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Cracking Crucible Tree Combining

– Poe Noob (Youtube)

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Basics

  • Only Same Weapon/Shield type can combine
    • One handed sword + One handed sword (YES)
    • One handed sword + One handed mace (NO)
    • Spine bow + Thicket bow (YES)
    • Evasion Shield + Armour Shield (YES)
    • Staff + Warstaff (YES)

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Basics

  • Tree A + Tree B => Tree C
    • Item of Tree A (upper of forge) destroyed
    • Item of Tree B retained
  • Merged Tree C will be on the same item of Tree B

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Basics

  • Nodes can disappear, stay or altered
    • “Altered” means mutated, tier upgraded, or tier downgraded
  • But the node positions won’t change
    • “Attack Speed” in Tree A at 2-1 pos can only be possible to appear at 2-1 in Tree C
      • Never possible to appear at 2-2

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Basics

  • Allocated nodes in Tree A or B has higher chance to be selected
    • Its odds will be covered later in slides

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Example

Tree A

Tree B

Tree C

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In-Depth Combine Mechanism

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Node Position Annotation

1-1

2-1

2-2

3-1

3-2

3-3

4-1

4-2

4-3

4-4

5-1

5-2

5-3

5-4

5-5

Layer 1

Layer 2

Layer 3

Layer 4

Layer 5

Full Tree

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Important Concept - CPL

1-1

2-1

2-2

3-1

3-2

3-3

  • Connectables in Previous Layer (CPL) for a certain node
    • Definition: the adjacent nodes in the previous layer that can be directly connected to this node
    • Example:
      • For 3-2, its CPL is 2-1 and 2-2
      • For 3-3, its CPL is 2-2

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Overview

Combine Algorithm has 3 steps below:

  1. Node Selection - In Tree C, for each position, it rolls dice to decide if it select node from Tree A or Tree B or be empty;
  2. Node Modification - mutate, upgrade, or downgrade selected nodes
  3. Add Bridges - to connect the selected nodes in Tree C

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Node Selection (Step 1)

  • In Tree C, from layer 1 to layer 5
    • For each pos in the current layer (top to bottom)
      • Check if any connectables in previous layer (CPL) exists in Tree C:
        • If no, leave this pos empty and skip
        • If yes, roll the dice (odds covered later) to:
          • select the node from Tree A
          • or, select the node from Tree B
          • or, leave it empty

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Node Selection - Odds

  • For a certain pos in Tree C, assuming has at least one CPL exist in Tree C:
    • If both Tree A & B have node
      • Tree C has 93% (150/161) chance to have node here
    • If only one of Tree A or B has node
      • Tree C has 70% (92/132) chance to have node
    • If none of Tree A or B has node
      • Tree C has 0% chance to have node

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Node Selection - Odds from Tree A or B

  • If Tree C decides to select a node, below is the chance whether from Tree A or Tree B
    • If only Tree A (or Tree B) has node
      • 100% chance to select from this tree (trivial)
    • If both Tree A & B has node, both allocated or unallocated
      • 50% chance to select from A or B (trivial)
    • If both have node, but only Tree A allocated it
      • 70% (18/26) chance to select the allocated node
        • Small data size for this number

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Node Modification (Step 2)

  • When node is selected in Tree C, it has
    • 6.6% (16/243) chance to be mutated
    • 2.1% (5/243) chance to be upgraded
    • 1.6% (4/243) chance to be downgraded
    • In total, 10.3% chance to be altered

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Add Bridges (Step 3)

  • Lastly, add bridges to all selected nodes in Tree C.
  • For each selected node, check how many CPLs exist:
    • If only one, 100% chance to connect to it
    • If two connectables both exist:
      • 1/3 chance to only connect to connectable_1
      • 1/3 chance to only connect to connectable_2
      • 1/3 chance to connect to both

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Example Step by Step

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Step 1, Node Selection

Tree A

Tree B

Tree C

: allocated

CPL exist?: N/A

Odds:

