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Here's a possibly interesting idea: in a game, randomly select from some of these distributions to generate objects (e.g. powerups, enemies, game balancing cons

Here's a possibly interesting idea: in a game, randomly select from some of these distributions to generate objects (e.g. powerups, enemies, game balancing constants) whenever the player appears to be doing well. You'd initially give them the impression that the behaviour is non-random, but then suddenly everything changes. Just thinking out loud here. =) In practice you'd probably need a solid game to begin with to even get the player to notice changes in the distribution used. I'd say lots of times you don't need more than a plain old uniform distribution though.

btilly 13y ago
In actual games with random behavior, the challenge usually lies in convincing people that they are just having an unlucky streak but the game is random and unbiased. Therefore I don't see the point. (I've encountered this at http://www.wargear.net/ http://www.wargear.net/ - and I've sadly needed to convince myself that it is truly random.)
- hdivider 13y ago
  Yeah, I suppose we humans are just too good at seeing patterns where none exist. Still, it's fun to experiment. =)
- dietrichepp 13y ago
  Well, classic problems in statistical analysis deal with "overdispersion"—e.g., the ratio of boys to girls in individual families has a variance too high to be modeled as a simple binomial distribution, so you can model it as a beta-binomial. In games, the challenge is the opposite: to generate distributions that with less variance in order to convince people that the random number generator is "fair". You don't have to do this, but some games will tweak the numbers so they're not independent, to keep the sample mean close to its asymptotic value. In other words, if you have a losing streak, the software steps in and breaks it for you, so that you think the RNG is "fair".
christopheraden 13y ago
Uniform's pretty much the go to distribution for stuff like that--or having a non-random piece and a small random component. That's how Pokemon determined Catch Rates[1]. The problem with a lot of these distributions is that while you may have a closed form expressed for the PDF, it doesn't always give you an easy way to generate samples from that distribution. There's a huge amount of research that goes into efficient ways to generate samples from these distributions, and they are often quite complex once you are unable to use the inverse probability transform [2]. There's a reason that the Metropolis-Hastings Algorithm was such a big breakthrough, and that's because sampling is often quite difficult. In the multivariate setting, sometimes you may have to throw away 10,000 random numbers before you finally get one that could come from your target distribution. For most of the univariate distributions, it's not tremendously difficult to sample, though, so you may be okay. [1]: http://bulbapedia.bulbagarden.net/wiki/Catch_rate http://bulbapedia.bulbagarden.net/wiki/Catch_rate (this article is total nerdvana, by the way) [2]: http://en.wikipedia.org/wiki/Inverse_transform_sampling http://en.wikipedia.org/wiki/Inverse_transform_sampling

btilly 13y ago

In actual games with random behavior, the challenge usually lies in convincing people that they are just having an unlucky streak but the game is random and unbiased. Therefore I don't see the point. (I've encountered this at http://www.wargear.net/ http://www.wargear.net/ - and I've sadly needed to convince myself that it is truly random.)

hdivider 13y ago
Yeah, I suppose we humans are just too good at seeing patterns where none exist. Still, it's fun to experiment. =)
dietrichepp 13y ago
Well, classic problems in statistical analysis deal with "overdispersion"—e.g., the ratio of boys to girls in individual families has a variance too high to be modeled as a simple binomial distribution, so you can model it as a beta-binomial. In games, the challenge is the opposite: to generate distributions that with less variance in order to convince people that the random number generator is "fair". You don't have to do this, but some games will tweak the numbers so they're not independent, to keep the sample mean close to its asymptotic value. In other words, if you have a losing streak, the software steps in and breaks it for you, so that you think the RNG is "fair".

christopheraden 13y ago

Uniform's pretty much the go to distribution for stuff like that--or having a non-random piece and a small random component. That's how Pokemon determined Catch Rates[1]. The problem with a lot of these distributions is that while you may have a closed form expressed for the PDF, it doesn't always give you an easy way to generate samples from that distribution. There's a huge amount of research that goes into efficient ways to generate samples from these distributions, and they are often quite complex once you are unable to use the inverse probability transform [2]. There's a reason that the Metropolis-Hastings Algorithm was such a big breakthrough, and that's because sampling is often quite difficult. In the multivariate setting, sometimes you may have to throw away 10,000 random numbers before you finally get one that could come from your target distribution. For most of the univariate distributions, it's not tremendously difficult to sample, though, so you may be okay. [1]: http://bulbapedia.bulbagarden.net/wiki/Catch_rate http://bulbapedia.bulbagarden.net/wiki/Catch_rate (this article is total nerdvana, by the way) [2]: http://en.wikipedia.org/wiki/Inverse_transform_sampling http://en.wikipedia.org/wiki/Inverse_transform_sampling