Video poker is one of the few casino games where the player's input has a major effect on the outcome of the game. Every time you push Deal you receive five new cards and have a total of thirty-two ways to play the hand. To be a successful video poker player, you have to make the best choice out of those thirty-two options as often as possible.

After the analysis is complete, the results will show the following items: (1) the analysis of the game when perfect strategy is used; (2) the analysis of the game when the basic strategy is used; (3) the basic strategy; and (4) the exceptions to the basic strategy. Pot-limit Omaha poker is a complex game, which makes it difficult to come up with the perfect strategy for playing it. There are a number of pointers that you can remember that can form the basis.

Since computers can mathematically analyze all thirty-two ways to play any given hand, it is possible to figure out the absolutely correct decision for every hand you receive. However, most players don't carry around high powered computers when they are in the casino, so how is this useful?

Well, fortunately for us, some video poker experts have taken it upon themselves to analyze every single hand that can come off the deck, and assemble their findings into easy to read charts that teach players how to play. Below we have strategy charts for the most common video poker games:

• Increase your preflop raise size when there is a weak player in the blinds. The main goal for this.
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• Keep in mind that the strategy chart on this page was specifically designed for full pay Bonus Deuces. However, many live and online casinos choose to offer less than full pay games, and if that is the case this strategy will be slightly off. It will still be very good, but might not be perfect.

Where to Play Video Poker Online

Most of our pages above list just an expert-level strategy chart that will get you to within 0.1% of the maximum payout percentage for the respective game. Some of the pages also list a beginner-level strategy chart that isn't as accurate, but is easier to follow. If you want to play video poker on your PC check out our guide here. Alternatively, you can also have a look at this site's list of ipad video poker app for real money.

How to Use a Video Poker Strategy Chart

The strategy charts on our site are actually very simple to understand, but to a beginner they may be a bit overwhelming at the start. To use a chart you follow these steps:

1. Analyze your hand. Make sure you look at all five of your cards before looking at the chart.
2. Start at the top of the chart and work down. You are looking for any spots on the chart where your hand matches up. For example, if you had four hearts in your hand as well as a pair of Kings, it would match up with 'Four to a Flush' as well as 'High Pair'.
3. Once you find a couple matches for your hand, observe which one is highest on the chart. Hold the cards indicated by the highest match.

If you still are a little confused, check out the below example to clear things up:

An Example Hand Analysis

Imagine you are playing a normal Deuces Wild video poker machine. You push 'Draw', and are dealt the hand below:

Ok, so what do we have here as far as options? Well, first of all, we have a Pat Straight, Seven to Jack - a made hand. We also have four clubs, so we have Four to a Flush. If we look at the chart below (a condensed strategy chart for Deuces Wild), we can see that a Pat Straight is just above Four to a Flush, so the Pat Straight is the better hand of the two.

But wait! Since all we need for a straight flush is the nine of clubs, we also have Four to a Straight Flush. Because Four to a Straight Flush is higher on the chart than both a Pat Straight and Four to a Flush, the correct play here is to hold the four clubs and discard the nine of spades in hopes of hitting the Straight Flush.

See - it really isn't bad at all, as long as you pay attention to all the cards in your hand.

How Accurate are Strategy Charts?

Another intelligent question to ask is how accurate are these charts? If you find a game that returns 100.5%, but your chart has 0.6% error in it, then you are actually only playing at a 99.9% return - also known as a losing gamble.

Well, the charts on our site are on roughly accurate to within 0.1% of perfect play. So, if you find that game that returns 100.5%, you would be actually earning about 100.4% with our charts - not too bad. Not many charts get much closer than 0.1% because they would have to be extremely long and complicated to explain the subtle differences in rare hands.

Video Poker Strategy Software

There are quite a few programs out there than can develop custom strategy charts for all kinds of games with various pay tables. We have reviewed quite a few of these programs, here are links to our reviews:

In game theory, trembling hand perfect equilibrium is a refinement of Nash equilibrium due to Reinhard Selten.^[1] A trembling hand perfect equilibrium is an equilibrium that takes the possibility of off-the-equilibrium play into account by assuming that the players, through a 'slip of the hand' or tremble, may choose unintended strategies, albeit with negligible probability.

Definition[edit]

First define a perturbed game. A perturbed game is a copy of a base game, with the restriction that only totally mixed strategies are allowed to be played.A totally mixed strategy is a mixed strategy where everystrategy (both pure and mixed) is played with non-zero probability.This is the 'trembling hands' of the players; they sometimes play a different strategy, other than the one they intended to play. Then define a strategy set S (in a base game) as being trembling hand perfect if there is a sequence of perturbed games that converge to the base game in which there is a series of Nash equilibria that converge to S.

Note: All completely mixed Nash equilibria are perfect.

Note 2: The mixed strategy extension of any finite normal-form game has at least one perfect equilibrium.^[2]

Example[edit]

The game represented in the following normal form matrix has two pure strategy Nash equilibria, namely ${\displaystyle ⟨\text{Up},\text{Left}⟩}$ and ${\displaystyle ⟨\text{Down},\text{Right}⟩}$. However, only ${\displaystyle ⟨\text{U},\text{L}⟩}$ is trembling-hand perfect.

