Since the laws of probability have already been discussed it is only fair to discuss the odds that have so much to do with the probability. Reviewing the basics of the odds, you need to remember that once you have picked up 10 cards you then have 42 cards that are unknown to you. That makes your odds 42 to 1 that you will pick up the card that you want. Each time a card is picked up and discarded, it lowers your odds significantly that you will get the card that you want. Now that you are familiar with the basics, let us move on to more advanced odds and how it works to have the odds in your favor.
Since the odds increase in your favor every time you pick a card from the unused stock, as well as when your opponent discards, it only goes to show that the odds for your opponent also increase. After you pick 5 cards for example, the odds then decrease from 42 to 1 down to 37 to 1. That means that there are 37 cards left unknown to you. AS more and more cards are exposed the odds again change, but they change more than just mathematically.
For example, if you have K ♦, Q ♦ then the only card in the deck that can fill that run is the J ♦. Until such time as you have seen any jacks played or you have seen the 9 ♦ and 10 ♦ played, the chances of your picking the jack are 1 against the balance of those cards remaining in the deck. However, if you have already learned through play that your opponent is saving jacks, could be saving jacks, or could be holding the 9 ♦ or 10 ♦, then obviously the odds are changing very dramatically that you will not be getting a J ♦. That is not exactly because of the mathematical percentages.
While the basic odds of any given play remain constant, the mathematical percentages that work for or against you are based not only on the odds of any given play, but on the advantages or disadvantages that increase to you. For example, if your opponent is on a triple schneid, and you are playing for a card that might let you go gin and will enable you to win a triple schneid, then taking a 10 to 1 shot, or even a 15 to 1 shot might seem worthwhile to you. On the other hand, if the situation were reversed, you would not conceive of taking such a long shot because the advantages of playing the hand in that manner are not worth what you might lose by taking this wild chance.
The expert play differs greatly from the average player because the expert is much more advanced in going beyond the ordinary percentages involved in any given play. That is, the expert measures these percentages or odds against the advantages and disadvantages to him on every play.