However it is true that doing something with a 10% success rate 10 times will net you an average of 1 success.
For the easier to work out case of doing something with a 50% success rate 2 times:
25% chance of 0 successes
50% chance of 1 success
25% chance of 2 successes
Gives an average of 1 success.
Of course this only matters for the sort of thing where 2 successes is better than 1 success:
10% chance of finding a monogamous partner 10 times yields 0.63 monogamous partners in expectation.
10% chance of finding a polyamorous partner 10 times yields 1.00 polyamorous partners in expectation.
However it is true that doing something with a 10% success rate 10 times will net you an average of 1 success.
For the easier to work out case of doing something with a 50% success rate 2 times:
25% chance of 0 successes
50% chance of 1 success
25% chance of 2 successes
Gives an average of 1 success.
Of course this only matters for the sort of thing where 2 successes is better than 1 success:
10% chance of finding a monogamous partner 10 times yields 0.63 monogamous partners in expectation.
10% chance of finding a polyamorous partner 10 times yields 1.00 polyamorous partners in expectation.