A penalty for your thoughts

Jun 5, 2005 11:36 PM

The first time I heard the term "penalty card," I had some horrible thoughts about some kind of new poker game. Had someone introduced a version of video poker in which an "anti-Joker" appeared and reduced the value of your hand? Or, as in hockey, would you have to sit out for two minutes if you drew a penalty card?

My fears proved to be unfounded as I discovered that a penalty card is a discarded card that lowers the expected value of the hand that we keep.

Let’s start with a simple example:




In the example above, the play is the 3-card straight flush, which according to our charts, has an EV of .61. However, because we are discarding a jack, the EV drops slightly to .60. In this case, there is nothing we can do about it, as there are no other possible plays that are better than this one.

Most of the time, penalty cards make no difference to how we are going to play the hand. Once in a while, a penalty card may cause a different play to have the higher EV.

These strategy changes are generally left to the most astute players. What we do learn from analyzing penalty cards is that expected values for many hands are not absolutes, but in fact, averages. When calculating an expected value, we take all the hands that result in a particular play (i.e. a 3-card straight flush with two high cards) and we sum up the possible results and take the average as an EV.

Some hands, such as a high pair, have the same EV regardless of what cards we discard. For many hands (especially straights, flushes, and straight flushes), the EV is impacted by the number of high cards. In some cases, we categorize the hands by the number of high cards, which can raise the expected value by the cards that are discarded.