I LOVE the free video poker strategy calculator you can find on the Wizard of Odds website: wizardofodds.com.
I care more about perfect strategies than most folks do. So I decided to look at 9/6 Bonus Poker Deluxe and see if I can learn something new. Normally from an unsuited AJ, the appropriate play is to hold both cards. But SOMETIMES you hold the J by itself. The “Basic Strategy Exceptions,” the fourth and final table of the calculator, lists 350 separate cases where you should hold the J over the AJ. These 350 separate cases are listed below:
The good news is that every possible type of exception is included. The bad news is that a list of 350 exceptions is far too unwieldy to use as is. When I’m creating an advanced strategy for my own use, my goal is to create as few rules as possible that cover all the exceptions. If there is a choice between two different sets of rules that both explain the exceptions, simpler rules are better than complicated rules.
Whether this list contains redundancies or not depends on your point of view. The very first example, 2♣ 3♣ 4♦ J♥ A♦, covers the specific cards A, J, 4, 3, 2, where the A4 are suited, the 23 are suited, and the J is totally unsuited. There are 24 unique hands that fit that criterion. The second example, 2♣ 3♣ 4♦ J♥ A♠, may look the same to you but in this case the A and 4 are unsuited with each other while the 2 and 3 remain suited. There are also 24 unique hands that fit these criteria and there is no overlap between these two sets of 24 unique hands.
The first nine hands on this list all contain the cards AJ432 and they are all played the same-namely, just hold the J. But each of these hands is different from each other with respect to which of the cards are suited with each other. And you don’t see any hands in this group of nine where there’s a 3-card straight flush among the possibilities, because a combination like A♦ 2♦ 4♦ would be higher ranking than holding either the J or AJ. Further, on this list you’ll see combinations with 3-card straight flushes such as 3♣ 4♣ 7♣ J♦ A♥, because a combination like 3♣ 4♣ 7♣ is less valuable than either a J or AJ.
I suggest you look at the list above and see if you can come up with some good rules as to when to hold the AJ and when to hold the J by itself. At the end of this article I’ll tell you what I came up with, but you’ll get a lot more out of the exercise if you try it yourself first.
The first thing I noted was that none of the 350 hands included a card suited with the J. I call this a ‘flush penalty,’ and abbreviate that ‘fp.’ On these hands, a flush penalty to the J lowers the value of the J alone by 2.8¢ for the 5-coin $1 player. Since, on the hands in question, the J by itself is NEVER worth as much as 2.8¢ more than the AJ, any flush penalty to the J means you hold AJ.
When we look at the straight penalties to the J, they come in several flavors. A K or Q would be a straight penalty to the jack, but now the choice is no longer between AJ and J. That is, from an unsuited AKJ you hold KJ and from an unsuited AQJ you hold QJ.
A ten (abbreviated as a T) is a penalty both to the J and the AJ. I had to make a special rule when a T was in the hand. We’ll come back to that.
A 9, 8, and 7 are each straight penalties to the J. Of the three, the 9 hurts the value of the J the most (because it lowers the chances for KQJT9, QJT98, and JT987). An 8 hurts the value of a J less (because it lowers the chances for QJT98 and JT987). A 7 is the weakest straight penalty (because it only lowers the chances for JT987). It turns out that which of these straight penalties is allowed depends on whether a T is in the hand. We’ll get to that soon.
In some games (such as Super Double Bonus, for example), when you’re choosing between an A, J, and AJ, you care about the flush and low straight penalties to the A (i.e., 2, 3, 4, and sometimes 5 depending on the pay schedule). Here we don’t care about these penalties to the A. Can you see why? It’s very basic but may not be obvious until you think about it.
The reason we don’t care if cards are suited with A, or how many cards in the 2, 3, 4, and 5 range exist is because we’re not considering holding the A by itself. We’re holding an unsuited AJ, and once we’re holding two unsuited cards it no longer matters how many other cards are suited or not. Similarly, with respect to the value of AJ, all cards in the range of 2, 3, 4, 5, 6, 7, 8, or 9 are equivalent.
Now we’re ready to create the rules. First we’ll start out with the hands that do not hold a T. If you go down the columns of these hands you’ll only see cards in the range of 2-7. Therefore our rule is:
With no ten in the hand, if the other three cards are all in the range of 2-7, hold the J by itself so long as no card is suited with the J.
If we now look at the exceptions that include a T, we’ll see that all of the cards in the hand are in the 2-6 range. Therefore our rule is,
From AJT, if the other two cards are in the range of 2-6, hold the J by itself so long as no card is suited with the J.
The way I phrase this on my own strategy chart is:
AJ is less than J with no fp, no 8p, no 9p, and no Tp+7p
You might want to phrase it differently. There are a variety of ways to do it. I’ve given you one example where the rule is spelled out in English and one example where symbols are used more. But if your goal is to play this game perfectly, you need to phrase it in some way that’s equivalent to these rules.
Back to the Wizard’s chart: While I don’t find a list of 350 exceptions directly usable, and find my rule much easier to use, it’s extremely useful to have a 100% complete list of the exceptions. I know if my rules will cover every exception listed, then I’m happy with my rules. And sometimes, as I wrote about last week, the Wizard’s 100% complete list teaches me a hand I didn’t know about.