Introduction

Inverted Dice® is a challenging tactic dice game for smart people. The game introduces a new way to look at dice rolls — a way to regard

*five*normal six-sided dice as*one*big twenty-sided die (with some odd probabilities).Inverted dice rolls

Normally, you would throw some dice and calculate the sum of the numbers being shown. In this game, you calculate the sum of the numbers

**being shown. Such a roll is called an***not**inverted dice roll*.To make an inverted dice roll, just roll your dice. The result is the sum of the values that are

**included in your roll. There are twenty possible results (1 to 20), some of which can be achieved in several ways.***not*How to play the game

The structure of Inverted Dice® is similar to games like Yahtzee, Yatzy and Yacht, with a score chart, five dice, and three rolls (or fewer) per turn.

There are twenty rounds in the game. In each round, players take turns rolling five dice, trying to reach one of the numbers from 1 to 20 (it must be a number that the player has not previously achieved or

*zeroed out*).After each inverted dice roll, the player chooses which dice to keep, and which to reroll. A player may reroll some or all of the dice up to two times on a turn, making a maximum of

*three rolls each turn*.If a player achieves an available result, it is registered in the score chart.

If the player fails (after three rolls), a number must be recorded as zero points.

Every turn ends when the player puts either

**or***a score***into a score box.***a zero*The game ends when all score boxes are used. The player with the highest total score wins the game.

Bonuses

Players can receive bonuses by achieving all scores in one or more of the following bonus sections.

**Top bonus**is 1 to 5. Getting all of these five numbers will earn you

**in the**

*50 points**upper*bonus row.

**Middle bonus**is 6 to 15. Getting these ten numbers will earn you

**in the**

*50 points**middle*bonus row.

**Bottom bonus**is 16 to 20. Getting these five numbers will earn you

**in the**

*50 points**bottom*bonus row.

Completing the circle

A player who reaches 290 points earns the right to be referred to as

*Inverted Master*.The highest possible score a player can achieve is 360. This is referred to as having

*completed the circle*, and the player is awarded with the lifelong and prestigious title*Inverted Grandmaster*.How to calculate

When calculating the result of an inverted dice roll, always remember these two facts:

- The result is the sum of the dice values that are
included in the roll.*not* - The sum of all numbers from 1 to 6 is 21.

*two*ways of calculating an inverted sum.The first method (

*Sum of values that you do*) is straightforward. Simply add the dice values that are not present in the roll.**not**seeThe second method (

*21 minus values that you*) is often a quicker way. First, calculate the sum of all values that are included in the roll (but only count each value**do**see*). Then, subtract this sum from 21.***once**Examples (the first method)

The result of an inverted dice roll is the sum of the numbers

**being shown.***not*1 2 3 4 5 is 6 because 6 is the only number

*not*being shown.1 2 4 5 6 is 3 because 3 is the only number

*not*being shown.3 3 4 5 6 is also 3 because 1 and 2 are

*not*shown, and 1 + 2 = 3.3 3 4 5 5 is 9 because 1 2 6 are

*not*shown, and because 1 + 2 + 6 = 9.1 1 4 4 4 is 16 because 2 3 5 6 are

*not*shown, and the sum of these numbers is 16.1 1 1 4 4 is also 16 because again 2 3 5 6 are

*not*shown.2 3 4 5 6 is 1 because 1 is the only number

*not*being shown.1 1 1 1 1 is 20 since 2 + 3 + 4 + 5 + 6 = 20.

Examples (the second method)

The result is

**21***minus*the numbers being shown. Only count each shown value**.***once*2 3 4 5 5 is 7, since 2 + 3 + 4 + 5 = 14 (count each value

*once*), and then 21 – 14 = 7.1 3 4 5 5 is 8, since 1 + 3 + 4 + 5 = 13, and then 21 – 13 = 8.

3 3 4 5 5 is 9, since 3 + 4 + 5 = 12, and then 21 – 12 = 9.

1 2 4 5 5 is 9, since 1 + 2 + 4 + 5 = 12, and then 21 – 12 = 9.

2 2 4 6 6 is 9, since 2 + 4 + 6 = 12, and then 21 – 12 = 9.

3 3 5 5 5 is 13, since 3 + 5 = 8, and then 21 – 8 = 13.

1 1 2 3 3 is 15, since 1 + 2 + 3 = 6, and then 21 – 6 = 15.

1 1 5 5 5 is 15, since 1 + 5 = 6, and then 21 – 6 = 15.

2 2 2 4 4 is 15, since 2 + 4 = 6, and then 21 – 6 = 15.

6 6 6 6 6 is 15, since 21 – 6 = 15.

5 5 5 5 5 is 16, since 21 – 5 = 16.

1 1 3 3 3 is 17, since 21 – 4 = 17.

1 1 2 2 2 is 18, since 21 – 3 = 18.

2 2 2 2 2 is 19, since 21 – 2 = 19.

Hints

It is rather easy to get the middle bonus. The top bonus is also within reach, but so are the scores 16, 17 and 18 (that's 51 points right there) so it might be rewarding to go for these large numbers instead of the top bonus.

When counting your final score, remember that the total sum of all numbers from 1 to 20 is

**210**. You only have to subtract the scores that were*zeroed out*from 210. After that, you add the bonuses.The easiest way to achieve 18 is to get nothing but

*ones and twos.*The easiest way to achieve 17 is to get nothing but

*ones and threes.*The easiest way to achieve 16 is to go for either

**or***twos and threes**ones and fours.*