Probability in Poker

Playing poker isn’t just about luck, as many think. It’s about using math and statistics. Although winning isn’t guaranteed, following a solid strategy based on probability in poker and odds can give you an advantage. Understanding poker math is crucial for knowing when and how to play your cards. It’s important to recognize the different types of poker hands and adjust your gameplay accordingly. Poker has three variables that we must focus on:

1. Outs: These determine the percentages in poker.
2. Pot Odds: Understanding the odds related to the pot.
3. Your Equity in the Pot: Calculating your share in the pot.

Poker in Probability — Poker Hands Probability

In poker, a player can create 2,598,960 different sets of 5 cards. Check out the poker probability chart below. It breaks down how these sets form different types of hands.

• Royal Flush: This is super rare, only happens 4 times in 2,598,960 tries. It’s like a 0.000154% chance, about 1 in 649,740 hands.
• Straight Flush: More common than a Royal Flush. It happens 36 times in 2,598,960 tries, which is a 0.00139% chance, like 1 in 72,193 hands.
• Four-of-a-Kind: This one’s more common, happening 624 times in 2,598,960 tries. It’s around a 0.0240% chance, like 1 in 4,165 hands.
• Full House: Happens about 0.1441% of the time, like 1 in 694 hands.
• Flush: There are 5,108 ways to get a Flush. It’s around a 0.1965% chance, like 1 in 509 hands.
• Straight: Happens 10,200 times in 2,598,960 tries. It’s around a 0.3925% chance, like 1 in 255 hands.
• Three-of-a-Kind: Happens 54,912 times, like 1 in 47 hands.
• Two Pair: With 123,552 possible combos, it’s around a 4.7539% chance, like 1 in 21 hands.
• One Pair: Pretty common, happening 1,098,240 times, like 1 in 2.4 hands.
• High Card: The most common, happening 1,302,540 times, like 1 in 2 hands.

Poker Hands Probability Chart

Understanding Chances in Poker

Poker involves specific odds that you should know about:

• Getting Certain Hole Cards in Poker
• Chances of making a strong hand after the first cards are revealed

Getting Certain Hole Cards in Poker

Let’s say you have AK. You can create 16 combinations by multiplying 4 Aces by 4 Kings. Out of these 16 combinations, there are 4 suited combinations and 12 unsuited combinations for unpaired hands. Pocket pairs, on the other hand, have six combinations each. Understanding these combinations helps in calculating probabilities.

For Pocket Aces, out of 1,326 combinations, you’ll get this hand once every 221 times. Specifically suited hands have 4 combinations each. Unpaired hands of specific values show up less often than pocket pairs. For example, an AK combination appears approximately once every 332 hands. This means you’ll see more AA cards than AK cards.

The Odds of Making a Hand after the first cards are revealed

Knowing the chances of forming a good hand based on the initial cards is crucial. Here’s a chart depicting the probabilities of different hands after the flop, based on your initial cards:

Unpaired Cards forming a Pair on the Flop: 29.0% chance, odds are 1 in 3.5.

Pocket Pair forming a Set on the Flop: 11.8% chance, odds are 1 in 8.5.

Connected Cards forming a Straight on the Flop (like JT thru 54): 1.3% chance, odds are 1 in 77.

Suited Connectors forming a Flush on the Flop: 0.8% chance, odds are 1 in 119.

Probability in Poker — The Basic Rules

Instead of constantly checking a chart for probabilities related to your hand and pot odds, here’s a handy trick:

Multiply the number of outs (cards that can improve your hand) you have after the flop by 4. This gives you a good estimate of the chances to complete your hand by the turn or river (the next two cards).

If you’re looking at the turn, multiply your outs by 2 for a clear estimate of the chances of improving your hand with the next card.

Now, adjusting your outs based on potential better hands is essential. For instance, if you anticipate a higher flush draw or a scenario where the board could give you a flush but your opponent might have a full house, you might slightly decrease your “outs” count (for example, going from 9 to 8.5). This tweak considers these possibilities when weighing against your pot odds and deciding your next moves in the game.

Determining the Probability of Draws

How do we figure out the chance of getting a draw? Let’s start by counting the possible outs. Consider all the cards that could improve your hand.

Next, use the “Rule of Two and Four” to estimate your odds of hitting an out. If both the turn and the river are yet to come, multiply your outs by four to get your chance.

