The Invisible CRT

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.