2-3
7) Dark Red, 4-5
8) Dark Purple, 6+

This could be modified to use less or more, depending on the range of options you want. You could eliminate the attack modes and only use 4 die. Or, you could keep the options and reduce the range of unit strengths, and use 6 die. Or you could increase the range and use 10 die. Etc, etc.
You could, in theory, use 20-sided dice. d20s will allow better granularity in the percentages, but the issue with d20s is that their faces are very small, maybe too small to put the required markings on. (Need space for 2 distinct icons)

1) During a player's turn, he may conduct attacks. Indicate which unit is attacking what, and compare the combat scores. Add in any modifiers if you have them, terrain, leaders, etc. (In the default set-up, +2 is a healthy advantage)
2) Find the score difference, select an attack mode, and roll the appropriate die.
3) Apply the results of the die.

Balanced attacks use the lighter colored dice. All Costs attacks use the darker colored dice. Cautions attacks use the darker colored dice, but any hits become no effect, and any eliminations become hits.

Die Markings:
For posting simplicity, I'm using typeable characters, but a small graphical icon would be better.
- Weaker unit scores a hit on the stronger unit.
+ Stronger unit scores a hit on the weaker unit.
e Weaker eliminates the stronger unit.
E Stronger unit eliminates the weaker unit.

If using the yellow dice (unit strengths roughly even) the attacker uses the stronger unit markings, and defender uses the weaker unit markings.

           Faces                                                       Stats: Hit Chance
Die          1     2     3     4     5     6     7     8     9    10         Weak (e)  Strong (E)

Y 0-1        -     -                - +   - +                +     +          40 (0)     40 (0)
Y 0-1 Spc    -     -     -    e +   - +   - +   - E          +     E          70 (10)    60 (20)  *Note

O 2-3        -     -                - +          +     +     +     E          30 (0)     50 (10)
O 2-3 Spc    -          e +   - +   - +   - +   - E    +     +     E          60 (10)    80 (20)

R 4-5        -                - +          +     +     +     E     E          20 (0)     60 (20)
R 4-5 Spc         - +   - +   e E   - E    +     +     +     E     E          40 (10)    90 (40)

P 6+              - +          +     +     +     +     E     E     E          10 (0)     70 (30)
P 6+ Spc    - +   - E    +     +     +     E     +     E     E     E          20 (0)    100 (50)

*Note: In order to make the special attacks useful, no mater if you are the stronger or weaker unit, and without increasing the number of die unacceptably, the 'units even' case has to be fudged a bit. The chance to eliminate the defender had to be increased, but the chance to hit was lowered to make up for it. Otherwise 'All Costs' and 'Cautious' have can't use the same die.

Statistical note: The statistical results are very close to the results you'd have gotten from rolling twice, once for each unit.
Look at line R 4-5, difference of 4-5 die, say units with score 2 vs 6. The 2 has a 20% chance to hit, and the 6 has a 60% chance to hit. Statistically, the possible outcomes are 2miss 6miss 32%, 2hit 6miss 8%, 2hit 6hit 12%, 2miss 6hit 48%. That die's faces yield 30%, 10%, 10%, 50% - within 2 percentage points of the expected results.

Examples:
Alice's unit is a 3, and she attacks Bob's unit, a 4. The difference is only 1, they are considered about even and, so she will use the yellow die. Because these forces are almost equal, you'll notice that outright elimination by either force is off the table, and both have a 40% chance to hit the other. Alice selects to make a normal, balanced attack. She rolls the die and it comes up ' +' meaning she has inflicted a hit. (Some games have no hit points, or 'shaken' mechanics. If this is the case, a hit could mean the hit unit has to lose ground, or move back.)

Now, however, let's say Bob's unit is positioned in some kind of protected position, a terrain advantage, perhaps, and gets a +1 to its score. Now it is 3 vs 5, and that's a difference of two, enough to push the odds down to the orange die for Alice. Repeating her last attack with the modified odds, her chances have dropped a bit. She now has a 30% chance to hit while Bob has 50%. In addition, there is a 10% chance for her to be eliminated outright. It's not a hopeless position, however, and can select an appropriate strategy to compensate.

