Statman's video poker site

Strategy Cards

Optimal strategy for video poker requires a fairly complex set of rules, and therefore strategy cards can help us remember what the optimal play is for a given hand. Unfortunately, the format of many strategy cards does not map well on to a mental structure that can be easily learned and modified.

Specifically, many strategy cards list the expected value of all possible hands. In contrast, the structures in our head are most likely some kind of procedural hierarchy. Instead of a list of expected values in our heads, we probably have hierarchies where individual hands are related together.

For example, every decent video poker player knows that 4 to the royal is better than a 5 card flush. At a finer level, playing 9/6 jacks or better, a pair of tens is better than 4 to the outside straight, unless the outside straight is 10-jack-queen-king. The important thing to know is the value of each hand relative to other possible hands that exist on the draw,not the exact expected value of the hands.

Also, where do you start when you look at a dealt hand? Do you look for pairs first or flush combinations - - what about high crds? Strategy cards that list the expected value give no hint on what to do or how to do it.

The strategy cards presented here attempt to present strategy information that optimizes our ability to learn, maintain and modify video poker strategies. In order to make these cards as useful as possible, I need your feedback. Please send your comments to sean@protos.lifesci.ucla.edu.

The strategy for 9/6 jacks or better is listed below

     These strategy cards present a well-defined procedure for playing video poker. Importantly, the card is a hierarchy and not just a list. Like all strategy cards, the goal is to reach a hand with the highest expected value. On the strategy card, the hands are placed so that higher hands appear higher on the card.
   To use the card, we start at the first box on the left, (which is a pair) and then try and improve on upon that by seeing if any connections lead to higher hands. If we find a connection to a higher hand, then we continue until we can go no higher. If we do not find a pair, we follow the arrows to the right and check the next boxt (which is the royal boxl). We continue this until we hit a boxed hand that is satisfied.
   If we cannot find a hand in one of the boxess in the top of the card, we move to the bottom (below the thick line) which is where we check for high cards. High cards are jacks, queens, kings and aces. Each number of high cards (printed in red at the left of the card) has it's structure. Like the top of the card, we try and find connections to higher hands.
    The hierarchy is user-friendly because it highlights the relationships between hands. For example, if we have two high cards, and they are KJ (and none of the previous levels of the hierarchy have been satisfied), then we keep them both unless we also have a Jack-Ten in the same suit. This is so because we can only go up by our connection from KQ/KJ to the JT hand. If we had a queen and a jack and reached this part of the decision tree, then we would be done (i.e. hold the queen and the jack) because there is nothing above queen jack that is connected to it here.

Some strategy card conventions
    Flush Combinations are in Blue
    Straight flush or Royal Combinations are in Magenta
    Gap counts are calculated by counting the number of physical gaps and subtracting the number of high cards. For example, Q-J-8 in the same suit is 0 gaps (not 2) because, although there are 2 physical gaps, there are also 2 high cards which produces a gap count of 0 (2-2).
    The "/" serves as an or. "KT/QT" means "Suited king-ten or suited queen-ten"
    A(HH) means keep the lowest two high cards if dealt AHH where H is jack or above.
    The only colored connecting lines are those that connect specific pairs with higher valued hands.

The strategy for 10/7 double bonus is listed below.
This strategy is not perfectly optimal, but will return within .01% of optimal.

    At the bottom of the card, there a quite a few more rules to deal with. Hopefully, the strategy cards highlights the important relationships between hands.
    For example, imagine you are playing 10/7 double bonus and you get dealt the following hand:
        Queen of hearts, Jack of diamonds, 4 of hearts, 8 of hearts, and ten of diamonds.
This hand is tough because there are lots of rules that are satisfied -- potential hands are:
    Queen-Jack
    Queen-Jack-Ten
    Queen-8-4 of hearts (3 to flush with 1 high card)
    Queen-Jack-Ten-8 (4 to inside straight with 2 high cards)
    Jack-Ten of diamonds (Two to the royal)
Using 10/7 strategy card at the left, we can see that none of the hands at the top of the card are satisfied (e.g. pair, 3 to royal, 4 to flush, 4 straight outside or 3 to sf with 1 gap or less), so we go to the 2 high card part of the strategy card.
The card highlights the fact that Queen-jack-ten is better than queen jack, but that a 4-card inside straight with two high cards is even better. There is no link between QJ and the 3-card flush with one high card, and there is no link between the QJ and the suited jack-ten, so you don't need to consider those.
In essence, the card conveys the rule - "If you have QJ, then QJT is better and 4-card inside straight (e.g. QJT8) is even better". The card is helpful because it limits the number of hands that you need to think about given that you are at a certain point in the hierarchy.

The strategy for Deuces Wild is listed below.
This strategy is very close to optimal (within .002% of optimal 100.763%). One of the important features of this strategy is that it holds 3 deuces over a five of a kind Although this reduces the expected value by a very small amount (less than .001%), this rule allows the strategy to be used with other high-paying deuces wild games (e.g. 17/10 or 15/10 loose deuces) and still retain an expected value which is near optimal for those games.
The strategy for deuces wild depends heavily upon how many deuces are dealt. Therefore, the card is divided into four sections (1 section for 0 deuce deals, 1 section for 1 deuce deals, etc..).

There are a few additional special notations for deuces wild.
No Pen= No penalty. This means that when you are holding a single deuce with an ace and another royal card in the same suit (e.g. 2, Ace of Spades, Ten of spades, see the furthest box to the right on the top part of the card), then the other two cards should not be in the same suit (e.g. a spade) or a high card (i.e., a queen) because both of these cards are penalties because they make straights and flushes harder to get on the draw (e.g., because if you throw away a spade, there are fewer spades to draw).
>6 = The highest card in a straight flush combination must be higher than 6. For example, if you are dealt 2 deuces and a 5 and 6 of spades, then you have 4 to the straight flush, but you do not hold the 5 and 6 of spades. This is so because there are fewer possible straights and straight flushes when you hold low cards. So you would hold 2-2-6-7 if the 6 and 7 are in the same suit (see the box immediately above the 2 deuces). This is also true with a single deuce. You do hold 2-6-7 if the 6 and 7 are in the same suit, but you do not hold 2-5-6 if the 5 and 6 are in the same suit (see the box that is the second box from the right on the top part of the card).

I appreciate any feedback that you can offer. Again, send comments to
vpstatman@hotmail.com

Feel free to print these off if you find them helpful.