

Players:  2  
Average Duration:  20 minutes  
Equipment:  10 dice  
Object:  To gain the most points by scoring high in several categories while forcing your opponent to score low. 

Apple Jack is a game based on the old game of Cheerio, the rules for which are included on this site. These rules assume that the reader is familiar with the rules of Cheerio.
The catch, essentially, is that players take their turns concurrently, and one of the two players  the caller  picks the category that both players will score in. Players take turns being the caller.
Since there is a small advantage to having the first turn at being the caller, a game of Apple Jack consists of two rounds, one where one player is the caller first, and one where the second player is the caller first. Within each round, players score once (and no more) in each scoring category, just as in Cheerio.
The winner is the player with the highest total score  the sum of his scores in all categories in both rounds.
Each player gets five dice.
After the caller is determined for the first turn, both players roll all of their five dice at the same time. The caller examines both his own dice and those of his opponent and chooses whether to reroll any of his own dice or not. If he chooses to reroll some or all of his own dice, he indicates this by picking up the dice he wants to reroll and holding them in his hand. If not, he says, "I'll hold."
In either case, the caller's opponent then chooses whether or not to reroll any of his dice. If he wishes to reroll any of his dice, he picks them up and rolls them, and the caller, at that point, rolls the dice he has previously picked up. If the caller's opponent holds, the caller rolls the dice he has picked up previously. If both players hold, the turn is over, and the caller chooses a category to score in (see below).
Unless both players hold, a second reroll occurs in the same fashion as the first: the caller holds or picks up those dice he wishes to reroll, and then the other player does the same. After the second reroll, the turn is over, and the caller chooses a category to score in. As in Cheerio, each player has had a chance to take up to two rerolls (for a total of three rolls). Once the caller has chosen a category to score in, each player's score in that category is determined by his own dice.
There are eight scoring categories: the seven categories in Cheerio, plus a "Sum" category, for which the score is the sum of all five dice. Ones are never wild in this category.
The scoring for the other seven categories is as it is in Cheerio with a few exceptions. (1) There is no bonus for rolling all five of the same number without wild ones. (2) Cheerio counts 10 points if wild ones are used to make a run of five; 20 points if it is honest.
After each turn, the other player becomes the caller. On the last turn of a round, there is only one category left to score in, so players may roll their dice independently of each other.
After the first round, a second round is started. For the first turn of the second round, the caller is whoever wasn't the caller first last time.
The winner of the game is the player with the highest score after all eight categories have been scored in both rounds.
Apple Jack can be played with three (or more) players, although the game becomes longer and more complex the more players there are. Each player needs his own set of five dice. As many rounds are played as there are players  one where each player gets a turn being the caller first.
As always, the caller is the first to choose which dice to reroll during a turn; after the caller has done this, the player to his left picks up the dice he wishes to reroll, and so on until all players have done so. Then players reroll simultaneously, as in the two player version.