mersenne twister

http://www.cs.gmu.edu/~sean/research/mersenne/MersenneTwisterFast.java http://www.cs.gmu.edu/~sean/research/mersenne/MersenneTwister.java

The strength of the RNG doesn't have a massive bearing on the effectiveness of random movement. Also I am pretty sure most of us are already well aware of the Mersenne Twister.

why not

The main issue seems to be that you can't move to a random independent GF on all waves because waves are fired faster than their travel time.

Because:

1. So few random numbers are generated that even a pretty mediocre pseudorandom number generator would be pretty much impossible to predict. You need to capture a decent chunk of data to crack even a bad PRNG's state.
2. Battles have other confounding factors (i.e. walls) which may hide what random number a bot chose.

As an aside, that mersenne twister implementation is not a suitable replacement for Math.random() even if PRNG quality mattered, because it's not really more secure (and it's apparently slower too according to the comments in it). If that was an issue, you'd want a cryptographically secure pseudorandom number generator, not a mersenne twister.

Also, an out-of-the-blue link to a mersenne twister page isn't really a useful post.