Too much fidling?

Calculating a fraction is too much work for players.

I am working on something that does the work for the players. And Then the roll for a group isn't needed either.

Thinking about having the number of hits as an output per card.

Not sure how yet. But I am thinking about having a couple of dice being rolled. Then the score will determine if a card has 1 or multiple hits. The multiple hits are based on the card having multiple projectiles.

Flamethrower has for example 3 projectiles of 1 damage each.
Each projectile is supposed to have a percentage chance to hit. Of course having 2 hits and 1 miss is linked to a certain score as well.

The "old school" variant had a basic accuracy of 50% and an extra accuracy of 50%. Thus 25% per projectile. The number of projectiles that at least can hit:
0: 100%
1: 87.5%
2: 50%
3: 12.5%

If I am to roll for example 4d6 for all cards. The scores needed to simulate those hits are:
0: 4; 100%
1: 11; 84%
2: 15; 44%
3: 19; 10%

A rifleman would have only 1 projectile.
1: 50% would translate into:
1: 15; 44%

So, as you can see, I am not sure about this.
The more dice, the better the result.
Perhaps 2d10 would be good as well. Because then I can round it down to %. And it would be a roll of "this" or less.

0: 100%
1: 88%
2: 50%
3: 13%

This... gives me an idea. I think a good one this time.

I used a very linear approach like this in my prototype board game. However, the board game had multiple dice rolling for it.

The card game needs like.... less.

Oh, how about this?
The player rolls 5 dice. Every die is worth 1/5th or 20%.

If the accuracy of a card is 4/6th. Then you roll the 5 dice. Those which are 4 or less count.

Let's say, the player rolls 1,1,3,5,6
The all cards with accuracy 1 or 2, get 40%.
All cards with accuracy 3 or 4 get 60%.
All cards with accuracy 5 get 80%.
All cards with accuracy 6 get 100%.

Obviously, 1 projectile needs to have an accuracy of 6 in order to be of use. Any less, and the player needs to roll 5 sixes.
2 projectiles need to have 60% or more, in order to have at least 1 hit.
3 projectiles can do with 40% or more.
5 projectiles or more, can do with 20%.

Let's assume we have:
60 of 1 accuracy
30 of 2 accuracy
20 of 3 accuracy
15 of 4 accuracy
12 of 5 accuracy
10 of 6 accuracy
And any hit here is 1 damage point.

Let's see how the results are with the averane and 1 standard deviation away from the average:
1 accuracy: 0 to 10 to 20 hits
2 accuracy: 4 to 10 to 16 hits
3 accuracy: 6 to 10 to 14 hits
4 accuracy: 7 to 10 to 13 hits
5 accuracy: 8 to 10 to 12 hits
6 accuracy: 10 to 10 to 10 hits

The total here is: 35 to 60 to 85 hits

The same can be done if I do 10% per die success. So the players can divide by a clean 10. Which might be best if I keep the basic accuracy separated. Dividing by 5 and then by 2 is a total of dividing by 10 :)

Let's see what the chances are to roll a factor for each accuracy

Accuracy 1:
0; 40%
1; 40%
2; 16%
3; 3%
4; 0%
5; 0%

Accuracy 2:
0; 13%
1; 33%
2; 33%
3; 16%
4; 4%
5; 0%

Accuracy 3:
0; 3%
1; 15%
2; 31%
3; 31%
4; 15%
5; 3%

Accuracy 4:
0; 0%
1; 4%
2; 16%
3; 33%
4; 33%
5; 13%

Accuracy 5:
0; 0%
1; 0%
2; 3%
3; 16%
4; 40%
5; 40%

Accuracy 6:
5; 100%

***

Most defences have an accuracy of 6. These would be numbers, easily given to the player. It would make the game a bit boring again.

But overall, I am happy with the results. Now for a good playtest.

I am going to try to explain it in terms of what players might be placing on the table.

Basics:
Tier 1, Costs 1, Armor 1 or Damage 1
Tier 2, Costs 2, Armor 3 or Damage 3
Tier 3, Costs 4, Armor 9 or Damage 9

Since units can defend AND attack, their damage weights twice. Either way, the list below are just many examples.

