Poker is a card game that has gained faithful crowds of players and fans over the years. Numerous international tournaments are played. There are no cases there. And although many people think that poker is a typical random game, it is actually different. Online poker in Australia It is becoming more and more popular because it excites and is public. It is much easier to play online than in person. There are really many possibilities, from the game at one table, after several games conducted in parallel. Regardless of which variant we choose, it is worth knowing what card systems are difficult to get. We present the 5 weakest systems and the chances of obtaining them, which result from the principles of mathematics. Their knowledge will certainly facilitate the game and bring closer to victory.

High card

Mathematics is inexorable for the so -called high hand. This type of system is simply such a list of cards that gives you a chance to complete your hand, to one variant. For example, if we have 2, 5, 7, 10, q, we can assume that thanks to this we can easily choose the missing cards and arrange a variant, otherwise it can't be. However, mathematics clearly indicates that the chances of it are rather slim.

The probability in a classic poker is calculated as follows:

P (high - card) = 1317888 - 10200 −5108 −36 −42 598960

Which gives you a chance in the order 50,11%.

For example, in Texas Hold'em, the chance to get a pair is calculated from the formula:

P (high - card) = 1499 * (47 - 756 - 4 - 84)

Which corresponds to 23 294 460 hand combinations, giving a probability at the level 17,4%.

One pair

A couple, or two identical cards (from different colors) are a system that seems to be the simplest to get. Remember, however, that its value is also important. It is best to have a few aces on your hand. How does mathematics see this?

In the game for five cards, the chances of getting a couple are calculated from the formula:

P (1 to) = 1 098 240/2 598 960

Which gives a probability of a row 42,25%.

However, in the case of Texas Hold' the pattern is used:

P (1 to) = [(13/6) - 71] 6 * 6 * 990

And in this game the chances are a bit more because 43,8%.

Two couples

A slightly stronger layout, because consisting of two pairs, is also more difficult to obtain, because it requires collecting four cards. Mathematics is merciless for him, because even knowing that this is the second system, it is still difficult to get.

The probability of this system in a classic poker is calculated from the formula:

P (2 pary) = 123 552 / 2 598 960

However, the chances of getting this hand only take 4,75%.

In Texas Hold', the pattern is used:

P (2 pary) = [1277 * 10 * [6 * 62 + 24 * 63 + 6 * 64]] + [(13/3) (4/2)^3 (40/1)]

Who calculates the chance for a pair up to 23,5%.


The system is much more stronger, i.e. three cards with the same elders (three kinds). And although they require gathering fewer cards than two pairs, they beat them. But what does it look like from the point of view of mathematics?

To calculate the likelihood of this hand, a formula is used:

P (3 type) = 54 912/2 598 960

In the classic hand, five cards are the chances of getting three 2,11%.

For comparison, in Texas Hold' the pattern is used:

P (3 type) = [(13/5) - 10] * (5/1) * (4/1) * [(4/1)^4 - 3]

It shows that the chances of getting this hand are 4,83%.


The statement closes with the Strit, i.e. the acquisition of five cards following, for example, 2, 3, 4, 5, 6, collected from different colors. This is a very similar arrangement to poker. This is a strong hand for which mathematics is raw.

What is the chance to get it, we'll find out using the pattern:

P (Strit) = (10240 - 36 - 4) / 2598960

And the probability for a classic poker is only 0,76%.

A pattern is used for Texas Hold'

P (Strit) = [217 * [47 * [47 - 756 - 4 - 84]] + [71 * 36 * 990] + [10 * 5 * 4 * [256 - 3] + 10 * (5/2) * 2268]

Which gives you a chance 4,62%.


Mathematics does not lie, it is fully objective, and the most true calculations. It is not difficult to notice that getting these systems - and the weakest hands in the whole game - is very difficult. And now let's think how low the chances of getting much stronger hands, such as full, color or royal poker. That is why playing poker is based on numerous strategies and emotional intelligence, because only happiness and entrusting everything to fate is very illusory. We invite you to read the article about it how much is worth spending on a poker game.

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