This post works with 5-card Poker hands drawn from a standard deck of 52 cards. The discussion is mostly mathematical, using the Poker hands to illustrate counting techniques and calculation of probabilities

Poker Odds Calculator Excel Formula
Poker Odds Calculator Excel Spreadsheet
Poker Odds Calculator Excel Spreadsheet

Working with poker hands is an excellent way to illustrate the counting techniques covered previously in this blog – multiplication principle, permutation and combination (also covered here). There are 2,598,960 many possible 5-card Poker hands. Thus the probability of obtaining any one specific hand is 1 in 2,598,960 (roughly 1 in 2.6 million). The probability of obtaining a given type of hands (e.g. three of a kind) is the number of possible hands for that type over 2,598,960. Thus this is primarily a counting exercise.

Different kind of online casino Canada free spins There are, different types of free spin casino bonuses you’ll be getting from our review. It might depend on factors like different online casino brands and different games, but it all comes down to just giving you free spins either on first deposit or without any deposit whatsoever. Spin Casino also prides itself on being regarded as the top online blackjack destination in Canada, making it the perfect place to refine your blackjack strategy. Put the theory to the test today and you could reap the rewards instantly. Free Spins Casino: Canada 2021. Online casinos in Canada have plenty of free spins for new and existing players. On this page, we've gathered all the best online casinos for free spins. While casinos offer many kinds of bonuses, casinos like LeoVegas and Quatro Casino are well known as the places to play for extra spins. You may even get no. A free spin is a chance to spin the reels on an online slot for free. Free spins give you a chance to win real money with no deposit required. Many casinos online offer deposit bonus spins all the time. All you have to do is to pick your favourite online casinos Canada.5 new free spins. Online casino spin.

The chance to have any 5 cards in poker is C(52,5) = 52! / 5!(52-5)!, so it is any 5 cards from all 52 possible cards. I tried using =prob(52,5,1,52) function, but I have no idea how to write it to get the correct outcome of 2598960. Poker Hand Calculator For Poker Ranges. To fully utilize the poker hand calculator, follow the steps below: 1. You obviously need a poker room to play. Make sure to check out one of the best poker rooms, William Hill. So, now you're playing at one of the poker rooms. You also have our range calculator available. Use first Free Poker Calculator on Windows 8! It can show: - winning and drawing probability - probability of having a certain combination Poker calculator has usable interface for maximum comfort and quick data input. To achieve better results it must be used with Enterra Poker software! This post works with 5-card Poker hands drawn from a standard deck of 52 cards. The discussion is mostly mathematical, using the Poker hands to illustrate counting techniques and calculation of probabilities Working with poker hands is an excellent way to illustrate the counting techniques covered previously in this blog - multiplication principle, permutation. Also informally referred to as odds calculators, these mostly browser-based tools are the oldest and simplest aids to understanding some basic poker math. They calculate the probability of a hand winning against one or more other hands, just like the percentages that show up in televised poker graphics.

___________________________________________________________________________

Preliminary Calculation

Usually the order in which the cards are dealt is not important (except in the case of stud poker). Thus the following three examples point to the same poker hand. The only difference is the order in which the cards are dealt.

These are the same hand. Order is not important.

The number of possible 5-card poker hands would then be the same as the number of 5-element subsets of 52 objects. The following is the total number of 5-card poker hands drawn from a standard deck of 52 cards.

The notation is called the binomial coefficient and is pronounced “n choose r”, which is identical to the number of -element subsets of a set with objects. Other notations for are , and . Many calculators have a function for . Of course the calculation can also be done by definition by first calculating factorials.

Thus the probability of obtaining a specific hand (say, 2, 6, 10, K, A, all diamond) would be 1 in 2,598,960. If 5 cards are randomly drawn, what is the probability of getting a 5-card hand consisting of all diamond cards? It is

This is definitely a very rare event (less than 0.05% chance of happening). The numerator 1,287 is the number of hands consisting of all diamond cards, which is obtained by the following calculation.

Lotto casino game. The reasoning for the above calculation is that to draw a 5-card hand consisting of all diamond, we are drawing 5 cards from the 13 diamond cards and drawing zero cards from the other 39 cards. Since (there is only one way to draw nothing), is the number of hands with all diamonds.

If 5 cards are randomly drawn, what is the probability of getting a 5-card hand consisting of cards in one suit? The probability of getting all 5 cards in another suit (say heart) would also be 1287/2598960. So we have the following derivation.

Thus getting a hand with all cards in one suit is 4 times more likely than getting one with all diamond, but is still a rare event (with about a 0.2% chance of happening). Some of the higher ranked poker hands are in one suit but with additional strict requirements. They will be further discussed below.

Another example. What is the probability of obtaining a hand that has 3 diamonds and 2 hearts? The answer is 22308/2598960 = 0.008583433. The number of “3 diamond, 2 heart” hands is calculated as follows:

One theme that emerges is that the multiplication principle is behind the numerator of a poker hand probability. For example, we can think of the process to get a 5-card hand with 3 diamonds and 2 hearts in three steps. The first is to draw 3 cards from the 13 diamond cards, the second is to draw 2 cards from the 13 heart cards, and the third is to draw zero from the remaining 26 cards. The third step can be omitted since the number of ways of choosing zero is 1. In any case, the number of possible ways to carry out that 2-step (or 3-step) process is to multiply all the possibilities together.

___________________________________________________________________________

The Poker Hands

Here’s a ranking chart of the Poker hands.

The chart lists the rankings with an example for each ranking. The examples are a good reminder of the definitions. The highest ranking of them all is the royal flush, which consists of 5 consecutive cards in one suit with the highest card being Ace. There is only one such hand in each suit. Thus the chance for getting a royal flush is 4 in 2,598,960.

Royal flush is a specific example of a straight flush, which consists of 5 consecutive cards in one suit. There are 10 such hands in one suit. So there are 40 hands for straight flush in total. A flush is a hand with 5 cards in the same suit but not in consecutive order (or not in sequence). Thus the requirement for flush is considerably more relaxed than a straight flush. A straight is like a straight flush in that the 5 cards are in sequence but the 5 cards in a straight are not of the same suit. For a more in depth discussion on Poker hands, see the Wikipedia entry on Poker hands.

The counting for some of these hands is done in the next section. The definition of the hands can be inferred from the above chart. For the sake of completeness, the following table lists out the definition.

Definitions of Poker Hands

Poker Hand	Definition
1	Royal Flush	A, K, Q, J, 10, all in the same suit
2	Straight Flush	Five cons

Poker Odds Calculator Excel