Disclaimer: My theory has as yet only been tested out on the original pacman, furnished by the DF site. But since all the pacman games were pretty much the same, (cept Pacman Lady) or whatever that absurd game was called... it probably works on all the games.

I have a theory that there is a predictable system governing whether or not a bonus item appears in the level undergoing play. I've narrowed it down to two elements.

Element number 1.

That there are two specific dots which, when eaten, cause the code governing the appearance of the bonus item (cherry, banana, donut, beer, whatever). In order that the game's challenge be maintained, there is a randomizing factor implanted into the code that governs the location of the two specific dots. In other words, eating a certain dot causes the bonus item to appear. The challenge here is finding out which dot governs the appearance of the bonus item. The formula for this theory is as follows.

## Theory number 1.
%Bonus_name==Cherry
Vector1,Vector2==B4,d3
Hexvalue1==4th row horizontal, 3rd pill vertical
## Whereas vector1 and vector2 are the directional co-ordinates and Hex equates to the actual location.
%bonus_name==Cherry
Vector1,Vector2=C5,h3
Hexvalue2==5th row horizontal, 3rd pill vertical
##Shuffle values follows
Shuffle1==8 rows horizontal, 11 pills vertical
Shuffle2==12 rows horizontal, 4 pills vertical

Element number 2.

Element number two is similar, but doesn't hinge upon the eating of a specific dot. My secondary theory concerning how to predict the appearance of the bonus items is that by merely staying alive a specific number of seconds, the time lock on the appearance of the bonus item is unlocked. That is, the code's on/off switch flips from off to on.

Conclusion

In support of element number 1, I have noticed multiple times that eating a specific dot on the screen it causes the bonus item to appear. In support of number two, I have noticed that on specific levels, the bonus item sometimes suddenly appears for no apparent reason. Given that I cannot detect the specific cause of the bonus items appearance in the secondary case, I suspect that it is somehow related to the number of time increments that has passed by.