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If you're looking to improve your video poker game, in addition to learning solid basic video poker strategy you should also learn how to perform your own analysis of the various draws that you may be faced with as you play the game.
Here we'll examine a method of performing your own analysis of hands with a single card discard using some very basic mathematics. Before you stop reading at the word "mathematics", this method can be performed using a calculator, so grab one and a piece of paper and pen and in just a few minutes you'll be able to thoroughly analyse a hand and increase your chances of winning the bets you make in video poker games.
Let's start by looking at a simple example. If you are dealt a hand containing the following cards in a Jacks or Better game: Ah Kh Jh Th 4h. You will want to determine the difference between how much you'll win if you keep your made hand and if you discard the four of hearts. To do this, begin by making a list of every possible payout you could achieve with your made hand in one column of your piece of paper, for the purpose of our example, this column would then include a high pair, straight, flush and royal flush. For each of these, you will then include the payout available for each possible combination. Assuming you are playing a 9/6 Jacks or Better Video Poker Game you'll earn 1x for a high pair, 4x for a straight, 6x for a flush and 800x for a Royal Flush.
Once you have written these values in another column you will then add another column that lists the number of cards that will give you each of those hands. To make a high pair there are three aces, kings and jacks that can form a high pair which is 9 cards in total. There are three ways that you can form a straight (the other three non-hearts suit queens), seven ways to give you a flush after you draw (keeping in mind that you are not able to access the 4h again and that the queen of hearts make a Royal flush). Finally, there is only one way to make a Royal Flush.
For each made hand that features on your list, determine the value that it contributes to the draw by multiplying the payout value for each hand by the number of cards that can be made in a specific draw and then divide the answer by 47.
Finally, add up the totals for each type of the made hands to get the total value of the current draw. You will note that this is worth considerably more than the 6x payout you'd stand to receive from discarding nothing, so for this example, drawing is the preferable option.
This may seem a little complex when you're starting out but do it a few times and you'll notice you get quicker and better at it each time and soon it will become second nature and you'll find yourself working it out in your head.