Rating ‘penalty cards’

Mar 22, 2004 10:31 PM

The first time I heard the term penalty card, I had these horrible thoughts of some new game that was created. Had someone introduced a version of video poker with some sort of anti-joker. If you drew the penalty card, was it just some useless card you drew that counted for nothing? Of course, being a sports fan, I also thought perhaps if you drew a penalty card, it meant that perhaps you had to sit out for 2 minutes!

As I read about them, it became a bit more obvious what a penalty card really is. Let’s start there. A penalty card is a discarded card that lowers the Expected Value of the hand we keep. Let’s start with a simple example:

 

5¨ 6¨ 7¨ J© 2ª

 

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.

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 make a different play have the higher EV. These strategy changes are generally left to the most ”˜professional’ 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 irregardless of which high pair of what 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 and by which cards are discarded.