方块公国 (Drop Duchy)

方块公国 (Drop Duchy)

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Drop Duchy - Advanced Tips on Combat Phase & Examples
由 jafferduo 制作
The Combat Phase Guide in game.

Combat Rules:
Your goal is to find a battle order that uses the groups' strengths and weaknesses to your advantages.
Swords counters Bows, Bows counters Axes, Axes counters Swords.

Combining:
You can combine two groups of the same team to change their type.
The new group keeps the type of the biggest group (or the destination's type if they're equal).

Attacking:
When two opposite groups meet, they subtract their numbers.
Each type has the advantage against a certain other type(Swords counters Bows, Bows counters Axes, Axes counters Swords), giving them +50% strength (meaning that 2 soldiers can eliminate 3 opponents).

------------------------------
[Now the part of my guides starts]

The idea of Combat Phase seems simple, however, it's much deeper than you think, actually. In fact, most players do not really play the Combat Phase to the best, or almost best.
Let me add more tips here, and I'll also put videos to show some situations/answers so you can know what's going on.

The basic is to take the highest advantage to all (or most) enemies while doing this, however, even if you think you've already achieved this, you may still haven't done it perfectly, let me explain them now.

Alright, let's get started.

I.
Assume that we have the advantage on soldier type, if we eliminate an enemy squad(and the squad we use still haven't reach zero), but the number of the enemy squad we eliminate cannot be divisible by 3, we'll suffer from a tiny exchange penalty.

For example:
1. We use 60 swords to eliminate 31 enemy bows, we'll spend 20(2x) to exchange 30(3x) first; however, the enemy still has 1 bow left, you'll be forced to make a 1:1 exchange for it(instead of 1:1.5), that's the tiny penalty.
2. Now assume we use 60 swords to eliminate 44 enemy bows, we'll spend 28(2x) to exchange 42(3x) first; however, the enemy still has 2 bows left, you'll be forced to make a 2:2(because 1 can only exchange 1.5 most of times) exchange for them(instead of 2:3), that's the tiny penalty, too.

In conclusion, one of the tip is try to make an enemy squad can be divisible by 3, when we eliminate it on type advantage.
There's an important note here: (Assume that we have the advantage on soldier type.) If your squad is eliminated instead, and the enemy squad you attack still has units left, you won't get the penalty from this scenario.

II.
There's a situation that can make you get tiny 1:2 exchange bonus.
The conditions are:
1. Your army type is in advantage against the enemy's.
2. The number of the ally squad must be odd(not even), assume it's 2x+1.
3. The number of the enemy squad must be at least 3x+2, or more.

At this situation, after you exchange 2x allies for 3x enemies, you'll have ONLY one troop left; however, since the enemy's type is being countered, and the enemy squad still has at least 2 or more troops left, it's impossible for the enemy to defeat the last ally unit with only 1, which will force enemy spend 2 for the last 1 ally instead.
Therefore, you can get 1:2 exchange ratio instead of 1:1.5, that's the tiny advantage you can try to get on Combat Phase.

In Conclusion, there are two tips for us to follow to make the best result on Combat Phase:
1. (On unit type advantage)When we want to fully eliminate an enemy squad, always try to make the number of that enemy squad can be divisible by 3.
2. (On unit type advantage)When the number of our squad is 2x+1(odd), and the number of the enemy's squad is at least 3x+2 or more, we can get tiny 1-exchange-2 advantage.

Now let me officially show some videos and more information below.
   
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IMPORTANT NOTE
All of the following situations in videos below don't own the technology card names "Strength in numbers", if you have this card, you'll have to consider the whole things differently on Combat Phase.

Strength in numbers: Obtain +7/+11/+15 allies when merging groups of the same type during the combat phase.

If I find some interesting situations, I may add extra examples here, most of them are below example 25.

