All I want to know is if there is a short-cut method to my long form calculation:

Of every product of every outcome and its probability, counting each outcome near the mean of zero units, how far from the mean would I need to go before I've added 95% of all of the outcomes? I thought that this is what a 95% confidence interval was, but it seems like I am wrong.

I still think you are incorrect for using the st.dev for one trial instead of calculating one for 100 trials to use in the standard error formula, but I have no authority to push this claim.

Thanks for biting, I was a little dismayed that it took so long to get a reply, so don't think I'm being argumentative here, I'm genuinely trying to understand this.