You have some interesting theories/ideas here that would be really cool if true, but your results are genuinely just happening cause you aren't using big enough sample sizes. 30 isn't nearly enough attempts to close in on the actual odds. I don't think anything less than 100 is gonna be enough to draw any conclusions, and even that is a really low number if you're trying to be accurate about it

Definitely need a larger sample size. For the first round I always go for Self-Self-Dealer. Out of 82 runs I've shot myself 50 times, so ~61% of the time. This is close to the expected value for 2/3 of ~66%, so I'm fairly certain that if they aren't completely accurate, the odds are at least close enough to the 1/3 that it doesn't really matter