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Understanding Poker Probability

Poker strategy is not all about sheer luck as people believe it to be. It has a lot to do with math and statistics. While winning a poker game is not in our hands, playing poker according to a correct strategy that follows the poker probability chart and odds will give you an edge over others. Poker math is essential while understanding how and when to play the cards. When looking at a poker deck, you should be familiar with the types of poker hands and play them accordingly.

In this blog, we will delve into the odds of poker and the probabilities associated with the game.

What is Probability?

Probability is a term in mathematics where you calculate the chances that when one outcome over other will occur. For example, a coin has two possible results- heads or tails. The probability that a coin will have heads as the outcome is 50%, and tails as the outcome are also 50%.

Poker Hands Probability

In poker, a player can make a total of 2,598,960 distinct 5-card hands that they can deal with. Let us have a look at the poker probability chart given below, which will show how these combinations will break down into the various ranks of hands.

Standard Odds & Probabilities in a Poker Game

The most common odds in a poker game are:

  • The odds of dealing with certain hole cards.
  • The odds of a made hand flopping.

The Odds of Dealing With Certain Hole Cards in Poker

Suppose you take a hand like AK, you can multiply 4 Aces by 4 Kings, and you can make sixteen combinations break of the AK hand in total- both suited cards and unsuited.

Out of these 16 combinations, there are 4 suits in poker; out of these, 4 will be suited, and the remaining 12 will be unsuited combinations of unpaired hands. In the case of pocket pairs, each value will have six combinations. With this information, you can determine certain events and probabilities of getting a hole card using math.

For Pocket Aces, out of 1,326 total combinations, divide six combinations to see that we’ll receive a particular hand once in every 221 hands. For any specifically suited hand, there are 4 combinations of each holding. You’ll receive non-paired hands pertaining to specific values less frequently than pocket pairs. On average, one in every 332 hands, you will have an AK combination. This means that you’ll have more AA cards than AK.

The Odds of Flopping a Made Hand

How to improve poker odds with hole cards on specific flops? The chart below shows the chances of flopping a made hand (of varying strengths).

Your Hole Cards Flop (Your Hand) Probability (%) Odds

Unpaired Cards- A Pair(Flop Hand)- 29.0% (Probability) 1 in 3.5 (Odds)

Pocket Pair- A Set (Flop Hand)- 11.8% (Probability) 1 in 8.5 (Odds)

Connected Cards- A Straight (Flop Hand) 1.3% (Probability) 1 in 77 (Odds)

(JT thru 54)

Suited Connectors- A Flush 0.8% 1 in 119

Facts To Understand About Poker Probability Calculation

  • The Probability of getting a pair in Poker is ~42%
  • The probability of getting a Full house in Poker is less than 1% or ~0.1441%
  • The Royal flush probability is 1 in 649,740 hands.
  • The Straight flush probability in poker is 1 in 72,193 hands.
  • The probability of getting four of a kind in a poker game is 0.168% only.

Basic Probability Rules Poker

Referring to a chart all the time for every hand to check the probability you have of improving and then relating it to the pot odds is sometimes inconvenient. There is a shortcut for using the following trick to help you calculate the possible hands and improving on them:

  • Multiply the number of outs you have on the flop by 4, and you can get a solid approximation for the possibility of making your hand by the turn or river. (i.e,. with two cards yet to come)
  • By multiplying the number of outs you have on the flop or the turn by 2, you will get a definite approximation for the chances of making your hand on the next card.
  • To improve your hand and to account for the chances of a better one, you are likely to vary the number of outs to play poker. Case in point, if you think that the opponent will have a higher flush draw or if the board pairs giving you a flush and your opponent perhaps a full house, you might lessen your “outs” slightly (e.g., 8.5 outs instead of 9). This adjustment will account for this possibility when relating it to your pot odds and how you should proceed with the hand.

What If I Wanted To Practice Poker Probability Myself?

You can certainly practice poker probability using the shortcut method. To do this, you need to add together the probabilities of specific outcomes occurring, for example:

  • Hitting one of your outs on the turn
  • Hitting one of your outs on the river, but not the turn

EXAMPLE PROBLEM #1: A Normal Flush Draw

To work through a typical poker probability problem, suppose you have a flush draw after the flop and want to simply know the chances of improving to a flush by the river. 

With 4 of 13 cards of the suit being revealed already, there are nine remaining cards (“outs”) that can help you.

And with two hole cards and three flop cards already accounted for, there are 47 unknown cards to you in the deck.

Knowing this, you can do the appropriate calculations and add the results together to determine your chances of making your flush:

  • Odds of hitting your flush on the turn: (9/47) = 19.15%
  • Odds of hitting your flush on the river: (39/47)*(9/46)= 16.23%
  • Odds of making your flush on the turn OR the river: 19.15% + 16.23% = 35.38%

Here, you can see the odds of making a flush by the river after flopping a flush draw is 35.38%. If you take the “shortcut” rule outlined above, you can see that nine outs multiplied by 4 equals 36%, which is pretty close to the exact answer here.

Calculating Probability of Poker Hands Heads-Up

The difference in equity spread in poker is when there is only one opponent versus multiple opponents in a poker hand with you. The equity of everyone’s respective hands against many players will be lower than if it was a heads up because it’ll be divided and spread out among the rest of the players.

