Savvy video poker players use a mathematically calculated strategy to get the highest possible return from their play.
I suspect most players do not really care about how the strategy is calculated, but a good understanding of the process can make it easier to understand the counterintuitive holds that are sometimes called for.
This article shows in some detail how the perfect playing strategy – the strategy that causes the highest possible return from each hand – is calculated.
1. Description of video poker strategy
Video poker strategy is a list of holds sorted from highest to lowest return. The player compares the dealt hand with the first line in the strategy. If it matches, the player holds the card(s) indicated.
If not, the next line is compared. This continues until there is a match or the end of the strategy – in which case, the entire hand is discarded.
In order to calculate the strategy, the total return of each possible hold for each possible hand must be calculated. The highest return for each possible hand is the best hold.
The rest of this article goes through the process used to determine this information, which also applies to online video poker such as at 888casino.
2. Possible final hands when holding five, four, three, two, or one card(s)
There are 2,598,960 different possible five-card hands in video poker. This includes every possible five-card combination from a 52-card deck.
For those who are interested, the mathematical formula for calculating this number is: 52/5*51/4*50/3*49/2*48/1. This first part states there are 52 cards that can appear in five different positions, the next states there are 51 cards that can appear in four different positions, etc.
Once five cards have been dealt, there are only 47 cards left in the deck. The formulas for determining the number of possible hands for each number of cards held are:
- Hold 5 – 0 no open slots.
- Hold 4 – 1 open slot: 47/1 = 47 (there are 47 cards remaining and only one spot for it).
- Hold 3 – 2 slots: 47/2*46/1 = 1,081 (47 cards for 2 slots, then 46 cards for 1 slot).
- Hold 2 – 3 slots: 47/3*46/2*45/1 = 16,215 (47 cards for 3 slots, 46 for 2, 45 for 1).
- Hold 1 – 4 slots: 47/4*46/3*45/2*44/1 = 178,365 (47 for 4, 46-3, 45-2, 44-1)
- Hold 0 – 5 slots: 47/5*46/4*45/3*44/2*43/1 = 1,533,939 (47-5, 46-4, 45-3, 44-2, 43-1)
3. Winning hands and pays
Next, the number of winning hands within the number of possible hands based on the number of cards held and the actual cards held is calculated. The number of each different winning hand (3-of-a-kind, full house, etc.) is the frequency,
The frequency of that winning hand is then divided by the total possible hands for the number of cards held, giving a probability percentage.
The probability of that hand is multiplied by the win amount for that hand giving an average return for that winning hand.
4. Examples and the final results
Here is an example of generating the best holds for one specific hand. This process is repeated for all possible holds to produce a strategy for each hand.
Example hand for full-pay (9/6) Jacks or Better: Kh Th 9d 4h 3c
Note: only two holds will be calculated to show the details.
Hold 1: Kh Th
-
Total possible resulting hands: 16,215
| Hand | Frequency | % of Total | Pays (@ 5) | Return |
|---|---|---|---|---|
| Nothing | 12,018 | 74.12 | 0 | 0 |
| Jacks or Better | 2,955 | 18.22 | 5 | 0.9112 |
| 2 Pairs | 711 | 4.38 | 10 | 0.4385 |
| 3-of-a-kind | 281 | 1.73 | 15 | 0.2599 |
| Straight | 110 | 0.68 | 20 | 0.1357 |
| Flush | 118 | 0.73 | 30 | 0.2183 |
| Full House | 18 | 0.11 | 45 | 0.0500 |
| 4-of-a-kind | 2 | 0.01 | 125 | 0.0154 |
| Straight Flush | 1 | 0.01 | 250 | 0.0154 |
| Royal Flush | 1 | 0.01 | 4000 | 0.2467 |
| Total | 16,215 | 100.00 | 2.2911 |
Hold 2: Kh
-
Total possible resulting hands: 178,365
| Hand | Frequency | % of Total | Pays (@ 5) | Return |
|---|---|---|---|---|
| Nothing | 119,047 | 66.74 | 0 | 0 |
| Jacks or Better | 45,456 | 25.48 | 5 | 1.2742 |
| 2 Pairs | 8,874 | 4.98 | 10 | 0.4975 |
| 3-of-a-kind | 4,102 | 2.30 | 15 | 0.3450 |
| Straight | 336 | 0.19 | 20 | 0.0377 |
| Flush | 210 | 0.12 | 30 | 0.0353 |
| Full House | 288 | 0.16 | 45 | 0.0727 |
| 4-of-a-kind | 52 | 0.03 | 125 | 0.0364 |
| Straight Flush | 0 | 0.00 | 250 | 0 |
| Royal Flush | 0 | 0.00 | 4000 | 0 |
| Total | 178,365 | 100.00 | 2.2988 |
This is the method to calculate the return for each hold from one hand.
To calculate the strategy for all possible hands for a specific game and pay table, this process must be repeated for every possible hand (2,598,960), and every possible hold combination (32). That would take an extremely long time, even for a computer.
Fortunately, there are programming shortcuts that cut the time to a few seconds. The results are the same as if all hold combinations of all possible hands were examined.
The results are then ordered by return with the highest listed first. Holds with the same return are many times combined into one line of strategy.
That is all there is to generating a video poker playing strategy!
Just kidding.
Though it is possible, it would take an incredible amount of time and effort to accomplish this by hand. Lucky for us video poker players, today’s computers and software make it much easier.
5. Summary
- Video poker strategy is simply a list of holds for various hands ranked from highest average return to lowest – with discarding the entire hand being the lowest.
- It is possible to calculate the strategy for the different video poker games and pay tables that are available.
- The calculations can be done by hand, but they require a lot of work.
- Computers make the process simpler and quicker.
Understanding what is necessary to generate video poker strategy can help players understand the seemingly counterintuitive holds that are sometimes produced.
