I played Pitfall on the Atari 2600 as a kid. I mapped out the whole game and still have my map.
Here is the easiest way to 20000 gold. Due to the virtual D-pad being horrible, the hardest screen is the croc screen where you have to walk on their heads. Using this route you will only encounter 3 of these and you will be going left, so if you die, you will spawn on the other side, so as long as you make it across one of them, you can do this. There are 255 screens in this game. The start screen is screen 1 and the screen to the left of that is screen 255. Since we will be going left, the screen numbers will count down:
1) On start screen, go down ladder and go left jumping over one scorpion and going up the ladder on the next screen. This is screen 250.
2) Go up ladder and right one screen to screen 251 and go down that ladder and to the left and jump over one scorpion. That will be the only time you ever go right.
3) Go up the next ladder and you are on screen 245. Now go left 6 screens to screen 239 and a money bag worth 2000
4) Keep going left 10 screens to screen 229 and you will get ring worth 5000
5) Go left 4 screens to screen 225 and go down ladder. Go left and jump over 4 scorpions. (you travel further when underground, so these are shortcuts).
6) Go up next ladder and you will be on screen 210. Now go left 3 screens to screen 207 and a money bag worth 2000
7) Go left 9 screens to screen 198 and a ring worth 5000
8) Go left 2 more screens to screen 196 and another ring worth 5000
9) You should have 20,000 now. If not go left 2 more screens to screen 194 for gold
and then 2 more left to screen 192 for another gold