14 April, 2006
A bit late today, due to some other deadlines in my life.
This challenge deals with random numbers, something I’ve talked about before. Here’s the challenge: Give specific examples of mechanics where it is better to use rolling with replacement or rolling without replacement. How can you use random numbers (with or without replacement) to avoid making the game feel arbitrary?
Read the more for definitions of rolling with/without replacement and my thoughts.
Rolling with replacement is like rolling a typical 6-sided die. In theory, any of the sides could face up, so any number could be chosen. This is the most random, but it has one flaw: It is entirely possible (but increasingly improbable) to get a string of numbers. The person that rolls the same number in a roll either feels very lucky, or very unlucky.
Rolling without replacement is like drawing cards from a deck, then discarding the card. So to simulate a die you could have a deck of six cards, each card having the number of a face of the die. The cards are shuffled and you pick one card to get a random result. When all cards have been chosen, you shuffle them and pick again from the deck. The advantage is that you don’t get the improbable, but possible, string of a single number as described above. On the other hand the rolls can get somewhat predictable, particularly if you have a small range of results.
Let me start with the second question first, how can you make the numbers feel more fair? If you are using rolling with replacement, you can use a non-linear random function. A physical example of this is to use the sum of multiple dice. For example, in some games you use 3d6 to roll a result. The results for this roll are actually a bell curve, so that the extreme results (3 and 18) are relatively rare, but the middle results (10-11) are very common.
For rolling without replacement, you can use multiple sets of cards shuffled together. So, in the example above we might have four sets of cards each simulating a 6-sided die, for a total of 24 cards. The rules are the same: shuffle the cards and discard them when chosen, reshuffling the deck when all cards are chosen. This gives you a bit less predictability, while still eliminating the “long sequence of a single number” problem. (Of course, in the example above you could still get a sequence of 4 of the same number.)
What mechanics are suitable for each type? As an example, I think any advancement mechanics, if they have a random component, should have rolling without replacement. This makes advancement more uniform, so that players will not advance too fast or to slow. Quest drops are another good example, so that a player does not get too frustrated at the lack of drops, and get even more frustrated when other players get all their drops quickly.
On the other hand I think skill use should use rolling with replacement. Why? Because a player could learn to game the system, particularly in PvP. Just use the skill until you are sure that you have made several “low” rolls, then go attack a player and you have several high rolls. This may sound laughable, but experience shows that some people will do this. You could do things to obfuscate the rolls in a rolling without replacement situation, but that would add complexity and start to eliminate some of the benefit of that method.
What do you think? What mechanics should use which method?