(1) First, A won from B as much as A had originally.
(2) Second, B won from C as much as B then had left.
(3) Finally, C won from A as much as C then had left.

The three players ended up with equal amounts of money.

Who began with 50 cents?

                 A          B            C
After 1st bet:   2*a        b-a          c
After 2nd bet:   2*a        2*(b-a)      c+a-b
After 3rd bet:   a-c+b      2*(b-a)      2*(c+a-b)

b     a     c
5     3     4
10    6     8
15    9     12
20    12    16
...
50    30    40