I am trying to calculate odds for a card game. Using a standard 52-card deck. Here is the basics of the game. You are given two cards, you add their values together. (Standard Blackjack values, suits don't matter) Once you know the total value of your two cards, you are given a third card face down and you then have to guess what the total value of your three cards are. What are the odds that you can guess your total?
As an example to illustrate. You draw two cards, let's say you get a 10 and a 5, what are the odds that you get a total of 25? (ie: Draw a 10). This example is a simple probability that I fully understand, however, the twist comes with calculating the odds of getting a total of 25 with any two-card combination with a value of 15? (ie: If you have 9 and 6, the odds of getting 25 are more than with a 10 and 5). Is there a way to generalize this into something like "Given all combinations of 15, what are the odds that your next card will be a 10?" That can be further generalized into "Given all combinations of X, what are you odds that you next card will be Y"?
The reason for this is because I want to have a list of odds to get any TOTAL value of 3 cards. For example, the odds of getting a total of 33 (Ace, Ace, Ace) is 1 in X. You'd have to calculate odds of getting an Ace when you already have 2. Simple enough, but gets very complication when trying to find the odds of getting 25 because your first two cards aren't as determined and there are only so many ways to get 25 from 3 cards, so the order in which you draw those cards matters as to the odds of getting the last one.
I hope this makes sense,