The Space Gamer 10
The Space Gamer 10
|
|
<TOC>
P:The Space Gamer
I:10
S:In This Issue 2^Where We're Going^Howard Thompson 3^Designer's Notebook^Steve Jackson 16^Feedback/Game Ratings 17^News & Plugs 23^Books 33^Letters
S:Speculations 5^TANK: Present, Future, Ogre^Charles Bowles 9^ATK: Basic Version^Winchell Chung
S:Features 10^Planetary Probabilities in SC^Christopher Chyba 13^SC: Alien Intelligences^Chet Edwards 19^WARCON III Report^Robert Taylor 20^SC Tournament at WARCON III^Shayne Gad
S:Reviews 24^Metamorphosis Alpha^Robert Taylor 25^Bunnies & Burrows^Steve Jackson
S:Fiction 26^Duel^Stephen Cole 27^The Dust of Briainas^G. Arthur Rahman </TOC>
Notes on a Steve Jackson Article
In the Designer's Notebook article, Steve Jackson solves the problem that vexed many of us who played D&D back in the early days: namely, how to generate the random numbers 1d4, 1d8, 1d12, or 1d20 without polyhedral dice. Some may recall the chits that were sold with some printings of the basic set.
The first observation is that one can generate a number from 1 to 5 with a six-sided die by re-rolling on a 6. Similarly a number from 1 to 4 can be generated by re-rolling on a 5 or 6. There is no limit to potential number of rolls, but the average number of rolls required to generate a number from 1 to N is 6/N, so in practice this is efficient.
The second observation is that a random number from 1 to 2 can be generated with a single roll. Let 1-3 be 1 and 4-6 be 2. Similary a random number from 1 to 3 can be generated by letting 1-2 be 1, 3-4 be 2, and 5-6 be 3.
The third observation is that if one can generate a random number from 1 to M and a random number from 1 to N, then one can generate a random number from 1 to MN via the formula (1-m)N + n, where m is the observed value of the first random number, and n is the observed value of the second. Thus it is possible to simulate all the polyhedral dice:
| Die Simulated | Avg # of d6 Rolls |
|---|---|
| 1d4 | 6/4 = 1.5 |
| 1d6 | 1 |
| 1d8 | 1 + 6/4 = 2.5 |
| 1d12 | 1 + 6/4 = 2.5 |
| 1d20 | 6/4 + 6/5 = 2.7 |
Jackson finds this technique is "as fast or faster" than the polyhedral dice, but overlooks the extra opportunities for cheating allowed by multiple rolls. He recommends that game designers avoid weird dice, though he sees value in using percentile dice uniformly throughout a game.
The June 1977 issue of the The Dragon also includes an article on how to get by without polyhedral dice.