If you're not good at calculating, you can enable the following function:
Main Menu Option[Top Right Corner] (or Esc, then Option when you're in a run.)
Gameplay.
Enable "Preview Battle Numbers"

If you have any interesting example of Combat Phase, or if you want me to check for improvement on your Combat Phase gameplay on YouTube or elsewhere, you can reply here with screenshot or video links. I'll check them out if I'm still alive on Steam:
https://psteamcommunity.yuanyoumao.com/app/2525310/discussions/0/603036300513197602/
Example 1
Starting easy.

Answer:
Combine all idle 3 enemies into bows, then exchange them with 2 swords.
Or combine all idle 3 enemies into axes, then exchange them with 2 bows.

If you kill them 1 by 1, you'll lose (at least) 3 units instead of 2.

Example 2
Starting easy.

Answer:
Enemy Ax*13 to Enemy Ax*14 = Eax*27
Enemy Ax*27 to Ally Bow*22 = Abow*4
Ally 4+5+28 = 37 allies left.

The first step makes enemy troops be divisible by 3, it's important.

If you choose the way that draw 22 bows to enemy 14 axes, then enemy 13 axes, you'll suffer from tiny exchange penalty that make you have only 36 units left instead of 37.

Example 3
Starting easy.

Answer:
Enemy Ax*13 to Enemy Bow*14 = Ebow*27
Enemy Bow*27 to Ally Sword*18 = 0
Ally Bow*40 left.

The first step makes enemy troops be divisible by 3, it's important.

If you choose the way that draw 18 swords to enemy 14 bows and combine in 40 bows for enemy 13 axes, you'll suffer from tiny exchange penalty that make you have only 39 units left instead of 40.

Example 4
Starting easy.

Answer:
Combine all enemies into 60 swords, which can be divisible by 3.
Then exchange them with 40 axes.

If you deal with the three 20 squads each by each, you'll lose 2 more units for this.

Example 4.5 [Extra]
Now we know we can combine all 3 20-squad enemy groups to make it 60, which can be divisible by 3 to erase tiny exchange penalty I mentioned before; however, none of the type of ours reach total 40 here, what should we do?

Answer:
Enemy Bow*20 to Enemy Ax*20 = Eax*40
Enemy Ax*40 to Ally Bow*15 = Eax*17
Enemy Ax*17 to Enemy Sword*20 = Esword*37
Enemy Sword*37 to Ally Ax*37 = Aax*12
12+16+20 = 48 allies left

We take a tiny 1:2 exchange advantage at step 2 (+0.5), then we take a tiny (3x+1) exchange penalty when we eliminate 37 enemy swords at step 4 (-0.5), both cover each other, like we exchange 60 enemies with 40 allies normally.
Example 5
Answer:
Enemy Sword*34 to Enemy Sword*34 = Esword*68
Enemy Sword*68 to Ally Ax*27 = Esword*27
Enemy Sword*27 to Enemy Ax*33 = Eax*60
Enemy Ax*60 to Ally Bow*70 = Abow*30
Ally Bow*30 to Ally*(15+31+4+50) = Ally*130

Step 2 has the tiny 1 exchange 2 advantage. And the rest enemies can be divisible by 3, which means we won't suffer from tiny exchange penalty when we eliminate them with correct type.

Example 6
Unable to take advantage of all enemies, try to take advantage as much as possible.

Answer:
Enemy Bow*22 to Enemy Bow*22 = Ebow*44
Enemy Bow*44 to Enemy Sword*23 = Ebow*67
Enemy Bow*67 to Ally Sword*5 = Ebow*59
Enemy Bow*59 to Ally Sword*35 = Ebow*6
Enemy Bow*6 to Ally Bow*18 = Abow*12
12+25 = 37 allies left
Example 7
Answer:
Enemy Bow*17 to Enemy Ax*18 = Eax*35
Enemy Ax*35 to Ally Bow*15 = Eax*12
Enemy Ax*12 to Enemy Sword*18 = Esword*30
Enemy Sword*30 to Ally Ax*31 = Aax*11
11+20 = 31 allies left
Example 8
The situation becomes wielder now, try to get the best result.

