Round 1:
Player 1's roll: [5, 4, 6, 4, 6]
Player 1's roll after re-roll: [4, 4, 2, 5, 1]
Player 1's roll after re-roll: [4, 4, 2, 4, 3]
Player 1 scored 17 for Three of a Kind.
Player 2's roll: [4, 4, 6, 5, 5]
Player 2's roll after re-roll: [4, 4, 5, 6, 3]
Player 2 rolled a Small Straight!
Player 2 scored 30 for Small Straight.
Player 3's roll: [1, 6, 5, 3, 2]
Player 3's roll after re-roll: [1, 6, 1, 6, 3]
Player 3's roll after re-roll: [1, 1, 3, 1, 1]
Player 3 scored 7 for Three of a Kind.
Player 4's roll: [1, 6, 1, 3, 4]
Player 4's roll after re-roll: [1, 1, 1, 5, 1]
Player 4's roll after re-roll: [1, 1, 1, 1, 3]
Player 4 scored 7 for Three of a Kind.

Round 2:
Player 1's roll: [3, 6, 3, 6, 6]
Player 1 rolled a Full House!
Player 1 scored 25 for Full House.
Player 2's roll: [2, 4, 6, 6, 6]
Player 2's roll after re-roll: [6, 6, 6, 2, 5]
Player 2's roll after re-roll: [6, 6, 6, 6, 5]
Player 2 scored 29 for Three of a Kind.
Player 3's roll: [1, 3, 5, 6, 1]
Player 3's roll after re-roll: [1, 1, 2, 1, 2]
Player 3 rolled a Full House!
Player 3 scored 25 for Full House.
Player 4's roll: [6, 3, 6, 3, 5]
Player 4's roll after re-roll: [6, 6, 1, 3, 1]
Player 4's roll after re-roll: [6, 6, 3, 1, 2]
Player 4 scored 18 for Chance.

Round 3:
Player 1's roll: [3, 6, 4, 6, 3]
Player 1's roll after re-roll: [3, 3, 2, 2, 6]
Player 1's roll after re-roll: [3, 3, 1, 4, 6]
Player 1 scored 17 for Chance.
Player 2's roll: [3, 6, 4, 3, 6]
Player 2's roll after re-roll: [3, 3, 1, 1, 6]
Player 2's roll after re-roll: [3, 3, 4, 5, 5]
Player 2 scored 20 for Chance.
Player 3's roll: [2, 6, 4, 1, 2]
Player 3's roll after re-roll: [2, 2, 4, 2, 3]
Player 3's roll after re-roll: [2, 2, 2, 5, 2]
Player 3 scored 13 for Four of a Kind.
Player 4's roll: [5, 1, 5, 4, 4]
Player 4's roll after re-roll: [5, 5, 1, 2, 2]
Player 4's roll after re-roll: [5, 5, 2, 1, 4]
Player 4 scored 10 for Fives.

Round 4:
Player 1's roll: [4, 3, 1, 3, 5]
Player 1's roll after re-roll: [3, 3, 1, 3, 2]
Player 1's roll after re-roll: [3, 3, 3, 5, 2]
Player 1 scored 9 for Threes.
Player 2's roll: [1, 2, 2, 1, 5]
Player 2's roll after re-roll: [1, 1, 2, 5, 3]
Player 2's roll after re-roll: [1, 1, 6, 4, 2]
Player 2 scored 6 for Sixes.
Player 3's roll: [4, 5, 6, 4, 3]
Player 3 rolled a Small Straight!
Player 3 scored 30 for Small Straight.
Player 4's roll: [1, 4, 2, 3, 5]
Player 4 rolled a Large Straight!
Player 4 scored 40 for Large Straight.