Say, she REALLY needs to inflict some damage, or move that unit. It's in the way, and she has the resources to sacrifice a unit or two to make it happen. She can select to use the 'All Costs' attack mode. This will double her chances to hit to 60% and even grant a slim 10% chance to eliminate Bobs unit. However, it's a suicide rush, and Bob is almost assured to do damage in return at 80% including a 20% chance of wiping out Alice's unit. (Also notice that Alice's single chance to score an elimination also comes with a hit in return.) She rolls the dark orange die is it comes up '- +' Both units take damage.

Now for a Cautions Attack example. Claire has a big, strong, and expensive unit say a 10, while David has a few 2s running around. Any attack Claire makes will use the purple 6+ die. Each time she attacks she'll mostly hit (70%) and have a fair chance of making an elimination too (30%). And while David only has a 10% chance to hit in return, that might end up being an expensive gamble if there are multiple units to deal with. If time is not an issue, Claire can instruct her commander to play conservative and use the Cautious Attack. This drops the unit's hit chance to 50% and there is no chance of scoring an elimination. But, at this big of a strength advantage, it completely eliminates the danger of the attack. It may, however, take many turns to clear out multiple small units this way. So she selects the dark purple die, and rolls a '- E' Now, since she selected Cautious, regular hits turn into misses, and eliminations are hits. So she has scored a hit.

David, on the other hand, when faced with this giant, cautious, unit has two options. He can run away, or be content to use his own turn to inflict damage. If that 10% chance only while attacking, not defending due to a cautions opponent, isn't good enough for him, then he can step up his attack intensity to 'All Costs' doubling his hit rate, still a only 20% though. However, that suicidal units is guaranteed a hit in return, and even odds to be eliminated. The score difference hasn't changed, so he'll use the same die. If he happened to roll the same result '- E' it means something different during the 'All Costs' attack. He inflicted a hit, but was eliminated in return.

As you can see, there is quite a bit of detail going on, but the nice thing is that it is all 'baked into' the system. All the player needs to know is the combat score difference, and select the appropriate die.

Sorry for the long post.
As I said, I'm still tweaking the percentages, and how some of the eliminations line up with opposing hits.

Desprez
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Joined: 12/01/2008
Other options

After thinking about some more, I can see other ways to increase the fidelity.
As it stands now, there isn't much fidelity between combat scores. Witness that every category jumps the percentage point spread between units by 20 points. 10 up and 10 down. This is quite large, and it is part of the reason that point differences were lumped into groups of two, so conceptually each combat point really represented a 10% point change.

I could use d20s, and have a die for each point difference, but as already mentioned, d20 sides are probably too small, and it would also yield 16 dice to cover the same possible score spread.
I'm not real happy about that.

But it occurs to me that I can instead of putting the total battle results on a die face, I could separate the weak and strong unit hits to take different sides and simply roll the die twice, once for each unit in combat. The space saved could be used to merge the special "battle mode" die into the main die.

If I did this I could cover a score spread of 7 using only 7 dice. Hit chance granularity could still be a problem, but by using different sided die, I might be able to find good categories. I can get smaller percent changes than a single die would allow by carefully switching it up.
For example, I can get a ~5% difference in chance to hit despite not using a d20. If you have 2 faces filled on a d8 for 25% chance to hit, you can decrease that to 20% in the next bracket by using a d10 with 2 faces filled, and drop it again to 16.5% on a d12 with 2 faces filled, then to 12.5% by moving back to a d8 with 1 face, and so on.
I implemented something similar in the past, and it worked pretty well. I'm just not sure if it can easily handle the different attack modes yet.

