Depends. Because 50% means that your anonymity set is reduced by 50% on each round as I explained in my other post above.
Example. If you are mixed with 10 others on each round, then only 5 will be anonymous (and one of the five might be you), so that means have 50% + 20% (1 in 5) chance to be non-anonymous. So 70% per round. You will need more rounds or you need larger mix sizes.
Also if it is same 10 you are mixed with every round (or any overlap), then anonymity is reduced. If always same 10 on every round, then you attain no better than 20% non-anonymous no matter how many rounds you use.
Also you have to factor in the non-anonymous rate of Tor and those inputs who didn't use Tor at all are not anonymous. This reduces your anonymity set, even if you use Tor.
I believe you've reversed the math, if each round offers a 50% chance of anonymity then five rounds should offer a 0.5^5 of being non-anonymous at the end, a 96.8% chance of remaining anonymous. You must be identified each round for you to be followed through, right?
Let me try again. I am getting very sleepy.
LimLims wrote if 20% non-anonymity for 3 rounds, then adversary needs cube root of .20 or 58.5% adversarial node coverage.
I normally do it like this. It would be 80% anonymity over 3 rounds requires 41.5% non-adversarial node coverage, i.e. allows 58.5% adversarial coverage, 0.585 ^ 3 = 0.20.
You can calculate it either way. I prefer your way, but I was following LimLims.
The above is for Sybil attack on nodes.
Now I discuss about Sybil attack on the inputs.
My point remains that the size of anonymity set is also a factor (which can be reduced by Sybil and by the adversarial node coverage), not just the adversarial node coverage alone.
I am talking about Sybil attack on the inputs not on the nodes. If there are only 10 inputs to a CoinJoin, then you have a 1 in 10 chance to be identified correct just by random selection. If 5 of the inputs are Sybil, then reduce the non-Sybil to 5, so now 1 in 5 or 20% chance to be identified by random choice. This might sound silly until you realize that over time people in your mix may be identified and thus the anonymity set reduces over time. The anonymity set size is not irrelevant. Otherwise we could simply mix with one other person every time.
And because the analysis of the adversary might have data such as "I know these 3 outputs are correlated to these 3 inputs". So as
overlapping anonymity sets decrease in size, then they can pinpoint identity.