This is not a topic I cover often. They were ignored by my father, Lenny Frome. There are some that took this as an error he made in his video poker analyses. Nothing could be further from the truth. He was quite aware of them. His goal for video poker - and all other games - was to give the Player a strategy he could utilize in the casino. Video Poker strategy is complex enough for most versions. Not everyone can master it. Adding another layer of complexity for a relatively tiny additional return just didn't seem prudent to him. For the most part, I agree.
Penalty cards in video poker are nothing like their name-sake in soccer. They are cards which are discarded which you might wish you could have back, depending on the draw. For example, if you are dealt:
5♦ 6♦ 7♦ J♣ K♠
The proper play is to hold the 3-Card Straight Flush. It has an expected value of 0.63 according to our strategy table while the 2 High Cards is only 0.49. If we perform an analysis on this exact hand, we find that the expected value is exactly 0.63, while if the J/K were a 2/10, the expected value is 0.6355. This is not much of an impact. And, in this case, it would make absolutely no difference to how we would play the hand. But, theoretically, it is possible that it would.
Why is there a difference in the expected values of these two hands? Because when you discard a 2 and a 10, you are getting rid of cards that cannot provide any positive impact on the final hand. But, when you discard a J and a K, you are reducing the probability of ending with a High Pair. Of course, when you hold a 3-Card Straight Flush, your brain is thinking Straight Flush, or Flush or Straight. But, the High Pair will pop up from time to time and in order to get one, you need to a draw a Pair of J's, Q's, K's or A's. If you discarded two of them, you've reduced your chances of getting one.
The overall impact to the payback of jacks or better is a few hundredths of a percent by following all of the penalty card logic. It requires adding more entries into the strategy table for the exceptions. In all honesty, I'm not even sure what the exceptions are exactly. I'm also not generally known for quickly dismissing a few hundredths of a point in terms of payback. My concern is what the cost is to the Player.
In Three Card Poker, there is not a huge difference in payback between playing Q-6-4 and higher vs. Q High. While it is a bit larger than the impact of using penalty card strategy, what makes me advocate for the proper Q-6-4 is not the extra payback but the sincere believe that everyone should have no issue in remembering Q-6-4 vs. Q. The cost to the Player is not negligible - it should be absolutely ZERO.
The same is not true with penalty card strategy. The strategy table for jacks or better has 36 entries in it. It takes a lot of practice to learn them all, and of course IN THE CORRECT ORDER. It is important to know that a 3-Card Straight is not playable. But you also have to know exactly how the 2-Card Royals stack up against the 3-Card Straight Flushes and the 4-Card Straights. Knowing a hand is on the strategy table is not the same as knowing what position it is relative to other hands.
Some of you may be wondering what the harm is of adding a few extra lines to the strategy table to gain a few hundredths of a point. If you can properly do it, nothing is wrong with it. But, if you try and fail, the cost may not simply be those extra hundredths. The impact might be that you begin to make more mistakes than if you didn't bother with the penalty cards at all. In that case, you'll actually reduce the true payback you are achieving because you will increase the overall error rate.
So, in the end, are penalty cards worth it? The answer is, if you can truly master the strategy then yes. But I would only attempt to do so after you've mastered the strategy without them.