Answer:
Enemy Bow*18 to Enemy Bow*14 = Ebow*32
Enemy Bow*32 to Ally Bow*26 = Ebow*6
Enemy bow*6 to Enemy Sword*13 = Esword*19
Enemy Sword*19 to Ally Ax*42 = Aax*29
Example 9
Answer:
Enemy Bow*23 to Ally Sword*15 = 0
Enemy Bow*23 to Ally Sword*4 = Ebow*17
Enemy Bow*17 to Enemy Sword*22 = Esword*39
Enemy Sword*39 to Ally Ax*41 = Aax*15
15+21 = 36 allies left

Get the tiny exchange advantage by exchanging 23 bows with 15 swords [(2x+1) allies exchange (3x+2 enemies) precisely], then cut down rest enemy bows a bit so we can combine them into 39 swords, which can be divisible by 3, we can exchange them with 26 axes perfectly without any tiny penalty.
Example 10
Try to get the advantage on attacking and switch enemies' type properly.

Answer:
Enemy Ax*65 to Ally Bow*24 = Eax*29
Enemy Ax*29 to Enemy Bow*30 = Ebow*59
Enemy Bow*59 to Enemy Ax*30 = Ebow*89
Enemy Bow*89 to Ally Sword*87 = Asword*27
27+30+37 = 94 allies left
Example 11
Answer:
Enemy Bow*33 to Enemy Ax*33 = Eax*66
Enemy Ax*66 to Enemy Bow*41 = Eax*107
Enemy Ax*107 to Ally Bow*41 = Eax*45
Enemy Ax*45 to Ally Bow*40 = Abow*10
10+8+18+8 = 44 allies left

Step 3 is very important, not only get the tiny 1-exchange-2 advantage, but also can make the rest enemies be divisible by 3, so you can defeat rest of them perfectly without tiny exchange penalty.
If you carelessly draw enemy 107 axes to ally 40 bows first, you'll be unable to get these advantages, and get 43(1 less) units at the end.
Example 12
This on is harder at this timing. If you want to do it yourself but unable to work it out currently, you may skip to next question first.

Answer:
Enemy Ax*60 to Ally Bow*27 = Eax*19
Enemy Ax*19 to Enemy Sword*55 = Esword*74
Enemy Sword*74 to Enemy Ax*60 = Esword*134
Enemy Sword*134 to Ally Ax*63 = Esword*39 (39 can be divisible by 3)
Enemy Sword*39 to Ally Ax*28 = Aax*2
2+78 = 80 allies left
Example 13
You'd learnt many thing in previous videos, this one is not that hard so you may do it yourself.

Answer:
Enemy Sword*35 to Enemy Sword*35 = Esword*70
Enemy Sword*70 to Ally Ax*45 = Esword*2
Enemy Sword*2 to Enemy Bow*35 = Ebow*37
Enemy Bow*37 to Enemy Ax*35 = Ebow*72
Enemy Bow*72 to Ally Sword*55 = Asword*7
7+93 = 100 allies left
Example 14
Answer:
Enemy Sword*23 to Enemy Sword*22 = Esword*45
Enemy Sword*45 to Ally Ax*20 = Esword*15
Enemy Sword*15 to Enemy Bow*23 = Ebow*38
Enemy Bow*38 to Ally Sword*19 = Ebow*9
Enemy Bow*9 to Ally Sword*30 = Asword*24
24+3 = 27 allies left
Example 15
There are more than 1 way to get the best result, though.

