Cheerio is not an original game -- it's quite an old game, similar to Yacht -- but the rules are included here because our game of Apple Jack is based on it.

The game is played with five dice. Players take turns trying to score points in one of seven categories. A player cannot score in the same category more than once. After each player has made a score in each of the categories, the game is over, and the points are tallied. The player with the highest score wins the game.

On a player's turn, he rolls all five dice. After the roll, he may either score it or take up to two optional rerolls. For each reroll, he may reroll all of the dice or select any of the dice to keep and only reroll the remainder. He may score at any time, thus ending his turn; after the second reroll (three rolls total) he must score it.

Scoring a turn begins by selecting a category to score in. The seven categories are ones, twos, threes, fours, fives, sixes, and Cheerio. Players may only score once in each category, so if a category has already been scored on a previous turn, it may not be scored in again.

For each of the number categories, the score is that number times the number of dice showing that number. For example, if, after a player's turn, he has rolled three fives and two sixes, he can score 15 points in the fives category (assuming, of course, he does not already have a score for fives), or 12 points in the sixes category (assuming he has not already scored in the sixes category). He may also score zero points in any other category; if both fives and sixes had been previously scored, he must.

Ones are wild and may be counted as any other number provided that there is at least one die showing that number. For example, three ones, a two, and a three may be counted as four twos or four threes (or three ones) but the ones cannot be used as fours, fives, or sixes.

A bonus is applied if the player rolls five of the same number without using any wild ones. The bonus is double the usual score. Five sixes, for example, are called "honest sixes" and score 60 points in the sixes category. Note that five ones are always honest and count 10 points in the ones category. If a player is scoring less than five of a number, there is no bonus for not using wild ones.

The Cheerio category is a run of five. A one, two, three, four, and five count as an "honest Cheerio," which scores 50 points. Similarly, a two, three, four, five, and six count as an honest Cheerio. When scoring Cheerio, unlike the other categories, wild ones can substitute for missing numbers. A run of five that uses wild ones (for example, a two, three, four, one, and six, in which the one substitutes for a five; or a six and four ones, in which the ones substitute for a two, three, four, and five) scores 25 points. If a player scores in the Cheerio category but does not have a run of five, zero points are scored.

After all players have scored in all seven categories, the points are added up, and whoever has the most points is the winner.