Some people here are a bit misinformed. First, there is no such thing as a "law of averages." I'm just going to quote Wikipedia here, because it says it best:

As invoked in everyday life, the "law" usually reflects wishful thinking or a poor understanding of statistics rather than any mathematical principle. While there is a real theorem that a random variable will reflect its underlying probability over a very large sample, the law of averages typically assumes that unnatural short-term "balance" must occur.
What you're trying to talk about is the law of large numbers (LLN), which states that the average of the results obtained from a large number of trials will be close to the expected value, and will tend to become closer as more trials are performed.

Now, as for the OP, what are you even trying to propose here? You've complained quite a lot these past few pages, but really offered no alternative solution. What you SEEM to be advocating is a pseudo-random system in which the game will increase the odds of you obtaining a mini-Cactpot with a possible 1-2-3 on the board each time you do not receive one.