(One of the)Answer:
Enemy Bow*57 to Ally Sword*39 = Asword*1
Ally Sword*1 to Ally Ax*(22+12) = Aax*35
Ally Ax*35 to Enemy Sword*56 = Esword*3
Enemy Sword*3 to Enemy Ax*56 = Eax*59
Enemy Ax*59 to Enemy Sword*56 = Eax*115
Enemy Ax*115 to Ally Bow*67 = Eax*14
Enemy Ax*14 to Ally Bow*58 = Abow*48
48+12 = 60 allies left
Example 16
(Note: The bottom-left sword group is 60.)

Answer:
Ally Sword*48 to Enemy Sword*55 = Esword*7
Enemy Sword*7 to Enemy Ax*60 = Eax*67
Enemy Ax*67 to Enemy Sword*55 = Eax*122
Enemy Ax*122 to Ally Bow*45 = Eax*54
Enemy Ax*54 to Ally Bow*40 = Abow*4
4+80+60 = 144 allies left
Example 17
All enemies are swords, most of allies are bows, and the number of other two types are too low.
If you just combine swords into axes, the 20 axes can only take out 30 enemy swords, there will still be 38 enemy swords left to punish your rest bows badly.
What should we do? How to cut down the damage?

Answer:
!Ally Bow*42 to Enemy Sword*22 = Abow*9!
Ally Bow*9 to Ally Ax*12 = Aax*21
Ally Ax*21 to Ally Sword*8 = Aax*29
Ally Ax*29 to Ally Bow*27 = Aax*56
Ally Ax*56 to Enemy Sword*23 = Aax*40
Ally Ax*40 to Enemy Sword*23 = Aax*24
24+37 = 61 allies left
Example 18
The best solution of this case is fantastic.

Answer:
Ally Ax*15 to Ally Sword*8 = Aax*23
Ally Ax*23 to Ally Sword*21 = Aax*44
Ally Ax*44 to Enemy Sword*33 = Aax*22
Ally Ax*22 to Enemy Sword*34 = Esword*1
Enemy Sword*1 to Enemy Sword*34 = Esword*35
Enemy Sword*35 to Ally Ax*23 = 0
28+18 = 46 allies left

I defeat 33 enemy swords at step 3 first, which can be divisible by 3, then I use the rest 22 axes to attack one of the 34-sword group and exchange 33 enemy swords. I do not eliminate that 34-sword group, so it's just a normal 2x exchange 3x, I do not suffer from any tiny exchange penalty here.
The last one enemy sword combines with another 34-sword group to become 35, which makes the last step become perfect (2x+1) exchange (3x+2), x=11. It's so great.
If you play like most players that combine all allies into axes and deal with the 3 enemy sword groups each by each, you'll have 45(1-less) allies left.
Example 19
The only odd(not even) number of ally squads is the 29-sword one.
Is there any way to get the tiny 1-exchange-2 advantage?

Answer:
Ally Bow*24 to Ally Sword*10 = Abow*34
Ally Bow*34 to Ally Sword*29 = Abow*63
Ally Bow*63 to Enemy Ax*30 = Abow*43
Ally Bow*43 to Enemy Ax*65 = 0
Enemy Bow*30 to Ally Sword*46 = Asword*26
26+4+52 = 82 allies left
Example 20
Answer:
Ally Bow*63 to Enemy Ax*95 = 0
Ally Bow*55 to Enemy Ax*75 = Abow*5
Ally Bow*5 to Ally Ax*34 = Aax*39
Ally Ax*39 to Ally Sword*8 = Aax*47
Ally Ax*47 to Enemy Sword*75 = Esword*4
Enemy Sword*4 to Enemy Sword*75 = Esword*79
Enemy Sword*79 to Ally Sword*(63+63) = Asword*47
Example 21
Act 1 boss battle, skeleton(neutral type that won't counter others or being countered.) type added.
Try to find the best solution, a few more questions of this will show up next.