Round 5:
Player 1's roll: [6, 1, 5, 5, 3]
Player 1's roll after re-roll: [5, 5, 1, 2, 2]
Player 1's roll after re-roll: [5, 5, 4, 5, 4]
Player 1 scored 15 for Fives.
Player 2's roll: [5, 1, 6, 6, 4]
Player 2's roll after re-roll: [6, 6, 1, 5, 4]
Player 2's roll after re-roll: [6, 6, 2, 5, 5]
Player 2 scored 10 for Fives.
Player 3's roll: [6, 1, 2, 5, 2]
Player 3's roll after re-roll: [2, 2, 3, 5, 5]
Player 3's roll after re-roll: [2, 2, 1, 3, 6]
Player 3 scored 14 for Chance.
Player 4's roll: [5, 4, 6, 2, 2]
Player 4's roll after re-roll: [2, 2, 4, 4, 5]
Player 4's roll after re-roll: [2, 2, 2, 2, 3]
Player 4 scored 11 for Four of a Kind.

Round 6:
Player 1's roll: [2, 4, 5, 5, 2]
Player 1's roll after re-roll: [2, 2, 2, 2, 1]
Player 1's roll after re-roll: [2, 2, 2, 2, 3]
Player 1 scored 11 for Four of a Kind.
Player 2's roll: [4, 6, 4, 6, 6]
Player 2 rolled a Full House!
Player 2 scored 25 for Full House.
Player 3's roll: [5, 3, 6, 2, 6]
Player 3's roll after re-roll: [6, 6, 5, 1, 5]
Player 3's roll after re-roll: [6, 6, 4, 5, 1]
Player 3 scored 12 for Sixes.
Player 4's roll: [3, 5, 5, 2, 6]
Player 4's roll after re-roll: [5, 5, 6, 5, 5]
Player 4's roll after re-roll: [5, 5, 5, 5, 3]
Player 4 scored 3 for Threes.

Round 7:
Player 1's roll: [4, 2, 2, 3, 5]
Player 1 rolled a Small Straight!
Player 1 scored 30 for Small Straight.
Player 2's roll: [3, 2, 4, 4, 4]
Player 2's roll after re-roll: [4, 4, 4, 1, 2]
Player 2's roll after re-roll: [4, 4, 4, 5, 3]
Player 2 scored 12 for Fours.
Player 3's roll: [2, 3, 5, 3, 6]
Player 3's roll after re-roll: [3, 3, 2, 6, 4]
Player 3's roll after re-roll: [3, 3, 2, 4, 3]
Player 3 scored 9 for Threes.
Player 4's roll: [5, 1, 5, 5, 6]
Player 4's roll after re-roll: [5, 5, 5, 6, 5]
Player 4's roll after re-roll: [5, 5, 5, 5, 6]
Player 4 scored 6 for Sixes.

Round 8:
Player 1's roll: [4, 3, 5, 6, 6]
Player 1 rolled a Small Straight!
Player 1 scored 12 for Sixes.
Player 2's roll: [3, 2, 6, 2, 4]
Player 2's roll after re-roll: [2, 2, 6, 5, 2]
Player 2's roll after re-roll: [2, 2, 2, 6, 2]
Player 2 scored 14 for Four of a Kind.
Player 3's roll: [4, 3, 1, 6, 5]
Player 3 rolled a Small Straight!
Player 3 scored 5 for Fives.
Player 4's roll: [4, 6, 1, 3, 6]
Player 4's roll after re-roll: [6, 6, 4, 1, 5]
Player 4's roll after re-roll: [6, 6, 2, 1, 3]
Player 4 scored 2 for Twos.

Round 9:
Player 1's roll: [3, 5, 5, 5, 1]
Player 1's roll after re-roll: [5, 5, 5, 1, 5]
Player 1's roll after re-roll: [5, 5, 5, 5, 4]
Player 1 scored 4 for Fours.
Player 2's roll: [2, 1, 1, 6, 1]
Player 2's roll after re-roll: [1, 1, 1, 6, 5]
Player 2's roll after re-roll: [1, 1, 1, 1, 5]
Player 2 scored 4 for Aces.
Player 3's roll: [5, 1, 6, 5, 6]
Player 3's roll after re-roll: [5, 5, 1, 6, 1]
Player 3's roll after re-roll: [5, 5, 1, 5, 2]
Player 3 scored 2 for Twos.
Player 4's roll: [1, 1, 5, 1, 5]
Player 4 rolled a Full House!
Player 4 scored 25 for Full House.

