Posted: Nov 19, 2018 3:41 am
There's also a lot that could be said about the difficulty of creating randomisation to an arbitrarily high level of precision, the importance of the variation of distribution parameters;
and how systemic biases can be exploited.
There are very famous cases of both blackjack and roulette where additional information allows probability distributions to vary a lot from the assumption:
https://www.newscientist.com/article/dn ... to-set-up/
https://en.wikipedia.org/wiki/MIT_Blackjack_Team
In the world of computing there's a lot to be said about the roles of PRNG and the ways it can be detected, for example:
http://www-users.math.umn.edu/~garrett/ ... /pRNGs.pdf
Or an analysis I once read about a game I played:
http://www.schwanenlied.me/yawning/XCOM/XCOMPRNG.html
That serves as an interesting introduction to the idea of Linear congruential generators and how strings of results can differ from random strings, via things like serial correlations even while individual results might fit a uniform distribution in their specified range.
and how systemic biases can be exploited.
There are very famous cases of both blackjack and roulette where additional information allows probability distributions to vary a lot from the assumption:
https://www.newscientist.com/article/dn ... to-set-up/
Packard should know. In the late 1970s, he and a group of other physics graduate students set out to create computers that could compute the sector of the wheel a roulette ball would land in. They hid these computers under their clothes or in their shoes, clicking buttons with their toes.
“In the best circumstances, we could predict the quadrant correctly,” says Packard. “We definitely got to the point where we were winning money, but we didn’t continue long enough to make large amounts.”
https://en.wikipedia.org/wiki/MIT_Blackjack_Team
The MIT Blackjack Team was a group of students and ex-students from Massachusetts Institute of Technology, Harvard Business School, Harvard University, and other leading colleges who used card counting techniques and more sophisticated strategies to beat casinos at blackjack worldwide. The team and its successors operated successfully from 1979 through the beginning of the 21st century. Many other blackjack teams have been formed around the world with the goal of beating the casinos.
In the world of computing there's a lot to be said about the roles of PRNG and the ways it can be detected, for example:
http://www-users.math.umn.edu/~garrett/ ... /pRNGs.pdf
Or an analysis I once read about a game I played:
http://www.schwanenlied.me/yawning/XCOM/XCOMPRNG.html
Given the nature of the algorithm, running any in-depth battery of tests against it is sort of a futile gesture. By the nature of the algorithm it uses, any stringent test suite will expose the fact that the LCGs just aren't that great.
That serves as an interesting introduction to the idea of Linear congruential generators and how strings of results can differ from random strings, via things like serial correlations even while individual results might fit a uniform distribution in their specified range.