Take Pocket Aces, for example. Against the following Villain range for your opponent(s) –

  • Any pocket pair
  • Any suited Ace
  • Any two broadway cards
  • Suited connectors: 54s to T9s
  • One-gapped suited connectors: 86s to J9s
  • Q9s, K9s

Here are the equity percentages that Pocket Aces has against:

  • One opponent: 83.4%
  • Two opponents: 70.6%
  • Three opponents: 60.2%
  • Four opponents: 51.4%

As you can see, the more opponents there are in hand, the lower the chance AA has of winning, which is why it is so advantageous to have these big pairs play out in a heads-up, low-Stack to Pot Ratio.

And for when you have drawing hands in a multi-way scenario, having more opponents may not change the number of outs you have to improve. However, the chances of someone else having a better draw than you or a hand that could later outdraw you certainly goes up with more opponents. 

Additionally, when action is multi-way, it is essential to note that players tend to bluff less and bet more for value if they do bet.

Therefore, considering the last two points, it is crucial always to remember how many opponents are in a hand and determine the best way to play accordingly.

Working Out the Probability of Draws

How does the probability of the draws come to be? First things first, see how many outs are available to you. Think of all the possible cards that will make your hand.

You should then use the “Rule of Two and Four” to determine how much chance you have of hitting an out. If you have both the turn and the river that are yet to come, multiply your number of outs by four to reveal your per

If you have both the turn and the river to come, multiply your number of outs by four to get r your percentage chance of hitting an out. If you only have the river to come, multiply the number of outs by two instead.

Using the above rule isn’t completely accurate. However, it’s the easiest way to work out approximate probabilities without resorting to more complex mathematics.

Examples of Probabilities of Hitting a Draw

Here are a couple of examples to illustrate how to calculate your probability of hitting a draw:

    •  You have 7-8 unsuited as your hole cards, and the flop comes 9-10-A. How much chance is there of hitting your straight? Well, you have eight outs – 6-6-6-6-J-J-J-J – so you take these eight outs and multiply them by four, as the turn and river are still to come. You, therefore, have a 32% chance of hitting your straight.
    • You have A-K of clubs, and the board shows 2-5-9-10, two of which are clubs. Only the river is left to come. In total, you have nine outs, so multiply nine by two, showing you have an 18% chance of hitting your draw.
    • It’s a good idea to continue practicing working out your outs for a while, so you can do so quickly when you’re in the middle of a game. If you’re playing online, you can also find poker software that will do the job for you more precisely. If you do want to use a specific piece of poker software, check that your poker platforms support it before making the purchase.The Importance of Probability in Online PokerIf you’re a new player, you might wonder why probability is so significant when playing online poker. After all, you never see the cowboys in Western movies counting up probabilities on their fingers and spending ages determining their pot odds, do you?Well, math is so important online that there are very few ways to get tells on specific players. This is unlike in physical games, where you’ll be able to look other players in their eyes and ascertain whether they’ve got the hand they’re trying to represent. So, instead, you simply need to consider the chances of them having a specific hand. Over time, if you play online poker using correct math, you’ll give yourself the best chance of making money.
    • It’s also important to use math as all other strong players will be doing the same. You might be able to get away with a poor grasp of poker math when playing a standard game at the very lowest stakes; however, you’ll come across more and more people using math as you advance through the antes. If you want to make it to the top of the game, poker probability is something you absolutely must understand.
    Dealing with Bad Beats

When dealing with probabilities, you have to accept that even outcomes with low probabilities can sometimes occur. You might be 99% favorite to win a hand, but the wrong card on the river could still lead to the player with a 1% chance of emerging victorious. When this happens, it’s known as a bad beat, and this can do terrible things to a player’s game.

It’s effortless to start thinking that luck is against you and that playing the probabilities during poker just isn’t working. This can lead to a player starting to play a different way, often more aggressively and focusing more on luck than statistics. Go too over-the-top, and the player can be considered to be on tilt. This is a hyper-aggressive state of mind when the player calls or raises everything, even if they have a tiny chance of winning.

If you want to avoid going on tilt, you need to remember that poker probability will work over a long period of time. If you’ve got a 75% chance of winning a hand and you lose, you have to look ahead and understand that you have a good chance of making money when in that exact same position in the future – the rule of probability says so. Have faith in the mathematics, and you should find yourself coming out on top in the long run.

If you do think that you’re at risk of going on tilt, give yourself a break. Leave the cash game you’re playing in and head back to the tables in a couple of hours. If you’re in a tournament, take a break for a couple of hands, if possible. You should find that a break allows you to calm down and regain your focus.

In Conclusion

Playing poker is not entirely down to luck, as with a coin flip. Instead, it requires several different skills, including the ability to use mathematics in your favor. If poker players fail to pay attention to poker math, and you’ll probably find your opponents will have a massive advantage over you from the moment you sit down at the table.

Madhuboni Banerjeehttps://www.mpl.live
A graduate in engineering who later completed her post-graduate degree in Mass Media. Writing has always fascinated her, and she wishes to pursue her interest in the same. She wants to discover and write about new themes and topics. She always likes to venture in various writing forms and continues exploring her interest there.

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