If the corresponding Upper Section box and all Lower Section boxes have been used, an unused Upper Section box must be used, scoring 0. Free choice Joker rule In the simpler, alternative version of the Joker rule the player retains the free choice as to which category to use, but the Yahtzee can only be used as a Joker if the corresponding Upper Section box has been used. If the corresponding Upper Section box is unused the Yahtzee would score 0 if the Full House, Small Straight or Large Straight categories were chosen. Original Joker rule The original game rules released in 1956 contain a difference from the above rules. The booklet stated that additional Yahtzees must be used as Jokers in the Lower Section and did not allow for their use in the Upper Section. This rule was changed when the game was re-copyrighted in 1961. The winner is the player with the highest total. The rules do not specify what happens in the event of a tie. Strategies Completing a Yahtzee The probability of completing a Yahtzee depends on whether a particular Yahtzee is required or any Yahtzee. Specific Yahtzee The probability of completing a specific Yahtzee is shown in the following table. Any Yahtzee The probability of completing any Yahtzee is shown in the following table. The strategy is to keep any Yahtzee, four-of-a-kind, three-of-a-kind or pair that is thrown and re-roll the others. With two pairs, either can be chosen. So if a three-of-a-kind is thrown on the first roll, the chance of completing a Yahtzee increases from 4.60% to 9.34%. Final round This section describes the last round strategy where there is no possibility of a Yahtzee bonus (i.e. there is a score of 0 in the Yahtzee box). These are the simplest situations to analyze, although the strategy may vary depending on the game situation even at this late stage. Upper Section box If the final box is in the upper section, the strategy is to keep any of the numbers required and re-roll the others. On average 2.11 of the number required will be gotten, scoring from 2.11 (for 1s) to 12.64 (for 6s). The distribution is as follows: Three-Of-A-Kind There are slightly different strategies depending on whether a player is simply just trying to get a three-of-a-kind or if they are trying to maximize their average score. Different strategies will also be