Little Help ? (Games, obfuscation...)

I considered writing a game like 'Scorched Earth' or even something like 'Gorillas' (GORILLAS.BAS, remember QBASIC?) to run in a web browser as a java applet that used the web server for multiplayer games. They're both turn-based games so there's less of an issue with lag and the performance penalties of platform-independant java.

My problem is how to make it difficult to cheat. I'm trusting the client with the game data but it'll be up to the server to determine when someone's actually won.
It'd be easy for someone to download the applet, decompile it and add code to dump out all sprite co-ordinates or go one step further and calculate and fire a winning shot.

Suggestions I've had so far:
- Have a variable that changed during the shot - wind for example. But I think this would just annoy human players

- Have the client receive the game area as a JPEG. It'd still be easy for someone to add code to determine the co-ordinates of the other player but it would involve a lot more work.

I'd like to see how it could be done without resorting to code obfuscators.

Thanks.