Notch's Lottery Question

Notch ( the creator of Minecraft ) posted  an interesting lottery problem.

Lottery Question

Lottery Answer

I quickly wrote this java to help people understand the results.

package com.jsa;

import java.util.Iterator;
import java.util.Random;
import java.util.Vector;

public class test {

    final static int LOTTOSIZE = 1000000;
    final static int WINSTOP = 3;
   
    public static void main( String args[] ){
       
        Vector<Vector> wins = new Vector<Vector<Integer>>(WINSTOP);
        Vector<Integer> oneWin = new Vector<Integer>(LOTTOSIZE);
        wins.add(oneWin);
       
        Random random = new Random( System.currentTimeMillis());
       
        boolean foundXWins = false;
        int draws = 0;
        while ( ! foundXWins ){
           
            Integer winner = random.nextInt(LOTTOSIZE);
            draws++;
           
            boolean notFound = true;
            for (Iterator iterator = wins.iterator(); iterator.hasNext() && notFound ;) {
                Vector<Integer> vector = (Vector<Integer>) iterator.next();
               
                if ( vector.contains(winner) ){
                    notFound = false;
                    vector.remove(winner);
                    if ( iterator.hasNext() ){
                        vector = (Vector<Integer>) iterator.next();
                    } else {
                        vector = new Vector<Integer>(LOTTOSIZE);
                        wins.add(vector);
                        System.out.println( "Someone has just won " + wins.size() + " times, after only " + draws +" draws. " );
                    }
                    vector.add(winner);
                }
            }
            if ( notFound ){
                oneWin.add(winner);
            }
           
           
            if ( wins.size() == WINSTOP ){
                foundXWins = true;
                int nonWinners = LOTTOSIZE;
                for (int i = 0; i &tl; wins.size() ; i++ ){
                    nonWinners -= wins.get(i).size();
                }
                System.out.println( "Win Limit Reached: " + wins.size() + " wins.");
                System.out.println( "There are " + nonWinners + " who have not yet won once." );

            }
           
            if( draws %10000 == 0 || foundXWins ){
                StringBuilder sb = new StringBuilder();
                sb.append( draws );
                sb.append( "," );
                for (int i = 0; i &tl; wins.size() ; i++ ){
                    sb.append( wins.get(i).size() );
                    sb.append( "," );
                }
                System.out.println( sb );
            }
           
        }
       
        }
   
}

Output was:

Someone has just won 2 times, after only 177 draws. 
10000,9902,49,
Someone has just won 3 times, after only 18936 draws. 
Win Limit Reached: 3 wins.
There are 981230 who have not yet won once.
18936,18605,164,1,

So in this instance it only took 18,936 draws before one of the lottery members won 3 times, and the vast majority of lottery players 981,230 had not won at all!

After running the program several times it seems like a 3 time winner will show up somewhere between 10,000 and 25,000 draws. This is quite a small number compared to the 1 mil players, Showing that It is much more likely that somebody else will win 3 times before you win once.