Round 10:
Player 1's roll: [6, 6, 1, 1, 6]
Player 1 rolled a Full House!
Player 1 scored 2 for Aces.
Player 2's roll: [1, 6, 5, 5, 4]
Player 2's roll after re-roll: [5, 5, 5, 4, 6]
Player 2's roll after re-roll: [5, 5, 5, 2, 6]
Player 2 scored 2 for Twos.
Player 3's roll: [1, 1, 4, 1, 5]
Player 3's roll after re-roll: [1, 1, 1, 6, 3]
Player 3's roll after re-roll: [1, 1, 1, 5, 2]
Player 3 scored 3 for Aces.
Player 4's roll: [4, 1, 1, 2, 4]
Player 4's roll after re-roll: [4, 4, 6, 1, 3]
Player 4's roll after re-roll: [4, 4, 3, 4, 1]
Player 4 scored 12 for Fours.

Round 11:
Player 1's roll: [5, 3, 6, 2, 5]
Player 1's roll after re-roll: [5, 5, 3, 3, 6]
Player 1's roll after re-roll: [5, 5, 4, 2, 1]
Player 1 scored 2 for Twos.
Player 2's roll: [3, 5, 5, 6, 6]
Player 2's roll after re-roll: [5, 5, 1, 3, 3]
Player 2's roll after re-roll: [5, 5, 6, 3, 3]
Player 2 scored 6 for Threes.
Player 3's roll: [2, 6, 5, 6, 5]
Player 3's roll after re-roll: [6, 6, 6, 6, 6]
Player 3 rolled a Yahtzee!
Player 3 scored 50 for Yahtzee.
Player 4's roll: [1, 1, 1, 1, 6]
Player 4's roll after re-roll: [1, 1, 1, 1, 2]
Player 4's roll after re-roll: [1, 1, 1, 1, 5]
Player 4 scored 4 for Aces.

Round 12:
Player 1's roll: [3, 4, 5, 5, 6]
Player 1 rolled a Small Straight!
Player 1 could not score any points.
Player 2's roll: [1, 6, 5, 4, 1]
Player 2's roll after re-roll: [1, 1, 2, 6, 4]
Player 2's roll after re-roll: [1, 1, 1, 4, 6]
Player 2 could not score any points.
Player 3's roll: [5, 2, 6, 2, 6]
Player 3's roll after re-roll: [2, 2, 6, 4, 2]
Player 3's roll after re-roll: [2, 2, 2, 6, 1]
Player 3 could not score any points.
Player 4's roll: [2, 5, 2, 3, 2]
Player 4's roll after re-roll: [2, 2, 2, 5, 5]
Player 4 rolled a Full House!
Player 4 could not score any points.

Round 13:
Player 1's roll: [5, 4, 6, 4, 6]
Player 1's roll after re-roll: [4, 4, 5, 4, 2]
Player 1's roll after re-roll: [4, 4, 4, 3, 4]
Player 1 could not score any points.
Player 2's roll: [5, 1, 3, 1, 5]
Player 2's roll after re-roll: [5, 5, 1, 6, 3]
Player 2's roll after re-roll: [5, 5, 2, 2, 2]
Player 2 could not score any points.
Player 3's roll: [3, 2, 3, 5, 3]
Player 3's roll after re-roll: [3, 3, 3, 6, 1]
Player 3's roll after re-roll: [3, 3, 3, 4, 3]
Player 3 scored 4 for Fours.
Player 4's roll: [5, 1, 5, 5, 3]
Player 4's roll after re-roll: [5, 5, 5, 2, 4]
Player 4's roll after re-roll: [5, 5, 5, 1, 2]
Player 4 could not score any points.

Round 14:
Player 1's roll: [1, 4, 2, 6, 1]
Player 1's roll after re-roll: [1, 1, 3, 6, 4]
Player 1's roll after re-roll: [1, 1, 6, 3, 1]
Player 1 could not score any points.
Player 2's roll: [3, 1, 6, 3, 4]
Player 2's roll after re-roll: [3, 3, 3, 1, 5]
Player 2's roll after re-roll: [3, 3, 3, 2, 6]
Player 2 could not score any points.
Player 3's roll: [3, 2, 2, 4, 6]
Player 3's roll after re-roll: [2, 2, 6, 4, 5]
Player 3's roll after re-roll: [2, 2, 3, 6, 1]
Player 3 could not score any points.
Player 4's roll: [4, 2, 1, 1, 1]
Player 4's roll after re-roll: [1, 1, 1, 4, 2]
Player 4's roll after re-roll: [1, 1, 1, 3, 5]
Player 4 could not score any points.

