Stay in Command: Optimal Play for Two Person Generala

Generala is a social multi-player dice game popular in Spanish and Portuguese speaking countries. Generala is similar to Yacht, Yatzy, Kniffel, and other close varieties. The most well known variant, a commercial game marketed as Yahtzee, still sells 50 million games each year. All five variants above use five dice and the player scores by matching the numbers on the dice with certain combinations. Generala has 10 such combinations: Ones, Twos, Threes, Fours, Fives, Sixes, Escalera (1-2-3-4-5 or 2-3-4-5-6), Full-House (XXXYY), Fourof-a-Kind (XXXXY), and Generala (XXXXX). In a turn, the player rolls all five dice and then may either stand or re-roll some of the dice. She may then re-roll some of the dice a second time, but after the third roll the player must score the five dice by matching them with one unused combination. Generala scores 50 points, Four-of-a-Kind 40, Full House 30 and Escalera 20. The Ones to Sixes score according to the number of dice with that value. For example, 1-1-3-4-4 scores 2 points as Ones, 3 points as Threes and 8 points as Fours. In some versions a player scores 5 or 10 bonus points when hitting a combination on the first roll, but here I will consider only the “Vanilla” version. The player may waive a combination, i.e. pick a combination which does not match the dice, for a score of zero. For example, a player might waive Generala with 1-11-1-5 if Ones is no longer available to score. Each combination can be scored exactly once. After completing one turn the dice pass to the player on the left, and this process continues until all players have completed 10 turns and either scored or waived all their combinations. The player with most points wins. As is true for most games, the origin and early history of Generala is mostly unknown, and it is simply considered a “traditional game”. Dice of various kinds pre-date recorded history and feature in 5, 000-year-old games such as Senet and the Royal Game of Ur