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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.

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Jan. 01, 2008

A Look at 1-deuce 4-card straights in NSU Deuces Wild

In both my November 13 and November 20 articles on this website, I mentioned the correct strategy when you are dealt W567-WTJQ in NSU Deuces Wild, where the W stands for wild card --- specifically the deuce. This rule is:

From W567 --- Hold the W only if the fifth card is an A, K, or Q.
Hold W567 if the fifth card is a T or J.

From W678 --- Hold the W only if the fifth card is a K suited with one of the three natural cards, or any 3 or A.
Hold W678 if the fifth card is a J, Q, or unsuited K.

From W789 --- Hold the W only if the fifth card is a 4 suited with one of the three natural cards, or any 3.
Hold W789 if the fifth card is a Q, K, or A or an unsuited 4.

From W89T --- Never hold the W by itself.
Hold W89T if the fifth card is a 3, 4, 5, K, or A (where the K or A must be unsuited with the T).

From W9TJ --- Never hold the W by itself.
Hold W9TJ if the fifth card is a 3, 4, 5, 6, or A (where the A must be unsuited with the J and T).

From WTJQ --- Hold the W only if the fifth card is a 3.
Hold WTJQ if the fifth card is a 4, 5, 6, or 7.

Sometimes you hold the deuce by itself and sometimes you hold the 4-card straight. What I didn't cover in those articles is the WHY of the matter --- mostly because that explanation would be lengthy and in those articles I wanted to stress other points. Today we look at the WHY.

All of these are "perfect" straights, meaning they are consecutive and have enough spaces above and below for the straights to be completed with either natural cards OR wild cards. All of these 4-card straights have the same value, and that value is exactly $5 for the 5-coin $1 player. That is, you get your money back exactly.

To see why the value of these 4-card straights adds up to $5 exactly, let's look at the 47 different cards we can draw. We'll take W567 specifically, but we could have used any in the group. First let's look at the cards that give you your money back ($5) exactly. There are nine of them (three each of 5s, 6s, 7s). (in this paragraph, the small "s" in "5s, 6s, 7s" and elsewhere refers to plural, not spades.) Now we look at the number of cards we could draw that will give us double our money ($10). There are 19 of them (four each of 3s, 4s, 8s, and 9s --- plus the other three deuces). The other 19 cards (four each of As, Ts, Js, Qs, and Ks --- except we only have three cards for the one rank that was the original extra card that was discarded.) Adding this up we have EV = ((9 * $5) + (19 * $10) + (19 * 0)) / 47 = $5.00. This is simple video poker math and any competent players should be aware of how to do these calculations.

If the 4-card straight is ALWAYS worth $5, then the decision about whether or not to hold the straight or the deuce by itself must depend on how much the deuce by itself is worth. Since the decision varies from case to case, then it is probably obvious that sometimes the deuce is worth slightly more than $5 and sometimes it is worth slightly less. The question now becomes WHY does the value of the deuce by itself vary?

The best explanation of this is found in Appendix A of the Dancer / Daily "Winner's Guide on NSU Deuces Wild." That explanation goes into a lot more detail than I have space for in this column, so serious students should consult the original to understand this better. I will, however, give you the gist of that appendix here.

The first principle of Appendix A is that if you look at the ranking of cards, excluding the deuce, as A3456789TJQKA, when you draw five new cards, or 4 cards to one deuce, the value is highest when the cards remaining in the pack of 47 cards are near the center of this ranking --- which is equivalent to saying the cards you're throwing away are near the top or bottom of this ranking. So if we're comparing W567A versus W567T, the first case has one extra ten remaining in the pack and the second case has one extra ace remaining in the pack. The ten is as central as you can get, given that any card between a 3 and a 9 will either complete a 5-card straight or give you a 3-of-a-kind and the ace is as extreme as you can get.

Since an additional ten adds more value to the deuce by itself than an ace does (which is as extreme as you can get), it turns out that you hold the W567 when the fifth card is the ten (because the value of the W by itself is 2¢ lower than the value of the straight) and you hold the deuce when the fifth card is a ace (because the value of the W by itself is 3¢ higher than the value of the straight.) If you check out the chart above you'll see a tendency to hold the deuce by itself when the fifth card is near the extremities (i.e. a 3, 4, K, or A). You'll see a tendency to hold the straight when the card is more central. In the two cases where the straight itself is smack-dab in the center of the ranking (i.e. W89T and W9TJ), you always go for the straight.

There are two cases where the suit of the fifth card matters, namely W678 with a K and W789 with a 4. These cases are covered by the second principle in Appendix A, which is that the value of the deuce alone is slightly higher if the remaining cards are totally unsuited than if two or more are of the same suit. This has to do with the possibility of ending up with a flush.

Even with the explanation that the cards remaining being unsuited and close to the extremities, you STILL have to memorize the rule. In EVERY deuces wild variation where straights pay 2-for-1, the value of W567 is exactly $5 and the value of the deuce itself is higher when the card you threw away was an ace than a ten. In Full Pay Deuces Wild, for example, the value of the deuce by itself is 5¢ higher when the fifth card was an ace than when it was a ten. But since the value of the deuce by itself is $5.135 and $5.185, these values are ALWAYS more than the $5 we get for the 4-card straight, so we NEVER go for the straight in that game. (These values assume you can find FPDW for dollars. Fat chance! But dividing all values by 4 to get the value for quarters doesn't change which play is correct.)

Finally, note that these are NOT penalty cards. Rather they are the OPPOSITE of penalty cards. Penalty cards are those cards, usually discarded although they don't have to be, that negatively affect the value of one or more of the combinations you are considering. To understand the examples today you need to see that the cards discarded are leaving valuable cards within the pack of 47 which will POSITIVELY affect the value of one of the options you are considering.