What is unknown to you doesn't matter, that's all part of "playing the percentages". Because the others may also hold few diamonds so a lot of cards that are not diamonds, leaving the deck rich in diamonds and elevating your chances. The calculation suggested is where it all "evens out in the end".
Think how the real pros must feel. My guess is they try to avoid getting sucked in to where a lucky opponent could take them down-- stay out and let your opponents deal with the newbies, the pro expects to win out in the long run when they can pick their own moments.

I read what your saying, Ken. I try to play tight in the early rounds, only coming in if I think I've got something close to being the nuts or to stay ahead of the average chips in the torny, and then loosen up as the game progresses from there. I have based my skill progression on the breaks...lol
There every hour for five minutes.
When I started playing I was lucky to clear the first thirty minutes, but now I get miffed if I don't make the second break.
I do get the days when the pockets are dire, and you spend your time just making the numbers up before the blinds eat you alive, and others where I can't seem to go wrong but will get caught by that better hand. Grrrr...
So far 114th out of nearly eight thousand players is my best result, but gonna chase that number one spot down... someday... soon... lol

__________________
I don't believe in mathematics. Albert Einstein

Biologically speaking, if something bites you it's more likely to be female. Desmond Morris.

Quantum analysis is scientific dithering

Professor Frink: My observations n'hey, n'hey, show the universe could be a torus Weh, uh, or toriod it may like the typewriters and bananas and the monkeys with big teeth the biting the screaming Mm-hai!

Homer: mmmmm... doughnuts!

Along the same lines as what Ken G said, but more drastic, why not extend that thought and try to take into account the order of the cards in the rest of the deck? Of course, then the true pot odds are either going to be 100% or 0, you'll either win or you'll lose. But that doesn't really tell you much.

That's the whole point of probability and statistics, to take the information that you actually know, and use it to compute something that will help you make a decision. Knowing that the "true pot odds" are different from what you compute doesn't really help that decision.

Yes, in fact people often use phrases like "my chances of winning are....", as though "chances of winning" was somehow a unique thing. Like hhEb09'1 says, your chances of winning are either 100% or 0% if you see all the cards, but if you only see some of them, they are different. Or if you judge something based on the betting, you may adjust your chances accordingly, where someone else without the ability to gauge the betting might not make that adjustment. The bottom line is, the "probability of winning" doesn't really mean anything more than a guide to your best strategy, based on what you know. The idea is, if you were in that exact situation 1000 times, what strategy would you follow every time to do the best you could, in your judgement based on what you know? The fact that you will likely only be in that exact situation once means that in reality you need to be able to group together 1000 different situations that are effectively similar, and base your strategy on the whole group. Bear that in mind the next time someone claims "the probability is...", as though that were some kind of absolute statement independent of the assumptions and knowledge involved (in physics as well as in cards). A probability is not a statement of absolute reality, it is a statement of your interaction with the reality that you have access to. Those following the other thread about "magical thinking" will recognize that any absolute claim that there "is a probability" of something happening, independent of the specifics of the knowledge, assumptions, and point of view of the person generating that probability, is a classic if subtle example of magical thinking.

You will improve your skill by playing a lot. However, you will likely not improve your understanding of the odds this way. Variance in results and psychology will surely lead you astray.

There is an excellent book called Mathematics Of Poker by Bill Chen and Jerrod Ankenman.

cheers