About two weeks ago, during the course of a game, we were resolving a combat situation in which each side tossed a 10-sided die, added his modifiers, and the higher total (die roll plus modifiers) won the combat.
In this case, one side had, say, some 4 points in modifiers... he added + 4... the other side had none. With a modifier of +4, one would think that victory was fairly well assured. But no, the - +4" guy tossed a " 1 ", giving him a grand total of 5, his opponent tossed a "7", and the fight was I lost.
The "+4" guy stated: "Well; with a 10-sided die, there was so much leeway here..." and his opponent agreed: "Yes, there's so much 'swing' in the die roll, it's no surprise you lost."
Swing
In the past, I've shouted about the so-called 'swing' of the 10-sided die... in fact, the 'swing' of any die. Many people believe that because there are 10 possible outcomes on the toss of a 10sided die, that there exists a huge 'swing' which invalidates any use of the die in the decision making process.
Not true. The 'swing' of the die, i.e., the fact that the range of the results will run from 1-through-10 has little to do with the resultant outcome. All that the numbers on the die do are to set up a certain probability that one side or the other will come out higher.
In Diagram (i) below, along the top, I've tabulated Side A's die rolls, ranging from 1 through 10. Side A is the "+4" guy, and each of his rolls will be augmented by adding +4 to it. Thus, just below Side A's rolls, I've listed his modified totals, which now range from 5 to 14.
| Side A's Die Roll | |||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|
| - | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | |
| Side A's Modified Die Roll | |||||||||||
| Side B's Die Roll | . | ||||||||||
| 1 | A | A | A | A | A | A | A | A | A | A | |
| 2 | A | A | A | A | A | A | A | A | A | A | |
| 3 | A | A | A | A | A | A | A | A | A | A | |
| 4 | A | A | A | A | A | A | A | A | A | A | |
| 5 | TIE | A | A | A | A | A | A | A | A | A | |
| 6 | B | TIE | A | A | A | A | A | A | A | A | |
| 7 | B | B | TIE | A | A | A | A | A | A | A | |
| 8 | B | B | B | TIE | A | A | A | A | A | A | |
| 9 | B | B | B | B | TIE | A | A | A | A | A | |
| 10 | B | B | B | B | B | TIE | A | A | A | A | |
If one counts boxes, one sees there are 6 occurrences in which a tie takes place, i.e., A's total equals B's total. Forget about the ties, since they will be rerolled. That leaves 94 remaining boxes, and of these 94, A will top B in 79 of them.
This means that, statistically speaking, Side A will win 79 out of every 94 tosses... which equates to 84 percent of the time. All that the die does, therefore, is set up a probability function based on the modifiers which adjust the die rolls. Given the above situation, there is absolutely no difference in tossing percentage dice, and stating that Side A wins if the result is 84 or under, or in each side tossing his own 10-sided die, Side A adding his modifier of +4, and comparing A's and B's results.
The 'swing' of the die, i.e., the fact that the die itself can range from I to 10, doesn't really come into play.
Another Way
There's another way to compute melee outcome using the 10-sided die and its modifiers, in this case +4. Instead of adding modifiers to the 10-sided die roll, multiply the die roll by the Modifiers. In Diagram (ii), I've compared both A's and B's results.
Side A's rolls of 1 through 10, when multiplied by +4, thus range from 4 through 40. Side B's rolls remain unchanged. Note that in this diagram, there are two ties, leaving 98 other occurrences. And of the 98, Side A will top Side B in 90 of the 98; A will win 90/98, or 92 percent of the time.
| Side A's Die Roll | |||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|
| - | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | |
| Side A's Modified Die Roll | |||||||||||
| - | 4 | 8 | 12 | 16 | 20 | 24 | 28 | 32 | 36 | 40 | |
| Side B's Die Roll | . | ||||||||||
| 1 | A | A | A | A | A | A | A | A | A | A | |
| 2 | A | A | A | A | A | A | A | A | A | A | |
| 3 | A | A | A | A | A | A | A | A | A | A | |
| 4 | TIE | A | A | A | A | A | A | A | A | A | |
| 5 | B | A | A | A | A | A | A | A | A | A | |
| 6 | B | A | A | A | A | A | A | A | A | A | |
| 7 | B | A | A | A | A | A | A | A | A | A | |
| 8 | B | TIE | A | A | A | A | A | A | A | A | |
| 9 | B | B | A | A | A | A | A | A | A | A | |
| 10 | B | B | A | A | A | A | A | A | A | A | |
All of which says... please don't refer to the 'swing' of the die; it's not the parameter of importance.
What's interesting to me is the shift in the probability of A's winning, using the same modifier, but changing the method from addition to multiplication. Side A went from 84 percent to 92 percent. It all depends upon the fella writing the rules... if he thinks a +4 modifier merits an 84 percent chance of success, so be it.
Back to PW Review September 1996 Table of Contents
Back to PW Review List of Issues
Back to MagWeb Master Magazine List
Copyright © 1996 Wally Simon
This article appears in MagWeb (Magazine Web) on the Internet World Wide Web.
Other military history articles and gaming articles are available at http://www.magweb.com