Round 15:
Player 1's roll: [6, 3, 4, 1, 5]
Player 1 rolled a Small Straight!
Player 1 could not score any points.
Player 2's roll: [2, 1, 6, 1, 4]
Player 2's roll after re-roll: [1, 1, 4, 1, 5]
Player 2's roll after re-roll: [1, 1, 1, 4, 1]
Player 2 could not score any points.
Player 3's roll: [6, 4, 4, 2, 3]
Player 3's roll after re-roll: [4, 4, 4, 6, 4]
Player 3's roll after re-roll: [4, 4, 4, 4, 2]
Player 3 could not score any points.
Player 4's roll: [5, 2, 1, 2, 6]
Player 4's roll after re-roll: [2, 2, 1, 3, 5]
Player 4's roll after re-roll: [2, 2, 6, 6, 6]
Player 4 could not score any points.

Round 16:
Player 1's roll: [1, 4, 1, 1, 2]
Player 1's roll after re-roll: [1, 1, 1, 2, 6]
Player 1's roll after re-roll: [1, 1, 1, 3, 3]
Player 1 could not score any points.
Player 2's roll: [3, 2, 3, 3, 6]
Player 2's roll after re-roll: [3, 3, 3, 4, 5]
Player 2's roll after re-roll: [3, 3, 3, 5, 6]
Player 2 could not score any points.
Player 3's roll: [2, 2, 1, 6, 1]
Player 3's roll after re-roll: [2, 2, 3, 6, 6]
Player 3's roll after re-roll: [2, 2, 3, 3, 6]
Player 3 could not score any points.
Player 4's roll: [2, 6, 5, 3, 3]
Player 4's roll after re-roll: [3, 3, 6, 5, 4]
Player 4 rolled a Small Straight!
Player 4 scored 30 for Small Straight.

Round 17:
Player 1's roll: [6, 1, 1, 4, 1]
Player 1's roll after re-roll: [1, 1, 1, 3, 4]
Player 1's roll after re-roll: [1, 1, 1, 5, 3]
Player 1 could not score any points.
Player 2's roll: [5, 4, 5, 5, 5]
Player 2's roll after re-roll: [5, 5, 5, 5, 4]
Player 2's roll after re-roll: [5, 5, 5, 5, 1]
Player 2 could not score any points.
Player 3's roll: [4, 6, 5, 3, 3]
Player 3 rolled a Small Straight!
Player 3 could not score any points.
Player 4's roll: [6, 6, 1, 3, 5]
Player 4's roll after re-roll: [6, 6, 4, 3, 3]
Player 4's roll after re-roll: [6, 6, 3, 2, 2]
Player 4 could not score any points.

Round 18:
Player 1's roll: [1, 5, 5, 2, 2]
Player 1's roll after re-roll: [5, 5, 3, 5, 4]
Player 1's roll after re-roll: [5, 5, 5, 1, 2]
Player 1 could not score any points.
Player 2's roll: [1, 3, 1, 1, 6]
Player 2's roll after re-roll: [1, 1, 1, 2, 2]
Player 2 rolled a Full House!
Player 2 could not score any points.
Player 3's roll: [6, 4, 2, 3, 1]
Player 3 rolled a Small Straight!
Player 3 could not score any points.
Player 4's roll: [1, 3, 6, 4, 1]
Player 4's roll after re-roll: [1, 1, 4, 3, 2]
Player 4 rolled a Small Straight!
Player 4 could not score any points.

