# Expected characteristic in Tunnels & Trolls character creation, with generalizations

Tommi Olavi Brander*

*Corresponding author for this work

Research output: Contribution to journalJournal articleResearchpeer-review

### Abstract

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.
Original language English Mathematics for Application 7 2 111-116 1805-3629 https://doi.org/10.13164/ma.2018.09 Published - 2018

### Cite this

@article{4f34403795e347e09a8a02889a048444,
title = "Expected characteristic in Tunnels & Trolls character creation, with generalizations",
abstract = "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.",
author = "Brander, {Tommi Olavi}",
year = "2018",
doi = "10.13164/ma.2018.09",
language = "English",
volume = "7",
pages = "111--116",
journal = "Mathematics for Application",
issn = "1805-3629",
number = "2",

}

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

In: Mathematics for Application, Vol. 7, No. 2, 2018, p. 111-116.

Research output: Contribution to journalJournal articleResearchpeer-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 -