Answer:
Enemy Bow*28 to Enemy Ax*28 = Eax*56
Enemy Ax*56 to Enemy Bow*28 = Eax*84
!!Enemy Ax*84 to Enemy Skeleton*75 = Eax*159!!
Enemy Ax*159 to Ally Bow*15 = Eax*136
Enemy Ax*136 to Ally Bow*18 = Eax*109
Enemy Ax*109 to Ally Bow*68 = Eax*7
Enemy Axe*7 to Enemy Sword*32 = Esword*39
Enemy Sword*39 to Ally Ax*27 = Aax*1
1+8 = 9 allies left


Yep, this one is actually won! It's so encouraging!

However, you should always try to outfield the wall by using a straight 1*4 block at the near end of deploying phase, so you can make the enemy troops in the wall ineffective.
Example 22
Answer:
Enemy Bow*27 to Enemy Bow*15 = Eax*42
Enemy Bow*42 to Enemy Skeleton*30 = Ebow*72
Enemy Bow*72 to Ally Sword*40 = Ebow*12
Enemy Bow*12 to Enemy Ax*20 = Eax*32
Enemy Ax*32 to Ally Bow*24 = Abow*2
Ally Bow*2 to Ally Ax*20 = Aax*22
Ally Ax*22 to Enemy Sword*15 = Aax*12


You should always try to outfield the wall by using a straight 1*4 block at the near end of deploying phase, so you can make the enemy troops in the wall ineffective.
Example 23
Answer:
Enemy Bow*11 to Enemy Ax*22 = Eax*33
Enemy Ax*33 to Enemy Skeleton*30 = Eax*63
Enemy Ax*63 to Ally Bow*12 = Eax*45
Enemy Ax*45 to Ally Bow*28 = Eax*3
Enemy Ax*3 to Enemy Sword*11 = Esword*14
Enemy Sword*14 to Ally Ax*30 = Aax*20
20+37 = 57 allies left


You should always try to outfield the wall by using a straight 1*4 block at the near end of deploying phase, so you can make the enemy troops in the wall ineffective.
Example 24
Act 1 boss battle, one of the enemy archer building got +12 boost and it makes the situation worse to handle with.
Anyway, try to get the best result.

Answer:
!!Ally Bow*22 to Enemy Skeleton*30 = Eskeleton*8!!
Enemy Skeleton*8 to Enemy Sword*11 = Esword*19
Enemy Sword*19 to Enemy Bow*11 = Esword*30
Enemy Sword*30 to Enemy Bow*23 = Esword*53
Enemy Sword*53 to Ally Ax*20 = Esword*23
Enemy Sword*23 to Ally Ax*32 = Aax*16
16+5 = 21 allies left


You should always try to outfield the wall by using a straight 1*4 block at the near end of deploying phase, so you can make the enemy troops in the wall ineffective.
Example 25
Another complicated situation, ready for the challenge.
The key to get the best answer here is to take more advantage exchange against enemies, and reduce the number by exchanging equally.

Answer:
Enemy Bow*28 to Enemy Bow*28 = Ebow*56
Enemy Bow*56 to Enemy Ax*28 = Ebow*84
Enemy Bow*84 to Enemy Skeleton*75 = Ebow*159
Enemy Bow*159 to Ally Sword*35 = Ebow*106
Enemy Bow*106 to Ally Sword*40 = Ebow*46
Enemy Bow*46 to Ally Bow*29 = Ebow*17
Enemy Bow*17 to Enemy Sword*32 = Esword*49
Enemy Sword*49 to Ally Ax*50 = Aax*17
17+30 = 47 allies left

Only 29 archers are exchanged equally in this solution, if I don't get it wrong, other solutions will result in more 1:1 kill and make the final result worse.
Example 26 [Extra]
Answer:
Enemy Bow*13 to Ally Ax*15 = Ebow*3
Enemy Bow*3 to Enemy Ax*6 = Eax*9
Enemy Ax*9 to Ally Ax*18 = Aax*9
9+5+40 = 54 allies left
Example 27 [Extra]
Answer:
Enemy Sword*23 to Ally Ax*10 = Esword*8
Enemy Sword*8 to Enemy Ax*8 = Eax*16
Enemy Ax*16 to Enemy Bow*(3+12) = Eax*31
Enemy Ax*31 to Enemy Skeleton*30 = Eax*61
Enemy Ax*61 to Ally Bow*(30+8) = Eax*4
Enemy Ax*4 to Ally Ax*15 = Aax*11