Round 19:
Player 1's roll: [6, 3, 2, 3, 5]
Player 1's roll after re-roll: [3, 3, 6, 4, 5]
Player 1 rolled a Small Straight!
Player 1 could not score any points.
Player 2's roll: [5, 5, 6, 6, 2]
Player 2's roll after re-roll: [5, 5, 2, 5, 4]
Player 2's roll after re-roll: [5, 5, 5, 4, 5]
Player 2 could not score any points.
Player 3's roll: [6, 4, 6, 5, 2]
Player 3's roll after re-roll: [6, 6, 3, 6, 6]
Player 3's roll after re-roll: [6, 6, 6, 6, 6]
Player 3 could not score any points.
Player 4's roll: [3, 6, 1, 3, 4]
Player 4's roll after re-roll: [3, 3, 5, 2, 4]
Player 4 rolled a Small Straight!
Player 4 could not score any points.

Round 20:
Player 1's roll: [1, 1, 2, 1, 2]
Player 1 rolled a Full House!
Player 1 could not score any points.
Player 2's roll: [3, 5, 4, 1, 4]
Player 2's roll after re-roll: [4, 4, 5, 2, 5]
Player 2's roll after re-roll: [4, 4, 6, 6, 1]
Player 2 could not score any points.
Player 3's roll: [4, 1, 6, 3, 2]
Player 3 rolled a Small Straight!
Player 3 could not score any points.
Player 4's roll: [5, 5, 2, 1, 2]
Player 4's roll after re-roll: [5, 5, 6, 1, 6]
Player 4's roll after re-roll: [5, 5, 1, 1, 6]
Player 4 could not score any points.

Round 21:
Player 1's roll: [5, 6, 1, 3, 2]
Player 1's roll after re-roll: [5, 3, 4, 6, 5]
Player 1 rolled a Small Straight!
Player 1 could not score any points.
Player 2's roll: [1, 1, 3, 2, 2]
Player 2's roll after re-roll: [1, 1, 2, 4, 1]
Player 2's roll after re-roll: [1, 1, 1, 1, 3]
Player 2 could not score any points.
Player 3's roll: [2, 3, 3, 2, 6]
Player 3's roll after re-roll: [2, 2, 4, 1, 5]
Player 3's roll after re-roll: [2, 2, 4, 2, 1]
Player 3 could not score any points.
Player 4's roll: [2, 1, 3, 6, 5]
Player 4's roll after re-roll: [2, 6, 5, 2, 3]
Player 4's roll after re-roll: [2, 2, 5, 2, 4]
Player 4 could not score any points.

Round 22:
Player 1's roll: [6, 5, 5, 3, 2]
Player 1's roll after re-roll: [5, 5, 3, 2, 6]
Player 1's roll after re-roll: [5, 5, 3, 3, 6]
Player 1 could not score any points.
Player 2's roll: [3, 1, 5, 1, 4]
Player 2's roll after re-roll: [1, 1, 2, 4, 3]
Player 2 rolled a Small Straight!
Player 2 could not score any points.
Player 3's roll: [4, 2, 2, 2, 1]
Player 3's roll after re-roll: [2, 2, 2, 3, 1]
Player 3's roll after re-roll: [2, 2, 2, 6, 5]
Player 3 could not score any points.
Player 4's roll: [2, 1, 4, 6, 5]
Player 4's roll after re-roll: [2, 5, 1, 3, 5]
Player 4's roll after re-roll: [5, 5, 4, 6, 2]
Player 4 could not score any points.

Round 23:
Player 1's roll: [5, 4, 3, 5, 6]
Player 1 rolled a Small Straight!
Player 1 could not score any points.
Player 2's roll: [1, 5, 1, 1, 3]
Player 2's roll after re-roll: [1, 1, 1, 4, 5]
Player 2's roll after re-roll: [1, 1, 1, 6, 1]
Player 2 could not score any points.
Player 3's roll: [2, 6, 3, 4, 2]
Player 3's roll after re-roll: [2, 2, 3, 5, 5]
Player 3's roll after re-roll: [2, 2, 6, 2, 4]
Player 3 could not score any points.
Player 4's roll: [6, 3, 5, 3, 4]
Player 4 rolled a Small Straight!
Player 4 could not score any points.

