There is a method to calculate the number of trial needed for statistical relevance for a required confidence level. It involves running a few trials and measuring the variance of the result, as trials continue the variance about the result reduces
Exactly. (But that is not necessary, because you can calculate the required number of hands without "running a few trials". The probability distributions are known.) But this is not part of the problem for you to solve. As the OP says, enough hands will be played for the outcome to be for all practical purposes be free of pure luck/statistically relevant or whatever you want. You should realize though, that the critical situation might not occur that often. A "few trials" will do you no good.
Why do you misunderstand EVERYTING on purpose. Even the "amusement thing" about getting raised $1???
Another lie:
Not as you believe this trial could be set up to run as there is not enough information about action prior to the scenario for a competent programmer to set it up.
This is so vague and whimsical that it is impossible to reply to. "...action prior to..." - LOL
Now, let us forget this for a moment.
The question for you to answer is: How much should you call in the described situation to be unexploitable?
Can you do that? Can you for a start avoid misunderstanding the QUESTION OF THE THREAD?
If not, please keep out of this thread.