I love getting fan mail and/or e-mails from readers. There are two reasons for this. The first is that it is always nice to know that someone is actually reading my column. It is especially gratifying when someone tells me that they ALWAYS read my column. The second reason is that a question from a reader can frequently become the basis for a particular week's article. There are times I sit down to write my column and I simply don't know what I want to write. I think of a topic and realized I covered it at some point. Of course, being that I have now been writing for Gaming Today for more than 8 years, it is possible that I last wrote about the topic in 2005 and by now there may be some new readers.
This week, I received an e-mail from someone who was questioning some of the strategy for Full Pay Deuces Wild. Full Pay Deuces can be found in several casinos in Las Vegas. As is the case for most 100+% machines, you won't find them on the strip. You're going to have to head to some of the local casinos (such as Station Casinos) if you want to find them. My source (www.vpfree2.com) shows that there should be 100+ machines scattered about at a variety of denominations up to a quarter.
While I've never been a big fan of Deuces Wild, this is just a personal choice. Any game that pays 100.6+% is hard to criticize and is a good game for the regular Player to learn and master. The strategy table is rather long, but when you break it down by the number of wild cards, you realize that it is not really a hard strategy to learn. With a paytable that begins paying at Three of a Kind, you don't have to worry about counting High Cards. The one thing, I strongly advise the beginner to learn is how to recognize hands with lots of wild cards in them. It can become very easy to not realize that 2 6D 9D 10D KH is a 4-Card Inside Straight Flush with 1 Wild Card.
The question I received this week was specifically about holding a 4-Card Inside Straight (presumably with no Wild Cards) versus throwing all 5 cards as a Razgu. The strategy table tells us that we hold the 4-Card Inside Straight. If you look at the strategy table in Winning Strategies for Video Poker, however, it lists both hands as having an expected value 0.3+ - although it does list the 4-Card Inside Straight higher meaning its "+" is greater than the Razgu "+".
While I write extensively on Video Poker in Gaming Today, I spend most of my time analyzing table games. Many years ago I did write my own video poker engine that allows me to analyze most video poker paytables. One of the limitations is that it does NOT do wild card games. Fortunately, I have both other resources available to me and the ability to quickly create a program to help determine exactly how much those "+" are worth.
Calculating the expected value of the 4-card Inside Straight was very easy. There are 8 ways to draw the Straight (4 Wild Cards plus 4 of the 'natural' way to complete the Straight). Each pays 2 units so we have a total return of 16 units. Divide this by 47 ways to draw and we have an expected value of 0.3404.
The Razgu is a bit more complicated. As I've written about in the past, the overall expected value as shown in a strategy table for a hand like a Razgu is the actually the AVERAGE of all the possible hands of that type. Often, no single hand will actually have EXACTLY the expected value shown.
About 20% of all hands in Deuces Wild are classified as a Razgu, each with their own subtleties. The exact make up of suits and ranks will have some impact on the exact expected value. For each 10 through Aces that is in the hand, there will be less chances to make a Natural Royal. The exact suit composition of the initial deal will impact the number of possible Flushes that can be made if we discard all five cards.
In this particular case, however, the reader was talking about a 4-Card Inside Straight, which does limit the possibilities. In order to get a more exact expected value, I quickly set up a program that had the initial deal set to 3D 4C 5H 7S 8S. I figured that by leaving in all of the High Cards I would leave the expected value about as High as it could go and we could see just how close of a decision this really is.
The expected value of this specific Razgu came back at 0.3267. So, it would be more accurate to say that a Razgu is about 0.33- and a 4-Card Inside Straight is 0.34+. It is not exactly a canyon between the two expected value, but there is a clearly superior choice.
To help me prove my work, I realized that we also sell a Deuces Wild tipsheet that my father created a long time ago. It has more detailed numbers on it. It actually lists the expected value to two decimal places. It lists the 4-Card Inside Straight 0.34 and the Razgu at 0.32. (When all the possible Razgus are considered, the average must wind up at below 0.325). It was good to know that my quick and dirty program was able to produce accurate results!
If you're interested in learning the strategy on Deuces Wild, we have the tipsheet for $2.95. It includes the strategy tables for Deuces Wild, Double Pay Deuces Wild and Triple Pay Deuces Wild. Or you can order Winning Strategies for Video Poker which includes these 3 paytables plus dozens more for only $5. Send a check or money order to Gambatria, P.O. Box 36474, Las Vegas, NV 89128.