Random number problems

I'm creating a horse racing game and I'm having a problem with my random number generator inside my threads.
I'm creating four threads and then inside each of them I'm using:
sleep(rand.nextInt(5) * 300);
Which I thought would make each horse thread sleep for a different amount. Instead, my first horse thread sleeps for a random amount, then my next THREE threads sleep for the exact same amount!
Is my random (class random) object not being seeded properly or something?
What could be causing this?

Ok, here is a snipped version of my code:
public class HorseThread extends Thread {
private Random rand;
public void run() {
rand = new Random();
draw();
private void draw() {
// Grab the graphics object out of our JPanel
Graphics g = panel.getGraphics();
try {
for (int x=0; x < 500; x+=25) {
// Erase our racing lane
g.setColor(Color.WHITE);
g.fillRect(startX, startY, 500, 75);
// Draw our horse
g.drawImage(horsePicture, curX + x, curY, 75, 75, null);
// Sleep a random amount
int sleepamount = rand.nextInt(5) * 500;
System.out.println("Horse [" + horseNum + "] sleeping for [" + Integer.toString(sleepamount) + "] milliseconds.");
sleep(sleepamount);
} // end for
} catch (InterruptedException e) {
e.printStackTrace();
} // end try
} // end draw()
} // end HorseThread()

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    ghstark wrote:
    cowwoc wrote:
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    Wasn't this covered in your [earlier thread|http://forums.sun.com/thread.jspa?threadID=5320382&messageID=10369834] ?
    You're right, but what bothered me about that thread is that the replies concluded that since there is no practical proof that SecureRandom has a problem that should be good enough. I'm looking for a code sniplet guaranteed by the specification (hence portable across implementations) to generate random numbers. No one has yet to provide such an answer.
    What's to guarantee that if I move to a different platform, vendor or even a different version of Sun's JVM that my code won't magically break? Verifying randomness isn't a trivial matter.

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