Rifleman:
Costs 2
Armor 1
Damage 1, accuracy 3

Grenadier:
Costs 3
Armor 1
Damage 3, accuracy 3

Rocket soldier:
Costs 5
Armor 1
Damage 9, accuracy 3

Guard Tower:
Costs 4
Armor 3
Damage 3 of 1, accuracy 4

Attack Buggy:
Costs 4
Armor 3
Damage 2 of 1, accuracy 3

Quad:
Costs 6
Armor 3
Damage 3, accuracy 6

Flamethrower:
Costs 5
Armor 1
Damage 3 of 1, accuracy 4

Wooden Fence:
Costs 1
Armor 1

Sand Bags:
Costs 2
Armor 3

Concrete Wall:
Costs 4
Armor 9

Combat Tank:
Costs 8
Armor 9
Damage 9, accuracy 3

Missile Tank:
Costs 10
Armor 3
Damage 3+3+3, with accuracy 3+4+5

Rocket Tank:
Costs 12
Armor 9
Damage 9+9+9, with accuracy 1+2+3

Flame ATV:
Costs 7
Armor 3
Damage 3 of 1, accuracy 5

Flame Tank:
Costs 9
Armor 9
Damage 2 of 1, accuracy 2
Damage 1, accuracy 3
Damage 2 of 1, accuracy 4

***

Ok, I hope I calculated those right.
Please notice, I didn't add any slow projectiles in there.

Let's say, a player can spend 30 credits.

Player A spends it on 15 riflemen.
Player B spends it on 6 flamethrowers.

Player A rolls 12356
Player B rolls 33456

A rifleman has an accuracy of 3. With the roll, 3 out of the 5 dice are a succes.
We have 15 riflemen.
Each shoots 1 projectile of 1 damage.
The projectiles hitrate is 3.

number of units x projectiles x succesrate = score

15 x 1 x 3 = 45
45 damage, 4 infantry units can be killed with this.

A flamethrower has an accuracy of 4. With the roll, 3 out of the 5 dice are a succes.
We have 6 flamethrowers.
Each shoots 3 projectiles of 1 damage.
The projectiles hitrate is 3.
6 x 3 x 3 = 54
54 damage, 5 infantry units can be killed with this.

After 1 battle, 10 riflemen and only 1 flamethrower remain.

***

Player C chooses to get 5 Attack Buggies and 5 riflemen.

Player C rolls 12356.

The Attack Buggies have an accuracy of 3. With the roll, 3 out of the 5 dice are a succes.
The same goes for the riflemen.
Each Attack Buggie shoots 2 projectiles of 1 damage.
The riflemen shoot 1 projectile of 1 damage.
5 x 2 x 3 = 30
5 x 1 x 3 = 15
45 damage in total. Just like player A.

While player A would be losing 4 riflement to player C.
Player C can choose to put the Attack Buggies in front.
45/3=15.
So only 1 Attack Buggie would die here.

If this was against player B. Then 54/3=18
And player B would also only be able to kill 1 attack buggy.

***

Player D chooses to get 3 Missile Tanks.
And rolls 12456.

The accuracies per projectile are: 3, 4 and 5.
This means that the projectiles with accuracy 3 have a succes of 2.
The projectiles with accuracy 4, have a succes of 3.
And the projectiles with accuracy 5, have a succes of 4.

3 x 1 x 2 = 6
3 x 1 x 3 = 9
3 x 1 x 4 = 12
Total of 27, but remember, the damage is 3 each.

Against player A and B, only 2 infantry units can be killed.
In return, A is able to kill 45/3=15, thus 1 missile tank.
In return, B is able to kill 54/3=18, thus 1 missile tank.

Against player C, things can go good or bad.
If player C uses the riflemen as fodder. Then D can kill 2 infantry units.
But if player C uses the attack buggies as fodder, Then D can kill 27x3/3=27, thus 2 attack buggies.
In return, C can also kill only 1 missile tank.

So far, D is doing the worst.

***

Player E chooses 3 Flame Tanks.
And 3 wooden Fences for the fun of it...

E rolls: 12345

Damage 2 of 1, accuracy 2
Damage 1, accuracy 3
Damage 2 of 1, accuracy 4

So, this means that accuracy 2 has a succes of 2, 3 has 3 and 4 has 4.
3 x 2 x 2 = 12
3 x 1 x 3 = 9
3 x 2 x 4 = 24
A total of 45.
Well then, 4 infantry units can die again.
Or 1 vehicle.

But the return fire from the players...
A has 45/9=5
B has 54/9=6
C has 45/9=5
D has 27*3/9=9

None of them reached 10. So none of them are able to kill a flame tank.

I am working at the combat mechanic, in terms of strategy now. And I want to go back to the freedom of war.

If a player attacks, it chooses targets. It is possible to send the entire army after one target. The enemy can now choose to protect the target. And send in cards to blcok incomming cards. 1 or multiple cards can be used for this as well. But you need to block each attacking card.

