Regardless, it's still 3:1, on your 1st attempt, or your 1,001st.
Yes, it is. And none of the individual fails in the 10+ fail series are in any way suspect for that. However if we look at the series as a whole, it becomes different.
Let's assume we threw a coin each day who has to do the dishes. On any given day in a year it is either me or you, and there will be series where one has to go for quite a while in a row without anybody raising an eyebrow.
But if I were to tell you every day of the year that by pure chance the coin said "whichone will do the dishes", you might suspect that I am not producing purely random results and that either the coin itself or my throwing of it might not be fair.
This whole type of experiment (either something happens or it doesn't, we do it repeatedly and check the number of "successes", each individual outcome is independent of anything that happened prior, and so forth) is called a "Bernoulli process" and pretty well researched. And indeed the probability of 10 "fails" in a row given the conditions in this game is low enough to warrant a check. Which Faerin did, so the issue is resolved.
We can go back to our scheduled "can we fuck mum yet?" now.