### Abstract

Original language | English |
---|---|

Journal | Mathematics for Application |

Volume | 7 |

Issue number | 2 |

Pages (from-to) | 111-116 |

ISSN | 1805-3629 |

DOIs | |

Publication status | Published - 2018 |

### Cite this

*Mathematics for Application*,

*7*(2), 111-116. https://doi.org/10.13164/ma.2018.09

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*Mathematics for Application*, vol. 7, no. 2, pp. 111-116. https://doi.org/10.13164/ma.2018.09

**Expected characteristic in Tunnels & Trolls character creation, with generalizations.** / Brander, Tommi Olavi.

Research output: Contribution to journal › Journal article › Research › peer-review

TY - JOUR

T1 - Expected characteristic in Tunnels & Trolls character creation, with generalizations

AU - Brander, Tommi Olavi

PY - 2018

Y1 - 2018

N2 - In the roleplaying game Tunnels & Trolls the characteristics of player characters are determined by rolling dice in the following manner: First, one rolls three dice and calculates their sum. If the three dice all give the same result, another three dice are rolled and added to the total. This is continued until the three dice no longer match. We calculate the average result of the stochastic sum: 10 + 4/5. We also consider a generalized dice rolling scheme where we roll an arbitrary number of dice with an arbitrary number of sides. This generalization is motivated by various exotic dice that are used in many roleplaying games. We calculate the expectation, and how much it diﬀers from the situation where we only roll the set of dice once, with no rerolling and adding. As the number of dice increases, or the number of sides the dice have increases, this diﬀerence approaches zero, unless there are two dice (with the number of sides increasing), in which case the diﬀerence approaches one.

AB - In the roleplaying game Tunnels & Trolls the characteristics of player characters are determined by rolling dice in the following manner: First, one rolls three dice and calculates their sum. If the three dice all give the same result, another three dice are rolled and added to the total. This is continued until the three dice no longer match. We calculate the average result of the stochastic sum: 10 + 4/5. We also consider a generalized dice rolling scheme where we roll an arbitrary number of dice with an arbitrary number of sides. This generalization is motivated by various exotic dice that are used in many roleplaying games. We calculate the expectation, and how much it diﬀers from the situation where we only roll the set of dice once, with no rerolling and adding. As the number of dice increases, or the number of sides the dice have increases, this diﬀerence approaches zero, unless there are two dice (with the number of sides increasing), in which case the diﬀerence approaches one.

U2 - 10.13164/ma.2018.09

DO - 10.13164/ma.2018.09

M3 - Journal article

VL - 7

SP - 111

EP - 116

JO - Mathematics for Application

JF - Mathematics for Application

SN - 1805-3629

IS - 2

ER -