By your math, "even money" would be the odds of one success in three attempts (1-(.8^3)=51.2%
the term "even money" is used when the chances of one event happening is roughly equal to that of another event.
Not exactly. When we're not talking about actual amounts of money, "even money" simply means that the chance of an event happening is equal to the chance of it NOT happening. i.e. 50/50. A bet where you're as likely to win as to lose. So you can't compare just any two events like the chance of success of one trial vs the chance of seven failures. That's apples and oranges. It has to be the two possible outcomes of the given proposition. If I have eight items to RE and I am wondering, ahead of time, what the odds are that I will get the schematic before I run out of items to RE vs. the odds of getting NO schematic then you can calculate that as:
The chance of succeeding on the first try, plus...
The chance of failing on the first try and succeeding on the second, plus...
The chance of failing on the first two tries and succeeding on the third, plus... etc, etc.
Or you could do it the easy way and take the chance of NO successes in all eight tries and subtract it from 100%. Which is what I did in my last post. The odds are substantially better than 50/50 that you will see that schematic. You are not beating the odds if you get the schematic even though we've all had those bad luck streaks that make us think success is a lot less likely than it really is. We forget the times that it DID only take 1 or 2 or 3 tries and we remember the times we failed 10 or 20 or more times.