When both the turn and river are pending, multiply the outs by four for the percentage chance. If only the river is left, multiply the outs by two.

However, this rule isn’t entirely precise. But it’s a straightforward way to estimate probabilities without diving into complex math.

Examples of Draw Probabilities

Let’s illustrate with a few examples how to calculate the probability of hitting a draw:

1. You hold 7-8 cards of different suits, and the flop shows 9-10-A. What’s the chance of hitting a straight? You’ve got eight outs – 6-6-6-6-J-J-J-J – so multiply these by four because the turn and river are yet to come. That gives you a 32% chance.
2. You have A-K of clubs, and the board displays 2-5-9-10, with two clubs. Only the river is pending. You’ve got a total of nine outs, so multiply them by two, giving you an 18% chance.

It’s advisable to keep practising calculating your outs so you can do it swiftly in the middle of a game. Online poker software can also assist in a more precise calculation. If you plan to use specific poker software, ensure your poker platforms support it before purchasing.

The Significance of Probability in Online Poker

If you’re new to poker, you might wonder why probability matters in online games. Unlike in physical games, reading tells on other players is limited online. So, understanding the likelihood of specific hands is crucial. Playing with correct math gives you the best shot at making money over time.

Strong players use math, and to stay competitive, you must too. While you might get away with less understanding at lower stakes, higher-level games heavily involve mathematical skills. To excel, you must grasp poker probability.

Coping with Unfavorable Outcomes

In dealing with probabilities, remember that even low-probability outcomes can happen. You might have a 99% chance of winning, yet the last card could change everything, leading to a “bad beat.”

Experiencing a bad beat might tempt you to abandon strategy for luck. This shift, called going on tilt, can be detrimental. Trust in the math; it works over time. Having faith in probability will lead to long-term success.

If you feel you’re tilting, take a break. Step away from the game to regain composure and focus. Returning with a clear mind often helps maintain a strategic approach.

Converting Pot Odds into Percentages

Now that we know how to figure out pot odds and the chances of improving our hand, it’s time to combine these to decide if calling is the right move.

When you use the “Rule of 2 and 4,” you’ll end up with a percentage while calculating pot odds gives you a ratio (like 2 to 1 or 2:1).

So, being able to switch percentages into ratios and vice versa is crucial if you want to quickly decide if a call is worthwhile.

Let’s start by understanding how to turn percentages into ratios.

Percentages into Probabilities:

If you use the “Rule of 2 and 4” with 9 outs and 2 cards remaining, there’s about a 36% chance of getting a flush. Through a simple calculation, we can figure out that roughly 64% of the time, our draw won’t be completed.

When converting percentages to ratios, always format them like this:

(probability of not improving your hand) : (probability of improving your hand)

Doing this will give us a ratio of 64:36, or about 2 to 1 – a ratio we can easily compare to our pot odds. The more you practice comparing pot odds to percentages, the better you’ll get at evaluating your hand’s chances of improvement.

Probabilities into Percentages:

Let’s flip the scenario and see how we can change pot odds into percentages. Imagine someone bets half the pot, offering 3 to 1 on a call (betting ₹50 into a ₹100 pot. The pot becomes ₹150, and you need to call ₹50 to join, resulting in pot odds of 3 to 1).

By converting this ratio into a fraction, we can easily find the percentage, as shown below:

(price you need to call/price you need to call + money already in the pot)

In this case, the amount we need to pay is ₹50. So, the total (amount to call) + (money already in the pot) equals ₹50 + ₹150, resulting in a fraction of ₹50/₹200.

50/200 = 0.25, which easily becomes a 25% percentage by multiplying 0.25 by 100.

This percentage, in relation to your hand’s strength, indicates that you’d need more than a 25% chance of winning the hand to make a profitable call.

If this still seems complex, don’t fret! The more you practice calculating odds, the more confident you’ll become.

Summing Up Probability in Poker

If you want to boost your chances of winning at poker, get comfy with understanding the odds and probabilities in the game. Know about outs and figure out your chances of improving. Quickly connect these with the pot odds you’re offered to decide if calling makes sense.

For more details on pot odds and how to bet, check out our Guide on Bet Sizing.

Also, remember, you don’t always have to just call when you’re waiting for a good card. Sometimes, it’s smart to bet or raise. This way, you might win by getting a better hand or making your opponent fold.