Round 24:
Player 1's roll: [4, 5, 6, 1, 1]
Player 1's roll after re-roll: [1, 1, 4, 6, 4]
Player 1's roll after re-roll: [1, 1, 5, 6, 1]
Player 1 could not score any points.
Player 2's roll: [5, 4, 4, 5, 4]
Player 2 rolled a Full House!
Player 2 could not score any points.
Player 3's roll: [4, 5, 3, 4, 6]
Player 3 rolled a Small Straight!
Player 3 could not score any points.
Player 4's roll: [2, 3, 2, 1, 2]
Player 4's roll after re-roll: [2, 2, 2, 5, 2]
Player 4's roll after re-roll: [2, 2, 2, 2, 5]
Player 4 could not score any points.

Round 25:
Player 1's roll: [3, 4, 3, 5, 3]
Player 1's roll after re-roll: [3, 3, 3, 1, 2]
Player 1's roll after re-roll: [3, 3, 3, 5, 1]
Player 1 could not score any points.
Player 2's roll: [6, 2, 4, 1, 3]
Player 2 rolled a Small Straight!
Player 2 could not score any points.
Player 3's roll: [6, 1, 1, 3, 2]
Player 3's roll after re-roll: [1, 1, 1, 6, 4]
Player 3's roll after re-roll: [1, 1, 1, 5, 6]
Player 3 could not score any points.
Player 4's roll: [1, 6, 3, 2, 2]
Player 4's roll after re-roll: [2, 2, 3, 6, 3]
Player 4's roll after re-roll: [2, 2, 5, 4, 4]
Player 4 could not score any points.

Round 26:
Player 1's roll: [1, 5, 4, 3, 3]
Player 1's roll after re-roll: [3, 3, 4, 6, 2]
Player 1's roll after re-roll: [3, 3, 4, 3, 4]
Player 1 could not score any points.
Player 2's roll: [3, 4, 3, 4, 5]
Player 2's roll after re-roll: [3, 3, 6, 2, 6]
Player 2's roll after re-roll: [3, 3, 1, 6, 1]
Player 2 could not score any points.
Player 3's roll: [6, 3, 4, 6, 6]
Player 3's roll after re-roll: [6, 6, 6, 4, 1]
Player 3's roll after re-roll: [6, 6, 6, 4, 6]
Player 3 could not score any points.
Player 4's roll: [4, 2, 6, 4, 3]
Player 4's roll after re-roll: [4, 4, 5, 6, 2]
Player 4's roll after re-roll: [4, 4, 6, 2, 5]
Player 4 could not score any points.

Round 27:
Player 1's roll: [5, 4, 3, 1, 2]
Player 1 rolled a Large Straight!
Player 1 scored 40 for Large Straight.
Player 2's roll: [6, 5, 6, 6, 3]
Player 2's roll after re-roll: [6, 6, 6, 5, 1]
Player 2's roll after re-roll: [6, 6, 6, 3, 4]
Player 2 could not score any points.
Player 3's roll: [5, 1, 5, 5, 4]
Player 3's roll after re-roll: [5, 5, 5, 2, 2]
Player 3 rolled a Full House!
Player 3 could not score any points.
Player 4's roll: [3, 5, 1, 3, 6]
Player 4's roll after re-roll: [3, 3, 4, 2, 4]
Player 4's roll after re-roll: [3, 3, 3, 4, 2]
Player 4 could not score any points.

Round 28:
Player 1's roll: [5, 6, 3, 3, 1]
Player 1's roll after re-roll: [3, 3, 3, 2, 1]
Player 1's roll after re-roll: [3, 3, 3, 4, 1]
Player 1 could not score any points.
Player 2's roll: [6, 4, 3, 1, 2]
Player 2 rolled a Small Straight!
Player 2 could not score any points.
Player 3's roll: [1, 3, 5, 3, 3]
Player 3's roll after re-roll: [3, 3, 3, 3, 6]
Player 3's roll after re-roll: [3, 3, 3, 3, 3]
Player 3 could not score any points.
Player 4's roll: [3, 4, 6, 5, 2]
Player 4 rolled a Large Straight!
Player 4 could not score any points.