Now, the player build intuition on which cards are easy targets or not. But there is a way to calculate by looking at the statistics of those cards.

There are 2 steps. One of them is knowing the RPS mechanics. But that can be viewed in different lights. It is better to look at the total costs and notice what the damage can be.

All players have to do then is knowing that a 9 damage, is worth only 1/9th on an infantry unit.
So, the only value that needs to be adjusted in the mind is the damage value.

The strategic value of a card
We need some value's to work with.
- Costs of the card
- Damage
- Accuracy
- Number of projectiles

Our most basic unit:
Rifleman:
Costs 2
Armor 1
Damage 1, accuracy 3
We don't need that armor.

We multiply damage with accuracy and divide by the costs.

1x3/2=1.5

1.5 is the strategic value of a rifleman. This means that any value higher than this, means that the unit is of more importance than the riflemen. And thus needs help of the rifleman.

Grenadier:
Costs 3
Armor 1
Damage 3, accuracy 3

3x3/3=3.0

3.0 means that this unit is twice as important than a rifleman. But only against vehicles and tanks.

1x3/3=1.0

1.0 means that the same grenadier has less strategic value than a rifleman, when facing infantry. Which is very logical due to the RPS mechanics. If a player faces many infantry, it is better to keep producing riflemen. But if there are many vehicles, then the grenadier is the primairy choice of the 2.

In fact, if you see 10 infantry and 5 vehicles. You might want to use these factors to see which unit is more usefull to get.
10 x 1.5 = 15
5 x 3.0 = 15
In this case, a nice mix might be the players best option.

Now for the other examples, higher needs more protection:

1.5 - 1.5 - 1.5 Rifleman
1.0 - 3.0 - 3.0 Grenadier
0.6 - 1.8 - 5.4 Rocket soldier
3.0 - 3.0 - 3.0 Guard Tower (defence only)
1.5 - 1.5 - 1.5 Attack Buggy
1.0 - 3.0 - 3.0 Quad
2.4 - 2.4 - 2.4 Flamethrower
0.0 - 0.0 - 0.0 Wooden Fence
0.0 - 0.0 - 0.0 Sand Bags
0.0 - 0.0 - 0.0 Concrete Wall
.375-1.125-3.375 Combat Tank
1.2 - 3.6 - 3.6 Missile Tank
0.5 - 1.5 - 4.5 Rocket Tank
2.14-2.14 -2.14 Flame ATV
1.67-1.67 -1.67 Flame Tank

Please note, this is only based on how much damage a card can do. Not on how much a card can block. That would be another list. The higher, the more strategic it is to use them as a block.

0.50 - 0.50 - 0.50 Rifleman
0.33 - 0.33 - 0.33 Grenadier
0.20 - 0.20 - 0.20 Rocket soldier
0.75 - 0.25 - 0.25 Guard Tower (defence only)
0.75 - 0.25 - 0.25 Attack Buggy
0.50 - 0.167- 0.167 Quad
0.20 - 0.20 - 0.20 Flamethrower
1.00 - 1.00 - 1.00 Wooden Fence
1.50 - 0.50 - 0.50 Sand Bags
2.25 - 0.75 - 0.25 Concrete Wall
1.125- 0.375- 0.125 Combat Tank
0.30 - 0.10 - 0.10 Missile Tank
0.75 - 0.25 - 0.083 Rocket Tank
0.429- 0.143- 0.143 Flame ATV
1.00 - 0.333- 0.111 Flame Tank

***

Well.... I don't see the player doing this though. But it sure is nice to have some comparisons.

I like how the flamethrower and the rocket soldier have the same protection value's. Now you can observe the differences in the weapons. And you can clearly tell that, while both are support units. Each has their own specific task. In the long run, you might want to sum the scores as well. And somehow the rocket soldier is slightly better of. However, the flamethrower is clearly a good option against the rocket soldier.

The best cards to use in order to block tier 3 weapons is the wooden fence. Although, maybe I should name it camouflage or something. There are also plenty of cards that can block plenty of tier 1 weaponry. The combat tank has a very good score on this, despite it being a unit. In fact, it scores better than the wooden fence.

I reconsidered the weight on the weapons. I can keep the options attack base, attack units, defend. Because this makes for interesting cards later on.

But I am troubled with having the right attribute names.
[Unit] and [Structure] doesn't cover everything.

***

Now for the d8.
Are these useful for the design?