You should always try to outfield the wall by using a straight 1*4 block at the near end of deploying phase, so you can make the enemy troops in the wall ineffective.
Example 28 [Extra]
Answer:
Ally Ax*5 to Enemy Bow*17 = Ebow*13
Enemy Bow*13 to Enemy Ax*16 = Eax*29
Enemy Ax*29 to Enemy Bow*25 = Eax*54
Enemy Ax*54 to Ally Bow*41 = Abow*5
5+5+20 = 30 allies left
Example 29 [Extra]
Answer:
Ally Ax*10 to Enemy Bow*27 = Ebow*20
Enemy Bow*20 to Enemy Sword*26 = Esword*46
Enemy Sword*46 to Ally Ax*(10+20) = Esword*1
Enemy Sword*1 to Enemy Bow*27 = Ebow*28
Enemy Bow*28 to Ally Bow*36 = Abow*8
Example 30 [Extra]
Answer:
Ally Ax*40 to Enemy Bow*18 = Aax*13
Ally Ax*13 to Ally Bow*15 = Abow*28
Ally Bow*28 to Enemy Bow*17 = Abow*11
Ally Bow*11 to Ally Sword*12 = Asword*23
Ally Sword*23 to Enemy Bow*27 = Asword*5
Example 31 [Extra]
Answer:
!Ally Bow*5 to Ally Sword*10 = Asword*15!
Ally Sword*15 to Enemy Bow*25 = Ebow*2
Enemy Bow*2 to Enemy Bow*13 = Ebow*15
Enemy Bow*15 to Ally Sword*16 = Asword*6
6+9 = 15 allies left
Example 32 [Extra]
Answer:
!Enemy Sword*18 to Ally Ax*16 = Aax*4!
!Ally Ax*4 to Enemy Skeleton*30 = Eskeleton*26!
Enemy skeleton*26 to Enemy Bow*29 = Ebow*55
Enemy Bow*55 to Ally Sword*35 = Ebow*2
Enemy Bow*2 to Enemy Ax*18 = Eax*20
Enemy Ax*20 to Ally Bow*7 = Eax*9
Enemy Ax*9 to Ally Bow*10 = Abow*4
Example 33 [Extra]
Answer:
Ally Bow*6 to Enemy Bow*9 = Ebow*3
Enemy Bow*3 to Enemy Ax*8 = Eax*11
Enemy Ax*11 to Ally Ax*20 = Aax*9
Example 34 [Extra]
Answer:
Ally Ax*12 to Ally Ax*10 = Aax*22
Ally Ax*22 to Enemy Ax*32 = Eax*10
Enemy Ax*10 to Enemy Sword*10 = Esword*20
Enemy Sword*20 to Ally Ax*18 = Aax*4
Ally Ax*4 to Ally Sword*8 = Asword*12
Ally Sword*12 to Ally Ax*10 = Asword*22
Ally Sword*22 to Enemy Bow*29 = Asword*2
2+12+10+6 = 30 allies left
Example 35 [Extra]
Answer:
!Ally Sword*25 to Enemy Bow*15 = Asword*15!
!Ally Sword*15 to Enemy Skeleton*30 = Eskeleton*15!
Enemy Skeleton*15 to Enemy Sword*15 = Esword*30
Enemy Sword*30 to Ally Ax*20 = 0
Enemy Bow*15 to Enemy Ax*15 = Eax*30
Enemy Ax*30 to Ally Bow*28 = Abow*8