required should a specific target be needed to achieve. The strategy to maximize the chance of getting a three-of-a-kind involves keeping any three-of-a-kind that is rolled. If a three-of-a-kind is rolled then after the first throw the player should keep any other 5s and 6s, while after the second throw the player should keep any other 4s, 5s, and 6s. An example is with 22225 the player keeps 2225 and throws the other 2. If a three-of-a-kind is not rolled the player should keep any pair that is rolled and re-roll the other dice, with two pairs the player should keep the higher pair, and with no pair the player should keep the highest die. Following this strategy gives a 74.32% chance of getting a 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 11166 maximizes the chance of getting a three-of-a-kind (a guaranteed score of 15) but keeping 66 maximizes the expected average score (17.54), although it introduces a 25/81 ≈ 31% chance of scoring nothing. The situations where the strategy to maximize the average score differs are all after the first throw and are as follows: keep 33, 44, 55, 66 rather than 111 (or 11155, 11166), keep 4, 5, or 6 rather than 11, keep 5 or 6 rather than 22, keep 336 rather than 33. For example, with 22456 the player should keep 6 rather than 22 and with 33456 they should keep 336 not 33. If they follow the strategy to maximize the average score they will get a three-of-a-kind 71.51% of the time and score an average of 15.19. Four-Of-A-Kind As with three-of-a-kind, there are slightly different strategies depending on whether a player is simply trying to get a four-of-a-kind or they are trying to maximize their average score. Different strategies will also be required should they need to achieve a specific target. The strategy to maximize their chance of getting a four-of-a-kind involves keeping any four-of-a-kind that they have. If they have a four-of-a-kind then after the first throw they will keep the other if it is a 5 or 6, while after the second throw they will keep the die if it is a 4, 5, or 6. So that with 22223 they keep 2222 and will throw