the 3. If they do not have a four-of-a-kind, the player should keep any three-of-a-kind or pair that they have and re-roll the other dice. With two pairs keep the higher pair. With no pair keep the highest die. Following this strategy provides a 29.08% chance of getting a four-of-a-kind. As with three-of-a-kind, this strategy does not maximize the average score, since there are a few situations after the first throw where it is better to keep other combinations. For instance, after throwing 11166, keeping 111 maximizes the chance of getting a four-of-a-kind but keeping 66 maximizes the expected average score (6.20 rather than 4.18). The strategy to maximize the average score differs after the first throw and is as follows: keep 44, 55, 66 rather than 111, keep 4, 5, or 6 rather than 11, keep 6 rather than 22. Following the strategy to maximize the average score one will get a four-of-a-kind 27.74% of the time and score an average of 5.61. Full House A player will keep a Yahtzee or Full House. A Yahtzee will score 25 under the Joker rule, even though it is not strictly a full house. Keep any four-of-a-kind, three-of-a-kind, or pairs that are thrown and re-roll the others. With two pairs keep both. On average one will succeed 36.61% of the time and score an average of 9.15. Small Straight The strategy is complicated by the fact that, because of the Joker rule, the player will score 30 if a Yahtzee is rolled. One keeps any Small Straight or Yahtzee that is thrown. After the first throw keep a run of 3 or 3 out of 4 (e.g. 124) if one is rolled. Otherwise, keep a 3 or 4 (or both) and a 2 or 5 if one also has a 3 or 4 (e.g. with 11245 one will keep 24 but with 11255 one will keep nothing). Do not keep just 2, 5, or 25. The only difference after the second throw is that one keeps 1111, 2222, 5555 and 6666, and will try to throw a Yahtzee unless the other die is a 3 or 4. On average one will succeed 61.60% of the time and score an average of 18.48. Large Straight Again the strategy is complicated by the fact that, because of the Joker rule, one will score 40 if one gets a Yahtzee. One will keep any