Round 29:
Player 1's roll: [3, 6, 5, 4, 3]
Player 1 rolled a Small Straight!
Player 1 could not score any points.
Player 2's roll: [4, 5, 1, 6, 6]
Player 2's roll after re-roll: [6, 6, 2, 5, 4]
Player 2's roll after re-roll: [6, 6, 3, 6, 2]
Player 2 could not score any points.
Player 3's roll: [2, 2, 3, 3, 3]
Player 3 rolled a Full House!
Player 3 could not score any points.
Player 4's roll: [2, 1, 3, 1, 3]
Player 4's roll after re-roll: [1, 1, 4, 1, 6]
Player 4's roll after re-roll: [1, 1, 1, 1, 5]
Player 4 could not score any points.

Round 30:
Player 1's roll: [4, 3, 1, 5, 6]
Player 1 rolled a Small Straight!
Player 1 could not score any points.
Player 2's roll: [1, 6, 1, 2, 3]
Player 2's roll after re-roll: [1, 1, 1, 2, 2]
Player 2 rolled a Full House!
Player 2 could not score any points.
Player 3's roll: [3, 3, 3, 6, 4]
Player 3's roll after re-roll: [3, 3, 3, 1, 2]
Player 3's roll after re-roll: [3, 3, 3, 1, 1]
Player 3 could not score any points.
Player 4's roll: [6, 6, 4, 1, 1]
Player 4's roll after re-roll: [6, 6, 1, 4, 3]
Player 4's roll after re-roll: [6, 6, 3, 5, 1]
Player 4 could not score any points.

Round 31:
Player 1's roll: [6, 6, 6, 4, 2]
Player 1's roll after re-roll: [6, 6, 6, 6, 1]
Player 1's roll after re-roll: [6, 6, 6, 6, 6]
Player 1 scored 50 for Yahtzee.

Player 1 has scored all categories!

Final Scores:
Player 1: 334
Player 2: 158
Player 3: 274
Player 4: 168

The winner is Player 1!

Statistics:
Total Rounds Played: 31
Yahtzee Probability: 16.9%
Large Straight Probability: 25.8%
Small Straight Probability: 78.2%
Full House Probability: 85.5%
Three of a Kind Probability: 96.8%
Four of a Kind Probability: 83.1%

The Elusive Yahtzee: A Deeper Dive into Probability

With a larger sample size of 31 rounds, our understanding of Yahtzee's probability landscape becomes even more nuanced. The data reveals a consistent pattern: while certain combinations remain common, others are stubbornly elusive, highlighting the game's inherent challenge and its appeal.

The Foundation of Common Outcomes: The consistently high probabilities of "Small Straight" (78.2%), "Full House" (85.5%), and "Three of a Kind" (96.8%) reinforce their status as the game's bread and butter. These outcomes require a basic degree of pattern or repetition, making them statistically likely within the five dice. This frequency encourages players to feel confident in their ability to score, fostering a sense of accomplishment.

The Shift in Rarer Outcomes: While the probability of "Four of a Kind" (83.1%) has significantly increased compared to the previous data, the probability of "Yahtzee" (16.9%) remains surprisingly low. This is particularly intriguing when compared to the "Large Straight" (25.8%), which has surprisingly risen to become more common than the coveted Yahtzee. These results suggest that while specific combinations might be rare, the probability landscape can be influenced by factors like strategic rerolling or simply the inherent randomness of the dice.

The Allure of the Uncommon: The low probability of Yahtzee remains a defining characteristic of the game. The thrill of achieving a Yahtzee, even with a reduced probability, still carries a significant weight. It represents a moment of pure luck and a testament to a player's ability to manipulate the dice.

Implications for Strategy: This data reveals that aiming for "Four of a Kind" might be a more realistic goal than previously thought. However, it also underscores the importance of strategic rerolling for those seeking to achieve the rarer outcomes like Yahtzee. While a Yahtzee remains elusive, the increased probability of "Large Straight" suggests that it's a more attainable goal, especially for players willing to take calculated risks.

Conclusion: This expanded dataset deepens our understanding of Yahtzee's probabilities. While the game is heavily reliant on chance, understanding these probabilities allows players to refine their strategy and maximize their chances of success. The game's inherent unpredictability and the thrill of the uncommon outcomes remain crucial to its enduring appeal, ensuring that each roll of the dice is filled with anticipation and possibility.