What happens when I copy Precursor Golem with Rite of Replication?

Question

I came across this issue with my friend a while ago and came up with many possible answers:

How many golems will you get if you copy Precursor Golem with a kicked Rite of Replication?

Answer 1

The short answer, assuming that your Precursor Golem still has (exactly) his two buddies with him: 28. The sequence goes something like this:

1. Rite of Replication (kicked) targets Precursor Golem. Note that the text of Rite now effectively reads 'Put five tokens that are copies of target creature onto the battlefield', and the copies of Rite of Replication will all copy that version of the text. (From rule 706.10: "A copy of a spell or ability copies both the characteristics of the spell or ability and all decisions made for it, including modes, targets, the value of X, and additional or alternative costs.")
2. Precursor Golem's ability copies Rite and targets the 'lesser' golems (the ones without the 'make extra golems' ability); note that these copies of Rite go on the stack on top of the original Rite (this isn't relevant here, but can be if you kick another Rite!)
3. The copies of Rite resolve, each one making an additional five 'dumb' golems; this puts 10 new golems into play. You now have 1 Precursor Golem and 12 'dumb' golems.
4. The original Rite resolves, making five additional Precursor Golems. Each of the five 'make two dumb golems' abilities of these new Precursor Golems goes on the stack. Right now you have 6 Precursor Golems and 12 dumb golems.
5. The new Precursors' token-making abilities resolve, giving you 10 more dumb golems. You end up with 6 Precursor Golems and 22 dumb golems.

Beyond this - well, beyond this things get interesting. The next step in the sequence - a second kicked Rite - brings you up to more than four million Golems; for the details, see https://docs.google.com/document/d/1L_FIQrjBdh5J66KKAT2JJ2gTx1KfbXJUfXrdydjzhrY/edit - which also goes into what happens if you kick yet a third Rite...

Answer 2

For a kicked Rite of Replication, you will get

• 15 new golems for each Precursor Golem on the battlefield (Five new Precursor Golems which will create two Golem tokens each)
• 5 new golems for each other golem on the battlefield

So if you have a Precorsor golem and the two tokens it created, you will get 25 new golems for a total of 28 golems.

Note: Your Rite of Replication will be copied for any golems other players control.

Answer 3

So I stumbled upon this question recently and I've seen so many different answers that I decided to tackle it myself so to calculate how many you should have after casting Rite of Replification, you can use this formula:

Total Precursors Golems = p*(6^p)
Total Tokens Golems = ((t-1)*(6^p))+6+(((p*(6^p))-p)*2)

Where 'p' is equal to the number of starting precursor golems
Where 't' is equal to the number of starting token golems

NOTE, this formula assumes that you've targeted a Golem Token

For those who would like to understand, read on!

Before we get ahead of ourselves, we need to understand a few things.
• Firstly, the initial target of the Rite of Replication will only ever have ONE copy of the Rite targeting it since the spell is not copied onto the initially targeted creature. This means that to ensure that the maximum number of Rites are affecting the Precursors (to ensure we get the best exponential effect in future Rites.), you must target one of the golem tokens.
• Secondly, the copies of Rite of Replication are not "cast". And will not trigger the Precursors ability.
• Lastly, When multiple Precursor Golems are in play, their abilities resolve one at a time and, as they do, the Rites they create will resolve before the next Precursor trigger.

For this example, we'll assume you played a Precursor Golem, so your started with:
1 Precursor Golem and 2 Golem Tokens:

• Rite One: 6 Precursors and 22 Tokens
    When you cast Rite of Replification for the first time, the target is irrelevant since each Golem will only get one copy of the spell regardless of the target. You will copy the Precursor 5 times (to get a total of 6 copies, and gain 10 tokens [2 per new Precursor ETB]). Then you will get an additional 10 tokens for the two Rites targeting your existing 2 tokens.

• Rite Two: 279936 Precursors and 3779142186 Tokens. No, seriously.
    These numbers are so large because, as stated above, each Precursor trigger will resolve one a time, putting the Rite of Replification copies on top of the stack causing them to resolve before the next Precursor trigger. I call these "waves". How many "waves" will we have? That is determined by the number of Precursor Golems in play when the spell was initially cast. In this example, we have 6 waves to go through.
    Wave One: All but one Golem (the initial target) is multiplied by 6 (5 new copies, and add on the original), then for each Precursor created this way we get two more Tokens for a total of 36 Precursors (6x6), and 187 Tokens (((22-1))x6+(30x2)+1). Then we just repeat this process until the final wave, wave 6.
    Wave 2: 216 Precursors and 1477 Tokens
    Wave 3: 1296 Precursors and 11017 Tokens
    Wave 4: 7776 Precursors and 79057 Tokens
    Wave 5: 46656 Precursors and 552097 Tokens
    Wave 6: One thing is different about wave 6. After resolving wave 6, our original spell finally resolves meaning that we DO NOT EXCLUDE the one Golem Token we initially targeted, leaving us at our final total. 279936 Precursors and 3779142 Tokens

I've made a spreadsheet you can view with the formulas, I've done as much as I can before Google Sheets just gives up on the math, have fun casting Rite 8 times without issue!

https://docs.google.com/spreadsheets/d/1O07ykGcr27JkW4hetw-yAf0AS2kt_PJ4qGcoH3ijNT8/edit?usp=sharing