For now, I used 1, 2 and 4 for the 3 tiers.
With accuracies that are divided by 6. This made designing a bit hard.

50% = 3/6
And that is the only one which fits the basic weight.

d8 offers me:
25% = 2/8
50% = 4/8
75% = 6/8

2 projectiles was hard with d6. Unlike my prototype where the basis was on a 30 weight. 1, 2 or 4 divided by 6 made it hard. Since 2, 4 and 8 divided by 6 also made things hard.

3 projectiles for an unit was easy enough for some proper design. Because 3x 1/6th would be 50% again.

d8 might offer a great solution. Not only that. But 1.5 times 4 is 6. While 1.5 times 3 is 4.5.
This for the slower weapons. So, d8 does help me here as well.

d8 does fit in more nicely. But I need only the normal ones. So that a simple comparison can be made.

I made a list of d6 and the accuracies of how they would be divided.
60 of 1, 30 of 2, 20 of 3, 15 of 4, 12 of 5 and 10 of 6.
This is a basic distribution. Only some math to tell me roughly how the cards accuracy should be distributed.

For d8, it will require higher numbers, because there is a new prime in there, 7.
840 of 1, 420 of 2, 280 of 3, 210 of 4, 168 of 5, 140 of 6, 120 of 7 and 105 of 8.
Obviously I am not going to use those numbers.

This is more understandable:
8 of 1, 4 of 2, 3 of 3, 2 of 4, 2 of 5, 1 of 6, 1 of 7 and 1 of 8. Something like that.

***

Some more testing showed me. I can have fun with that d8 in terms of design :)

A list of tanks:
All tier 3 armor
All tier 3 damage
Each accuracy of 1 adds exactly a cost of 1.

Also, if the accuracy is 4.
And the weapon has to wait for 1 or 2 subturns. Exactly 1 accuracy is added each subturn. This will make for a great design:

Missile Tank:
Costs 8 (not 10)
Armor 3
Damage 3 per missile.
First missile accuracy 4
Second missile accuracy 5 with a charge of 1
Third missile accuracy 6 with a charge of 2

For this game at least :)

As for how we always looked at the dice and the results?
When we need an accuracy of for example 5. We simply need the roll to be 5 or less. This would equal a chance of 5 out of 8. And we can actually use the 5 in the calculations for balance.

If we say, you need to roll 5 or higher for a succes. The balance calculation is reversed. Still a good option though. But not something we are used to.

Now, having an accuracy of 1, and having to roll an 8 is very counter intuitive for most tbh. Unless we use 8, which would be "in-accuracy". A higher number would be worse in this regard...

***

Why more dice?
1 die gives lineair results.
But 2 dice already create a bit of a normal distribution.
And the more dice I use, the higher the reward can be with a good roll.
While a bad outcome like 0 becomes rare.

1d would give 0 or 1.
2d can give 0, 0.5 or 1.
3d can give 0, 0.3, 0.7 or 1.
4d can give 0, 0.25, 0.5, 0.75 or 1.
5d can give 0, 0.2, 0.4, 0.6, 0.8 or 1.

An accuracy of 1 on 8. Can mean, with a good roll, this weapon is like at most 8 times more powerfull.

By the way, I used Anydice.com for my calculations.

The chances to roll 0 succes for accuracy 1, with a number of d8:
87.5% with 1 die
76.6% with 2 dice
67.0% with 3 dice
58.6% with 4 dice
51.3% with 5 dice

As soon as a succes is rolled, the accuracy of 1 already paid itself back. No matter how many dice I use.

Another way to look at this is:
A card can have 1 projectile with accuracy 8 or 8 projectiles with accuracy 1.
With 5d8, we always have 5 hits with accuracy 8. However, this is 100% (or 5x 20%).

As soon as 1 die is a succes for the 1 accuracy, we got 8 hits. Or 160%.
The chances on the number of hits can be seen as following:
_0: 51.3% equals 0.0
_8: 36.6% equals 2.9
16: 10.5% equals 1.6
24: 1.50% equals 0.4
32: 0.11% equals 0.0
40: 0.00% equals 0.0

If you sum the last column, you get your 5 again.

Those cards that attack, can't defend the next round.

Also, if a flying unit blocks ground forces with ground weapons. This should not be the case. The flying unit will simply be able to deal damage. And the ground forces will still attack whatever they where targeting. In fact, just like my prototype board game. I am planning to have the rule that excess damage will go through until all targets are eliminated.

And if something can't block, it cannot block. That rule should be known to the players. This is where it is different than MtG.