We can define V(k,C) as the value obtained applying optimal strategy of being at round k (k=2,3,4) with C being the last card drawn. Next, we reason backward and start with k = 4. In order to find the optimal strategy we compare the expected value of the prize we obtain by drawing with the one we get if we don't draw and choose of course the maximum value.
As already stated, at round 4 we should draw with everything but a 2 (notice that we might have at most a Jack at round 4). So we have for instance that V(4,2) = 400 (we don't draw), while V(J,4) = 15000 (we draw and we have 3/4 of winning the big prize).
Next, we analyze step 3, and again we compare how much likely is to pass from (3,C) to (4,D) (D<C), where we know how much is the expected winning. Again, we compare the draw vs don't draw options. Eventually, we calculate V(3,C) for every C and, in turn, we also can calculate V(2,C). This is what I get (alert: I might have made some mistake along the path).
Code:
card value2 value3 value4
A 0.0000 0.0000 0.000
K 1853.9320 0.0000 0.000
Q 1361.5238 6155.1020 0.000
J 967.0748 4930.6122 15000.000
T 659.7007 3842.1769 13333.333
9 428.5170 2889.7959 11666.667
8 262.6395 2073.4694 10000.000
7 151.1837 1393.1973 8333.333
6 100.0000 848.9796 6666.667
5 100.0000 440.8163 5000.000
4 100.0000 200.0000 3333.333
3 100.0000 200.0000 1666.667
2 100.0000 200.0000 400.000
When you see a value in the table above greater than the prize of that round, it means that you should draw. At round 4, you draw everything but a 2. At round 3, you draw 5 or higher and at round 2 you draw 7 or higher.
