Springfield wrote
Lost Mine Chance of Factual Data Formula
For each independent clue considered in the challenge, assume 50% chance of factual error per degree of separation from factual source. Results may vary depending on seeker's level of objectiveness. [© 2013, Justin Case, all rights reserved]
The conundrum
The fewer the number of clues, the better chance they are cumulatively accurate, but fewer clues reduce the chances of success. A greater number of clues increases success, but decreases their cumulative reliability.
Calculation Example
Assume 3 clues, 3 degrees of separation. For example, the LDM Legend. Waltz (1st degree) tells Dick Holmes (2nd degree) and info is published (3rd degree): (0.50)(0.50)(0.50) x (0.50)(0.50)(0.50) x (0.50)(0.50)(0.50) = 0.2% chance of totally reliable information.
Calculating odds can be helpful, if you are a spreadsheet type of person, however even at that, it is also misleading.
The example given, three clues, and a 50-50 chance, indeed gives you the 0.2% chance or 1 in 500 that all three clues are correct.
The same calculation, to arrive at whether two of the three clues are correct, is far different - for you actually have two chances (3 clues) to end up with two correct - or
(0.50)(0.50) x (0.50)(0.50) x (0.50)(0.50) x 2 (possible matches)= 12.5% that two are correct
The odds of one of the three being correct are even better, for while the original "rules" are in place reducing the odds for a single clue to be correct means 12.5% yet you get three tries, or 37.5%
This may sound like LONG odds for anyone to go out looking for any lost mine, however consider this.
The odds of being struck in your lifetime is 1 in 3,000. <source, Natl Geographic>
Your chance of winning the lottery on a single ticket is one in 175 million. <found several such estimates in a quick search on google>
Also, there are at least 100 different clues to the LDM (obviously, many do not apply of course) and you can have more than one "shot" at finding it by looking more often. You can also filter out some false information by research. Even further, it is assumption that the odds of the info being correct from a source is 50%. A person may be a known liar, or known to get things wrong, or known to be truthful etc. Reiney for example, was accused by his relatives of having not paid attention well enough. They seem to have had the impression that he had gotten something very wrong, so we ought to keep that in mind when considering anything from that source.
Roadrunner - the Holmes manuscript has issues; for one, the author has allegedly disowned having written it, though others say they saw him writing it. Right in the text there are known erroneous info, such as Waltz not having filed a claim because he was not a citizen, when it is known that he had won his citizenship before ever arriving in Arizona. So keep that in mind when weighing out the Lost Dutchman legend as perceived by the Holmes manuscript.
Don Jose de la Mancha el Tropical Tramp wrote
oeo blanca de Tayopa: first my coffee, I need it. You may not actually believe it, but I agree with you 100%, Tayopa is Tayopa and the Spanish mine is just that. But I have gotten a few into thinking out of the "box" as they say.
Start by eliminating one clue at a time, or simply modifying it Eventually you should have success. Having had to do that with my mine, I know just how hard it is to do, but it may be necessary. The prize is worth it.
Also remember, you posted " you have to go up, then down to get to my mine" which roughly simply indicates that it is at the bottom of the upper cliff of double cliff system. Yer Welcome, however if not clear, ask me..
Don Jose de La Mancha ( el unrepentant one)
Have to disagree with your last statement there amigo - it need not be a cliff system to fit such a vague discription - a simple ledge/ridge on a slope, that you would have to get up and over to get to the mine will also fit, as is the case for the Fortuna. You must go up and over that ridge, then down a bit, to reach the mine; it need not be a series of cliffs, which would make for difficult access by mules.
Good luck and good hunting amigos - have to sign off but will try to pop in later and catch up.
Oroblanco