1. I'm glad that we're still on good terms but I admit that I'm having trouble interpreting your tone. For example, you referring to my use of DigitalOcean as a "claim," implying that it may not be true, i.e., that I might be lying. Why would you make such an unnecessary implication? And telling me that I was only using 1 core of a 16 core computer, contradicting my claim that I was using 16, when you really have no evidence of what I have or haven't done?

3. The reason my simulations are limited to a relatively small number of hands is because that's what's computationally feasible on a cell phone processor if you want immediate results.

4. I disagree. I have two bodies of code that generate EVs, one does it exactly by enumerating and summing probabilities and the other does it via simulation. My app uses one or the other depending on what the situation calls for, but I also have diagnostic/test code that runs both and compares the results to make sure there aren't bugs in either. The test code does simulations of 100k hands and reports an error condition if the algorithms differ by more than 0.01. These errors are exceedingly rare, which proves to me that Monte Carlo simulation with 100k hands is actually quite accurate.

Given that, I would respectfully suggest that if you aren't seeing the same convergence rate with your Monte Carlo algorithm, you might have some bugs in your code. I hope you don't take that as an unjustified insult--I invite you to download my app and check some of its EVs yourself if you don't believe me.