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Bob Dancer writes a video poker column for beginners to experts. He also writes a column with Jeffrey Compton, "Player's Edge", featuring information on promotions at various Las Vegas casinos. Player's Edge is published each Friday in the Neon section of the Las Vegas Review-Journal. Click here to send Bob Dancer an e-mail.

For a 3,000-word preview of Bob's juicy new novel, "Sex, Lies, and Video Poker", visit www.bobdancer.com.

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Nov. 21, 2006

Penalty Cards and Video Poker for Winners!

The strategies in Video Poker for Winners! are "penalty free," meaning that they're the best possible without including penalty cards. Penalty cards are evaluated in the background, of course, and the resulting strategy is a weighted average of all of these cases.

As an example, consider 9/6 Jacks or Better -- for most, the easiest game to learn and play, and the one with the fewest penalty cards. The VPW strategy says that it's better to hold 3-card royal flushes than it is to hold 4-card flushes in this game. This is unquestionably the best play, on average. But there are two types of exceptions to this rule.

If you're one who believes that considering penalty cards is useless -- perhaps because you think that the strategy becomes too complicated for too little value in return -- then simply go with the basic strategy. If you're like me, however, and want to play every hand as perfectly as possible, you’Дфll be interested in the tools available in VPW that will help you do this.

To get a report from VPW for the case just discussed, click on ANALYZE --> STRATEGY --> SHOW REPORT. Below we see the top two lines of the 12-line report. Let's go over it.

Example	Strategy	Perfect	Strategy	Number	Total
Hand	Play	Play	Error	of Hands	Error

TH TD 2H JH AH	RF3 'AHT'	FL4 2h	0.00462535	288	1.33210080
2H TH JD QH AH	RF3 'AHT'	FL4 2h	0.03700280	576	21.31361280

Video Poker for Winners! uses quote marks to indicate suited cards, a "T" to indicate a 10, and the symbol "H" to indicate a high card lower than the first one indicated, so the phrase RF3 'AHT' includes 'AKT', 'AQT', and 'AJT'. The phrase FL4 2h means a 4-card flush with two high cards, where "high cards" means cards that will give you your money back if you get a pair of them.

The first example refers to cases that combine the worst type of 3-card royal flush (i.e., one with both an ace and a ten -- with a 4-card flush.) The fifth card is another ten. When this combination occurs, holding the 4-card flush is worth 0.0046 coins (almost a half-cent for a dollar player) more than holding the 3-card royal.

The "Number of Hands" column shows that this happens 288 times (out of the 2,598,960 possible deals). Let's see how this number is determined. There are four different suits for the royal, and three different possible types of hands for the royal, namely 'AKT', 'AQT', and 'AJT'. There are eight different possibilities for the non-royal flush card (namely the 2, 3, 4, 5, 6, 7, 8, or 9). Once the royal suit has been determined, there are three different suits available for the ten. When you multiply these numbers together (4 * 3 * 8 * 3), the product is 288.

The final column is the product of 288 and the size of the error (in the column marked "Error"). When all 12 error types are listed on this chart, the total error for this strategy is merely the sum of this final column.

The second line gives us 'AHT', a flush card, and an unsuited and unpaired high card. When this happens, the error is considerably larger, about 3.7¬ў, and happens twice as often. We count the occurrences as 4 suits for the flush, 3 variations of 'AHT', three suits for the offsuit card, 2 values for the offsuit high card (that is, if you start with 'AKT', the offsuit high card may be either a J or a Q), and the 8 possibilities for the flush kicker. Multiply 4 * 3 * 3 * 2 * 8 and you get 588.

The total error in the strategy presented is 0.00099927%, meaning that an 800-hand-per-hour dollar player gives up 4¬ў an hour. Learning the two plays discussed here cuts that down by about a penny an hour. Is it worth it? It is to me (partly because I play for larger stakes than dollars), but mostly because, if I take the time to learn these hands as well, then I've studied enough that I'm not confused by hands such as KhQhJc9c8c.

This is a hand without penalty cards that takes a considerable amount of study before you can be confident that holding the clubs is the best play. Many players who take the "penalty cards aren't relevant" attitude figure that if they ignore penalty cards, they're automatically getting the other hands correct. This is simply not true. Taking the time to study all facets of the game increases both your ability and your confidence.

Even if you don't want to learn penalty cards, seeing how these calculations are made in video poker will pay dividends when you're trying to analyze promotions in the future.

Video Poker for Winners! is now available for a free 3-day trial at www.videopokerforwinners.com/Default.asp