You’re right and wrong. Churning will reduce the traces linking back to you, but you’re still exposed at 1 churn per output, when including 10 outputs. You would even be exposed when spending 2 outputs from the same source

As you know, each ring currently has 16 transactions, including you. This means, on average (more or less because of other factors, but still), each output will be featured in 16 transactions. We can therefore assume that 1 in 16 of those transactions is real (in reality the distribution is not that perfect, but as an average, it is important to know the consequences).

You now have a 1 in 16 chance of being traced. Statistically, the transaction you made has 6,25% chance of being made by you. That’s pretty high for a single poisoned output, right?

Now imagine you spend 2 poisoned outputs… the distribution algorithm is not evenly distributed: older outputs are less likely to be picked than newer. This means you get a situation where the older your 2nd poisoned output is, the more you’ll stand out. The math is not that easy the make, but just knowing that each output will only be included 16 times on average, and that there are a lot of transactions so a lot of outputs, it becomes really unlikely that 2 of the poisoned outputs that are linked to the same individual end up in the same transaction if it was not made by the individual of question itself.

With 3+ poisoned outputs you basically confirm that it was the same person. Might not hold up in court, but they’ll definitely know

10+ poisoned outputs? Definitely you.

Churning each output only multiplies the number of possibilities by 32 (16 for one output, 32 in reality because 2 outputs are generated). This will certainly throw off the basic chain analysis methods, but if you’re a person of interest, all the linked outputs will be analyzed. All outputs that are created by including poisoned inputs might be considered, effectively multiplying the number of possibilities by 32 as said earlier. If I tried to spy on someone with this, I would probably set a higher suspicion level on the first transaction level, then less on the second… assuming chain analysis software does that as well, churning would actually divide the chances of being caught by more than 32 but lets assume they don’t do that as it’ll be easier. You now have 1 chance on 16^2=256 so 0,39% chance of having done a transaction with a churned output in between for a single poisoned output. Still pretty high if you want my opinion. If you do that multiple times, you’ll stand out for sure. Including multiple outputs will also expose you a lot. Spending 10 churned poisoned outputs will definitely expose you.

I should just make a blockchain analysis program and test transactions with it 😂

My recommendation: if you’re going to spend multiple poisoned outputs at once: churn them together into 1 output (it’s called sweeping afaik), then churn this individual output. The initial churn merge will make the transaction stand out, but since you only have one output to churn, you reduce the traces.

Please correct me if I’m wrong, I have put a lot of time thinking about all of this but I might have forgot to include some specific things. I already noticed that all transactions include 2 outputs (at least), so the possibilities are multiplied by 32, not 16 as was my initial assumption