Wasabi counts it as linear, Samourai counts it as exponential. Wasabi tries to consider the worst case and Samourai considers the theoretical case. The theoretical case is pretty straightforward.

  1. Recognize anonymity set model doesn’t make sense for remixing.
  2. Recognize probability model makes sense for remixing.
  3. Recognize the anonymity set model can be extended based on the probability model.

The probability model goes like this:

  1. If I mix 1BTC with 5 participants, then the probability of my mixed UTXO being originated from my unmixed input is 1/5.
  2. If I remix it again, then the probability of my remixed UTXO being originated from my mixed input is 1/5 again.
  3. However in that case the probability of my remixed UTXO being originated from my unmixed input is (1/5)*(1/5) -> 1/25.
  4. And now we can extend the anonymity set model with the insight we got from the probability model and say that 25 is the anonymity set.

But again, remix 3 times with Wasabi and your anonset would be 100*100*100 = larger number than the total number of Wasabi users. This is where I can see that the probability model cannot be applied to the anonset model, or maybe it can, I’m not sure, I have not yet tried to think this further, nor I am sure it makes sense to do so. Thus it’s safer to go with the linear model in terms of what to show to the user. Although it’s hard to justify mathematically, but it’s the practical thing to do with the available information I currently possess.

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