129007254816 rolls of the 470184984576 rolls. Or 27.437553101%
static final int SIDES = 6; static final int MINROLL = 1; public long combinatoricaldice(int d0, int d1) { int[] dist0 = convolvedistribution(d0); int[] dist1 = convolvedistribution(d1); long wins = combdice(dist0,dist1); System.out.println(d0 + " dice wins " + wins + " vs. " + d1 + " dice."); return wins; } public int[] convolvedistribution(int dice) { int[] roll = new int[((SIDES -1 + MINROLL) * dice) + 1]; for (int i = 0; i < SIDES; i++) { roll[i + MINROLL] = 1; } return convolvedistribution(roll,dice-1, new int[roll.length]); } public int[] convolvedistribution(int[] roll, int dice, int[] temp) { if (dice == 0) return roll; Arrays.fill(temp, 0); for (int i = 0, s = roll.length; i < s; i++) { for (int q = i + MINROLL, m = i + SIDES + MINROLL; q < m && q < s; q++) { temp[q] += roll[i]; } } System.arraycopy(temp, 0, roll, 0, temp.length); return convolvedistribution(roll, dice-1, temp); } public long combdice(int[] sumdistribution0, int[] sumdistribution1) { long winning = 0; for (int m = 0; m < sumdistribution0.length; m++) { long s0 = (long) sumdistribution0[m]; long winsagainst = Arrays.stream(sumdistribution1).limit(m).sum(); winning += (s0 * winsagainst); } return winning; } public boolean incrementDice(int[] dice) { for (int m = 0; m < dice.length; m++) { if ((dice[m] - MINROLL) + 1 < SIDES) { dice[m]++; for (m = m - 1; m >= 0; m--) { dice[m] = MINROLL; } return true; } } return false; } public int[] sumdistribution(int d0) { int[] dice = new int[d0]; Arrays.fill(dice, MINROLL); int[] dist = new int[((SIDES - 1 + MINROLL)*d0) + 1]; do { int sum0 = Arrays.stream(dice).sum(); dist[sum0]++; } while (incrementDice(dice)); return dist; }