I also found that you could use the battle modes in other ways too.
In a game where leadership was important, you might say that if a leader is hurt or absent, a unit may only perform 'cautions' attacks. Or a certain berserker talent to perform 'all costs' attacks.
Long range attacks, like artillery, might only perform the standard attack, and ignore the possibility of getting hit back (while attacking).
In a magic setting, some kind immunity might allow the undead soldiers to ignore return hits, allowing judicious use of 'all costs' modes, only to have the defending player perform some kind of surprise cancellation of that immunity leading to massive losses on the undead.

Some things to think about.

Anyone got any other types of attacks that might be implemented?

Desprez
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Joined: 12/01/2008
Different Table

Ok, here is an alternate table. It has better granularity in the score differences and uses seven eight-sided die. The mechanics and options are the same, with the exception that when a units makes an attack, you'll also need to roll again for the defenders chance to strike back.

If using this system, one of your challenges as a designer will be how to make the hit/eliminate icons useful at a glance. The things you'll need to fit on a die face (note that d12s have a larger area): 2 icons, and a number indicating witch die it is. The spaces is there, it's just a matter of presenting it clearly. So, one icon for normal attacks, and one for special mode attacks. Each icon needs to indicate whether the weaker, or stronger, or both units hit, and whether that hit is an elimination. You could also conceivably make the elimination hit a smaller separate icon, but I'm finding that the die face becomes a bit busy that way.

Interestingly, this chart was harder to make. I hadn't realized it at the time, but the way the previous chart worked it just happened to neatly sidestep some issues in the increments. Also, the base hit chance was raised slightly, which works better for units that don't always die instantly from one hit.

So, when a units attacks (say a 2 attacks a 4) you roll the appropriate die and are looking for '-' or 'e' (or whatever your icons are) to score hits. Then the stronger defender unit fires back looking for '+' or 'E'

d12                                        Faces
Die         1     2     3     4     5     6     7     8     9    10    11    12     Stats:   Hit Chance %
Score Diff                                                                                  -  (e)    +  (E)

0 White                                               +     +     +     +     +            42  (0)   42  (0)
                              +     +     +     +     +     +     +     E     E            75 (17)   75 (17)

1 Blue      -     -     -     -     -           +     +     +     +     +     +            42  (0)   50  (0)
            e     -     -    - +   - +   - +   - +   - +    +     +     E     E            67  (8)   75 (17)

2 Green     -     -     -     -           +     +     +     +     +     +     E            33  (0)   58  (8)
            e     -    - +   - +   - +   - +   - +    +     +     E     E     E            58  (8)   83  (25)

3 Yellow    -     -     -     -     +     +     +     +     +     +     E     E            33  (0)   67  (17)
            e     -    - +   - +   - +    +     +     +     E     E     E     E            42  (8)   83  (33)

4 Orange    -     -     -     +     +     +     +     +     +     E     E     E            25  (0)   75  (25)
            e    - +   - +   - +    +     +     +     E     E     E     E     E            33  (8)   92  (42)

5 Red       -     -     +     +     +     +     +     +     E     E     E     E            17  (0)   83  (33)
            -    - +   - +    +     +     +     E     E     E     E     E     E            25  (0)   92  (50)

6+ Purple   -     +     +     +     +     +     +     E     E     E     E     E             8  (0)   92  (42)
           - +   - +    +     +     +     E     E     E     E     E     E     E            17  (0)  100  (58)

EDIT: Fixed some table errors

End of Time Games
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Joined: 04/16/2009
This sounds interesting. It

This sounds interesting. It will take me a while to get through all of this. I read the upper portion. Is this sort of like a way to get rid of what RPG gamers call the "wiff factor" where at the last minut the game is ruined by a dice role?

Desprez
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Joined: 12/01/2008
Not exactly. Though, since

Not exactly.
Though, since there is a difference between a hit and an elimination, there is a little less impact of wild chance swings.

Really, it stemmed from trying to get around the limitations of having an attack OR defense score, while trying to retain the smoothness of a single stat. Interestingly, this also allowed the option to include 'attack modes', without really reducing play speed - though it does make the dice themselves more complex, and may be a challenge on graphic design, and component cost. FWIW, I have a design solution that seems to work so far.

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