I'm working to understand the differences between Odds, Probability and Chance. I've come up with a hypothetical situation to show where I'm having a bit of an issue.
Chad shuffles a standard deck of playing cards (52 cards, 4 suits (spades, hearts, clubs, diamonds), 13 cards per suit (2 through ace)), with the deck sufficiently shuffled to produce a random outcome. Chad then looks through the cards in the deck and memorizes their order.
Joe is asked what are his odds of drawing an Ace from the top of the deck, to which he replies 1 to 12. He is then asked what is his probability and his chance of drawing an Ace from the top of the deck, and he replies about 7.69% probability and 7.69% chance. Chad is asked what are the odds of Joe drawing an Ace from the top of the deck, to which he replies 1 to 12. Chad is then asked what is Joe's probability and chance of drawing an Ace from the top of the deck, and he replies 7.69% probability and 100% chance.
Joe draws the first card, and gets an Ace of Hearts.
As I understand it, the odds and probabilities don't change based on whether the outcome is known prior to the resolution, and probabilities are calculated as (Number of Positive Resolutions) / (Total Number of Resolutions). Chances seems to be similar to probabilities, but still different enough though, based on whether the resolution is known or not.
Since, after Chad shuffles the deck, the order of the deck is static, was Joe's chance of drawing an Ace from the top of the deck ever really 7.69%? Was Joe incorrect? Is there a fallacy in there somewhere? Or is the correctness of an answer for chance truly dependent on foreknowledge of the resolution?
Is there another mathematical concept that defines or attempts to quantify what the actual resolution will be, without the participant (e.g. Joe) knowing, but others may know, the resolution beforehand?
Edit: Daniel makes a point that the semantics may be an issue, so to facilitate an answer, and avoid the slippery slope of this becoming a semantics discussion, these are the best standard definitions I could find that state how I currently understand the terms:
Odds: "Betting odds are calculated in the form r:*s*('r to s') and correspond to the probability of winning P=s/(r+s). Therefore, given a probability P, the odds of winning are (1/P) - 1:1." http://m.wolframalpha.com/input/?i=odds+mathematical+definition&x=0&y=0
Probability: "Probability is a measure or estimation of how likely it is that something will happen or that a statement is true. Probabilities are given a value between 0 (0% chance or will not happen) and 1 (100% chance or will happen). The higher the degree of probability, the more likely the event is to happen, or, in a longer series of samples, the greater the number of times such event is expected to happen." http://en.wikipedia.org/wiki/Probability
Chance: I can't find a rigorous definition, just English definitions (http://m.wolframalpha.com/input/?i=chance+definition&x=0&y=0), but I believe my problem description most closely follows Baysian probability for chance, because according to the Wikipedia page (http://en.wikipedia.org/wiki/Probability) it "includes expert knowledge as well as experimental data to produce probabilities", which allows for Chad's foreknowledge of the order of the deck.