Complex numbers always carry a certain air of oddity with them. As a teacher of the elementary calculus, I routinely need to tell students that e^(ix) = cos x + i sin x. Sadly, they're only rarely happy about it. They always put on faces full of disappointment 
.i^i is a tricky thing. Using the formula above, it can be checked that i = exp(i pi/2), so i^i should be equal to [e^(i pi/2)]^i = e^(i × pi/2 × i) = e^(-pi/2) = 0.208... = 1/4.81... So you get that 1/4.81 pounds = 1 dollar, which agrees pretty nicely with your story.
But here's the trickery: cos and sin are intimately connected with the circle. So if you increase or decrease the angle you put into them by a full circle (2 pi), you get to the exactly same point on the circle, and so cos and sin (and e^(ix)) have exactly the same values. But that means that i is also equal to e^(-3 pi i/2), and so, by the same logic, i^i is also equal to e^(3 pi/2) = 111.32... In fact, you get an infinite amount of possible values for i^i: e^(-pi/2), and any other number that you can obtain by multiplying or dividing this number by an integer power of e^(2 pi) = 535.49...
And probability is a box full of weird things. One little example with a story: Suppose there are two hospitals, A and B, that both treat a certain rare disease. Both of them are trying to convince people that they're better at it than the other hospital. So hospital A says that they have cured a larger fraction of patients than hospital B. Hospital B says that they have cured a larger fraction of men than hospital A, and also a larger fraction of women than hospital A. Is it possible that they both tell the truth?...
