Going back to rolling the dice thingy, 'cause I know nothing of IVF.
Roll a dice once, chances of a six are 17%
Roll a dice four times, chances of a six are 51%
Good luck to your friend with her treatment. Tell her that having a baby is way easier than having Dopers explain probability theory 
I’m a bonehead.
I’ve just gotten out of bed, and haven’t had my first cuppa joe yet.
So take this for what it’s worth.
One chance in four is 25%. Two chances in four is 50%. Three chances in four is 75%. Four chances in four is 100%.
A 50% chance is 100% better than a 25% chance. 25 + (1.00 * 25) = 50
A 25% chance is 50% worse than a 50% chance. 50 - (0.50 * 50) = 25
A 75% chance is 200% better than a 25% chance. 25 + (2.00 * 25) = 75
A 75% chance is 50% better than a 50% chance. 50 + (0.50 * 50) = 75
.
Sorry for throwing too much in there at you.
I’ll pull out the important details. (I’m using ‘try’ to mean ‘chance’ in the sense of attempt, to distinguish it from ‘chance’ in the sense of probability.)
It seems to me that each follicle is a distinct chance from the others, hence the tries are independent.
The precise value depends on what the probability of a single try is. Hopefully this is clear enough. If the procedure is almost guaranteed to work, then extra tries won’t do much for you. If it’s an extreme long shot, then they’ll be more useful. Obviously, extra tries will always increase the odds of success given independent tries.
The “bad” news: 4 tries is only 2 times better than 2 tries if the chance of success is nearly zero. (It was mentioned briefly upthread that the chance of a single try needed to be very small, e.g. like lottery tickets).
Probably the most important thing that maybe hasn’t been said clearly enough yet:
In order to answer the question properly, you must have some idea of what the probability of a single try is.
As for your specific cases:
I’ll describe the value you would like to express in terms of a graph. Call it the ‘improvement ratio’. This is as a function of the probability of a single try.
2 vs. 1 : This is a straight line from (0,2) to (1,1). The ‘improvement ratio’ drops directly proportionally to how large the chance of a single try is, but is somewhere between 2 and 1.
4 vs. 2 : A parabola (in the sense of ‘application’, not ‘parable’) which opens facing upward, and curves down from (0,2) to a minimum at (1,1). This improvement ratio drops a bit faster than a straight line, but if the chance is small, it’s close to a line.
4 vs. 3 : A straight line from (0, 4/3) to (1,1). Similar to 2 vs. 1, but between 4/3 and 1. There’s less range of variation because the values are closer together.
3 vs. 1 : Another parabola, but it drops more sharply from (0,3) down to (1,1).