  • 100% has node
  • 30% select from A
  • 70% select from B

Pos: 1-1

Result: selected from B

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Step 1, Node Selection

Tree A

Tree B

Tree C

: allocated

CPL exist?: Yes (1-1)

Odds:

  • 93% has node
  • 30% select from A
  • 70% select from B

Pos: 2-1

Result: selected from B

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Step 1, Node Selection

Tree A

Tree B

Tree C

: allocated

CPL exist?: Yes (1-1)

Odds:

  • 93% has node
  • 50% select from A
  • 50% select from B

Pos: 2-2

Result: selected from A

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Step 1, Node Selection

Tree A

Tree B

Tree C

: allocated

CPL exist?: Yes (2-1)

Odds:

  • 70% has node
  • 100% select from A

Pos: 3-1

Result: empty

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Step 1, Node Selection

Tree A

Tree B

Tree C

: allocated

CPL exist?: Yes (2-1, 2-2)

Odds:

  • 70% has node
  • 100% select from B

Pos: 3-2

Result: selected from B

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Step 1, Node Selection

Tree A

Tree B

Tree C

: allocated

CPL exist?: Yes (2-2)

Odds:

  • 93% has node
  • 50% select from A
  • 50% select from B

Pos: 3-3

Result: selected from A

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Step 1, Node Selection

Tree A

Tree B

Tree C

: allocated

CPL exist?: No

Odds:

  • Skip

Pos: 4-1

Result: empty, skip

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Step 1, Node Selection

Tree A

Tree B

Tree C

: allocated

CPL exist?: Yes (3-2)

Odds:

  • 70% has node
  • 100% select from B

Pos: 4-2

Result: selected from B

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Step 1, Node Selection

Tree A

Tree B

Tree C

: allocated

CPL exist?: Yes (3-2, 3-3)

Odds:

  • 93% has node
  • 50% select from A
  • 50% select from B

Pos: 4-3

Result: empty (bad luck)

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Step 1, Node Selection

Tree A

Tree B

Tree C

: allocated

CPL exist?: Yes (3-3)

Odds:

  • 0% has node

Pos: 4-4

Result: empty

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Step 1, Node Selection

Tree A

Tree B

Tree C

: allocated

CPL exist?: Yes (4-2)

Odds:

  • 0% has node

Pos: 5-2, 5-3

Result: empty

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Step 1, Node Selection

Tree A

Tree B

Tree C

: allocated

CPL exist?: No

Odds:

  • Skip

Pos: 5-1, 5-4, 5-5

Result: empty, skip

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Step 2, Node Modification

Tree A

Tree B

Tree C

: allocated

Pos: 3-3

Result: mutated

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Step 3, Add Bridges

Tree A

Tree B

Tree C

: allocated

CPLs: 1-1

Odds:

  • 100% conn 1-1

Pos: 2-1

Result: connect 1-1

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Step 3, Add Bridges

Tree A

Tree B

Tree C

: allocated

CPLs: 1-1

Odds:

  • 100% conn 1-1

Pos: 2-2

Result: connect 1-1

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Step 3, Add Bridges

Tree A

Tree B

Tree C

: allocated

CPLs: 2-1, 2-2

Odds:

  • 33.3% only conn 2-1
  • 33.3% only conn 2-2
  • 33.3% conn both

Pos: 3-2

Result: connect 2-1

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Step 3, Add Bridges

Tree A

Tree B

Tree C

: allocated

CPLs: 2-2

Odds:

  • 100% conn 2-2

Pos: 3-3

Result: connect 2-2

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Step 3, Add Bridges

Tree A

Tree B

Tree C

: allocated

CPLs: 3-2

Odds:

  • 100% conn 3-2

Pos: 4-2

Result: connect 3-2

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Disclaimer

  • Hypothesis of the combine mechanism, based on data
  • Data is from my 30-40 combines, not 100% reliable
  • Will provide raw data and statistics for your personal analysis
  • Not take responsibility for any gamble loss