Assume player 1 (the row player) is playing a mixed strategy${\displaystyle (1-\epsilon ,\epsilon )}$, for .

Player 2's expected payoff from playing L is:

${\displaystyle 1(1-\epsilon )+2\epsilon =1+\epsilon }$

Player 2's expected payoff from playing the strategy R is:

${\displaystyle 0(1-\epsilon )+2\epsilon =2\epsilon }$

For small values of ${\displaystyle \epsilon }$, player 2 maximizes his expected payoff by placing a minimal weight on R and maximal weight on L. By symmetry, player 1 should place a minimal weight on D if player 2 is playing the mixed strategy ${\displaystyle (1-\epsilon ,\epsilon )}$. Hence ${\displaystyle ⟨\text{U},\text{L}⟩}$ is trembling-hand perfect.

However, similar analysis fails for the strategy profile ${\displaystyle ⟨\text{D},\text{R}⟩}$.

Assume player 2 is playing a mixed strategy${\displaystyle (\epsilon ,1-\epsilon )}$. Player 1's expected payoff from playing U is:

${\displaystyle 1\epsilon +2(1-\epsilon )=2-\epsilon }$

Player 1's expected payoff from playing D is:

${\displaystyle 0(\epsilon )+2(1-\epsilon )=2-2\epsilon }$

For all positive values of ${\displaystyle \epsilon }$, player 1 maximizes his expected payoff by placing a minimal weight on D and maximal weight on U. Hence ${\displaystyle ⟨\text{D},\text{R}⟩}$ is not trembling-hand perfect because player 2 (and, by symmetry, player 1) maximizes his expected payoff by deviating most often to L if there is a small chance of error in the behavior of player 1.

Trembling hand perfect equilibria of two-player games[edit]

Video Poker Perfect Strategy

For 2x2 games, the set of trembling-hand perfect equilibria coincides with the set of equilibria consisting of two undominated strategies. In the example above, we see that the equilibrium <Down,Right> is imperfect, as Left (weakly) dominates Right for Player 2 and Up (weakly) dominates Down for Player 1.^[3]

Trembling hand perfect equilibria of extensive form games[edit]

There are two possible ways of extending the definition of trembling hand perfection to extensive form games.

• One may interpret the extensive form as being merely a concise description of a normal form game and apply the concepts described above to this normal form game. In the resulting perturbed games, every strategy of the extensive-form game must be played with non-zero probability. This leads to the notion of a normal-form trembling hand perfect equilibrium.
• Alternatively, one may recall that trembles are to be interpreted as modelling mistakes made by the players with some negligible probability when the game is played. Such a mistake would most likely consist of a player making another move than the one intended at some point during play. It would hardly consist of the player choosing another strategy than intended, i.e. a wrong plan for playing the entire game. To capture this, one may define the perturbed game by requiring that every move at every information set is taken with non-zero probability. Limits of equilibria of such perturbed games as the tremble probabilities goes to zero are called extensive-form trembling hand perfect equilibria.

The notions of normal-form and extensive-form trembling hand perfect equilibria are incomparable, i.e., an equilibrium of an extensive-form game may be normal-form trembling hand perfect but not extensive-form trembling hand perfect and vice versa.As an extreme example of this, Jean-François Mertens has given an example of a two-player extensive form game where no extensive-form trembling hand perfect equilibrium is admissible, i.e., the sets of extensive-form and normal-form trembling hand perfect equilibria for this game are disjoint.^{[citation needed]}

An extensive-form trembling hand perfect equilibrium is also a sequential equilibrium. A normal-form trembling hand perfect equilibrium of an extensive form game may be sequential but is not necessarily so. In fact, a normal-form trembling hand perfect equilibrium does not even have to be subgame perfect.

Problems with perfection[edit]

Myerson (1978)^[4] pointed out that perfection is sensitive to the addition of a strictly dominated strategy, and instead proposed another refinement, known as proper equilibrium.

References[edit]

1. ^Selten, R. (1975). 'A Reexamination of the Perfectness Concept for Equilibrium Points in Extensive Games'. International Journal of Game Theory. 4 (1): 25–55. doi:10.1007/BF01766400.
2. ^Selten, R.: Reexamination of the perfectness concept for equilibrium points in extensive games. Int. J. Game Theory4, 1975, 25–55.
3. ^Van Damme, Eric (1987). Stability and Perfection of Nash Equilibria. doi:10.1007/978-3-642-96978-2. ISBN978-3-642-96980-5.
4. ^Myerson, Roger B. 'Refinements of the Nash equilibrium concept.' International journal of game theory 7.2 (1978): 73-80.

Further reading[edit]

Perfect Video Poker Strategy

• Osborne, Martin J.; Rubinstein, Ariel (1994). A Course in Game Theory. MIT Press. pp. 246–254. ISBN9780262650403.

Poker Strategy Charts