Video Poker Math

gambling mathsVideo poker is an electronic form of the traditional five-card draw poker that dates back to the 70 years of the 20th century. It is played in the standard way – the player is dealt five cards and is then given the chance to replace any number of the cards in the hand by an equal number of cards the dealer is to draw from the deck.

The outcome and the amount that is to be paid out to the player is determined by the rank of the resulting hand and the bet size. Of course, mathematics is different to the various type of video poker games, but there are some major principles that are applied to both Jacks or Better, Deuces Wild, etc.

Video Poker Mathematics

As a matter of fact, improving your video poker game is not only done by learning a helpful basic strategy. In fact, players should bear in mind the fact that they should also learn how to make their own analysis of the variety of draws they may be face over the gameplay.

Mathematics is a crucial part of both the traditional game of poker and its video variation. Even for more inexperienced players, mathematics should be a key factor, especially when it comes to probability and how it actually is associated with poker. When it comes to probability, dealing certain hands is always involved in making strategy and relates to mathematics in order for a player to understand what the likelihood of them winning is. In addition, understanding the video poker mathematics can really help players remain emotionally stable and focus on their decisions.


Likelihood, most commonly known as probability, is one of the major terms when it comes to video poker. It is exactly what has a lot in common with the possibility for a certain outcome to occur.

The theory of probability is easy to understand when a coin is flipped, but things get a lot harder when card games are concerned, as a large number of eventual outcomes occur. Each card deck in the game of poker consists of 52 cards divided in four suits and thirteen ranks.

This makes the odds of the player getting an Ace as their first card equal to 7.7%, or 13 to 1. On the other hand, for example, the odds of holding a spade from any of the four suits as a first card are about 25%, or 4 to 1.

Poker mathematics is also considered as not so easy as expected because every card alters the outlook of the remaining part of the deck after being dealt. For instance, when a player receives an Ace as their first card, there will only three more Aces left in the remaining deck of 51 cards. This basically means that the odds of getting another Ace card are 3 in 51, or 5.9%, which makes them much smaller than the chances at the beginning, before the first Ace to be dealt.

Pocket Pairs’ Pre-Flop Likelihood

Players would probably be interested in finding the chances of being dealt a pair of Aces. In order to that, they need to multiply the chances of getting such a card twice.

Getting an Ace has the probability of 4/52, but the odds of getting another Ace are 3/51. Then, players would have to multiply (4/52)x(3/51) to get 1/221, which is about 0.45%. So, if a player enters a long gaming session and is dealt an overall of 30 hands an hour, they could expect to be dealt the so-called pocket Aces once in every 7.5 hours.

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Pre-flop Probabilities of Hand against Hands

After all, no matter if players are posed in the conditions of a land-based or online casino, their hands are always measured up against the ones of the player’s opponents, especially in the cases when a player uses the all-in option before the flop.

There are several most common probabilities that need to be considered. First, if a player holds a High Paid, and their opponent have two Low Cards, the probability for them to win equals 83%. In case of the player holding a High Pair, and their opponent having a Low Pair, the probability of winning is reduced to 82%.

If the player holds a Middle Pair, and the other player holds one High and one Low card, the probability for the first to win is about 71%. This percentage is even lower in the cases when the first player holds two High cards, and their opponent – two Low Cards. The probability of winning equals 55% when the player has two High Cards, while their opponent holds a Low Pair.

Post-Flop Probabilities

Of course, there is a chance for a certain event to occur while playing certain starting hands. Players should be aware how to take the best advantage of them without overvaluing them what is normally the case with suited cards. Unfortunately, such cards do not make flushes quite often. The same also applies to pairs, which make a set on the flop in only 12% of the time.

When it comes to the probability that certain starting hands will occur at the flop, players could be interested to check the information below.

The probability that Non-pairs will pair at least 1 card equals 32%, which makes the odds 2 to 1. When it comes to two suited cards that could make a flush, the odds are pretty small – 15 to 1, while the probability is only 6.50%. The probability of two suited cards to flop a flush is 0.85%, as the odds amount to 118 to 1.

Players are provided with a 10.90% probability of two suited cards flop a four flush, which means that the odds would equal 9 to 1. The probability of a pair flopping a set, on the other hand, is 12.00%, and the odds for that to happen amount to 8 to 1. And last but not least, the probability for a pair to flop four of a kind is 0.25%, making the odds 400 to 1.

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