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One has to make a distinction between the use of random numbers (or pseudo-random numbers), and the actual mechanic to generate those numbers.
The use of random numbers to compute/approximate/simulate… mathematical equations is a well-respected discipline in numerical analysis, going back to even before computers were invented. Techniques such as Monte Carlo integration or Markov Chain methods are well known in many application areas. In some areas, the use of random numbers is sometimes discouraged, e.g. when you need reproducability of a certain calculation, or coherency over a set of calculations. Since random numbers invariably introduce stochastic noise in the result, this might or might not be a problem.
In a (war)game, we typically want to generate a random outcome, chosen from a list of plausible outcomes. Hence, in the game, stochastic variation is often seen as a good thing. It means you can play the game various times, with different results each time.
A total different matter is how you generate these random numbers. In the old days (i.e. before computers generated random numbers), there were tables with “random numbers”, and you had to pick a number from the table. But in games, we often use devices such as dice, cards, etc. to generate a random numbers. Although statistically it usually doesn’t matter what device you use, the actual device or mechanic often determines the look and feel of the game, and might even instill a degree of trustworthiness in the players.
Suppose you have to determine the outcome of an event in a wargame, with a 50% chance of succeeding. And we have different mechanics for doing so:
- roll a D6, 4+ is a success
- roll a D100, 51+ is a success
- draw a card from a deck, red card is success
- draw a marble from a bag full of white and black marbles, white marble is a success
- look at a digital clock when you need a number, an even minute past the hour is success, an odd minute is failure
- put 6 pingpongballs in a bag, 3 are painted with a yellow pokemon face, 3 have a black pokemon face
- Play paper/scissors/stone to determine the outcome
- Etc…
I guess if you used the pokemon balls in a wargame, many wargamers would complain about the “sillyness” of the thing, and it might even transfer to the perceived quality of the rules. Cfr the many debates wargamers have about using cards in a wargame. Same goes for other professions that want to use random numbers.