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There's been a long history of people saying they think various backgammon programs cheat. Much (all?) of it is people's impressions, suspicions, etc. When asking for actual evidence, however, the arguments typically come up wanting. In the situation with Optime's (free) backgammon program for the iPhone, the situation is a bit different...
This version of backgammon allows you to undo plays, either playing the checkers differently or re-rolling the dice. You can back up moves presumably all the way back to the beginning of the game (although I haven't tried to go back that far). Messing about with this feature, I discovered something rather disturbing.
At any point in the game, if the player rolls a non-double, the computer always rolls a particular value, but if the player rolls a double, the computer always rolls a different value. So, for example...
Let's say at some point the player rolls 5-3, or 6-3, or 4-1, or..., the computer will always roll a 3-1 for its subsequent roll. However, if the player rolls a d6, or d5, or ..., the computer always rolls a 6-4. No matter what the player rolls at that point in the game, if they don't roll a double the computer rolls a 3-1, but if they do roll a double it rolls a 6-4.
These values are just for illustrative purposes. The point is, the computer's rolls are influenced by whether the player is rolling a double or not. I've played this through multiple moves, and found the computer's rolls mostly consistent even across multiple plays.
Now why would someone code a RNG for rolls that are dependent upon the player rolling doubles? If the computer always rolled the same value after backing up, that would make some sort of sense. It would mean for example the player RNG and computer RNG are independent, and the programmer may have wanted that as a "feature" to test the AI for various player moves.
However, the computer rolls are clearly dependent upon the player rolls. This is infinitely repeatable, so others can try this out. In the "real world" this would be evidence enough for investigation, and maybe even a search warrant. :) However, in our "virtual world", I'm not sure anyone really cares. I post this simply because I thought others might find the analysis interesting. Also, because of how easy it is to test, others can verify these findings if they wish.