Poker Math for Beginners
Not surprisingly, poker math (let alone terminology) may seem intricate and convoluted to novice players. It can appear so perplexing that one might struggle to understand all concepts fully. However, in truth, there is nothing inherently complex about them. This section addresses articles that cover mathematical aspects of the game in simple and understandable language, so even people who are bad at maths will comprehend everything. You can explore all the provided materials or directly delve into the topic that piques your interest.
Understanding the basic concepts and principles is a pivotal factor that sets winning professionals apart from amateurs. Your game strategy will be vague without the ability to calculate your hand equity and pot odds. Any information becomes clearer when accompanied by examples; therefore, we will demonstrate a hand with a thorough mathematical analysis.
When Should You Use Poker Math
People new to the game all ask the same question: "Is there a mathematical way to play poker?" And the answer is unequivocally yes. Maths first comes into play when you need to calculate the probabilities of your hand improving and decide whether it's profitable to try to catch your outs concerning the pot odds. At the same time, we should not assume that individuals who do not rely on mathematics will not be successful. Nonetheless, applying certain principles can significantly improve your game and give you an edge over opponents who neglect them.
Players make decisions based on two factors:
- Outs – specific cards that can help them improve their hand.
- Pot odds – the ratio between the bet they face and the current pot.
In order to enhance your understanding of calculation principles, let's examine the theory in practice. Suppose we are playing NL $0.50/1.00 with the following scenario:
- Hero in the button (BU) with K♣ 9 ♣, raises to $3
- SB: fold
- BB: call $2
Pot size on the preflop: $6.50
- Flop: Q♣ 8♣ 2♥
- BB: bet $3
What decision should Hero make? 🤔🤔🤔
Counting Your Possible Outs
It is best to start learning poker mathematics with Texas Holdem since players hold only two cards. When calculating the number of outs, we proceed from how many pieces are left in the deck and which can improve our hand.
Getting back to the example above, Hero has the second-strongest flush draw. They also have an overcard – K (king). If any K appears on the turn or river, Hero will beat their opponent, provided they hit just a single pair on the flop. So, how many cards can improve Hero's hand?
- Flush – there are 13 clubs in the pack, and we see 4 of them (two on the board and two as Hero's pocket cards). Nine possible outs (clubs) are still in the deck, and they can give Hero a flush.
- K – there are four Kings in the deck, and Hero holds one of them. Hence, those three kings remaining in the pack can improve Hero's hand.
Conclusion: Hero has nine outs to complete their flush and three outs for a King, which adds up to 12 outs.
The rule of 4 and 2
To calculate the percentage of winning your hand, multiply possible outs on the flop (before the turn) x4 and on the turn (before the river) x2. This method offers a quick and easy way to estimate your chances of emerging victorious in the current match.
In our case, Hero has 12 outs on the flop. By applying the given rule, we can quickly determine that the probability of improving their cards is 12 (outs) x 4 = 48%. Well, the exact percentage is 46.7%, but the rule gives us fairly close numbers.
If Hero doesn't improve on the turn, their probability of hitting one of the outs on the river will be 12 (outs) x 2 = 24% (or, more precisely, 27.3%).
Probabilities of hand improving on the flop and turn
|Number of outs||Chances to win on the flop |
|Actual chances to win on the flop||Chances to win on the turn |
|Actual chances to win on the turn|
The x4 and x2 rule does not provide an exact value of your hand equity, but it helps quickly and easily assess your approximate chances of improvement. Don't hesitate to apply it in your game 😉
These outs have the potential to strengthen your combination, as well as make your opponent's hand even more powerful. To identify which cards are not favourable for you but beneficial for your opponents with accuracy, you should competently approach to estimating their range.
Let's use the previous hand as an example: Hero holds K♣ 9♣, and the flop comes down Q♣ 8♣ 2♥.
What cards could Hero’s opponent have when making a donk bet?
- The player in the BB could have cards like KQ, K8s, and K2s. Therefore, even K hitting the turn or river may not improve Hero’s hand.
- It is also possible that the rival holds eights or deuces, and considering the flop, they managed to hit three-of-a-kind. Afraid that someone may complete a flush draw on further streets, they bet themselves. In this case, K may not be helpful for Hero.
- Additionally, the opponent could hold A♣ x♣ and thus has a stronger flush draw.
Discounted outs have the power to strengthen your opponent's hand. So do not relax and remain vigilant at all times 🧐
The math behind poker implies the following: to play profitably, you must correctly assess your opponents’ ranges when counting outs. Now that you know your chances of making a better hand, it’s necessary to understand whether attempting to catch your outs will be profitable for you relative to the existing pot.
Quick Guide to Pot Odds
As mentioned above, this is the ratio between the current pot size to the required bet amount for a call. When calculating pot odds, we aim to know how much money we can win and how much we need to bet for that.
What are Hero’s pot odds in the given hand?
Total pot on the flop is: $6.50 + $3 (opponent's bet) = $9.50
Hero must contribute $3 to see the turn card and potentially win $9.50. This gives pot odds of 3 to 1. For calling in this hand to be profitable, Hero only has to win 1 out of 3 times (25% of cases).
Hero should call in this spot, as their chances of improving in the ongoing game exceed the pot odds. This decision is advantageous and valuable in the long run:
- Chance of improvement = 48% (46.7%)
- Required pot odds for a profitable call = 25%
Reverse implied pot odds
When evaluating your implied odds, you determine how much and how frequently you will win if you catch necessary outs to complete your draw. Reverse implied odds give you an understanding of how much you might lose if you hit your draw but end up with a weaker combo compared to your opponent. Calculating RIPO is similar to calculating regular IO. Players can only continue playing with implied odds if their actual pot odds are favourable. It would be unwise to chase your draw if they are poor.
In order to play a poker hand appropriately in terms of mathematics, it is necessary to do the following sequence of actions:
- determine the strength of your hand;
- count your outs;
- discount any outs that could also help make your opponent's combination better;
- calculate your pot odds;
- make a favourable decision;
Although novices may find this sequencing too complicated, you will execute these steps automatically and make sound decisions as your skills and experience grow.
Bear in mind that poker is a game of skill, psychology and mathematical probabilities, rather than pure luck. Every time you decide on an action, you should be confident that you are making profitable moves in the long run. Only then can you achieve consistent profits. Our easy-to-understand mathematics of poker with examples will quickly turn you from a neophyte to a winning pro!
Mathematics plays a fundamental role here, as poker strategy is based on the probabilities of game events. This discipline allows us to determine our chances of winning in the ongoing hand, proceeding from our hole cards and those on the table. Additionally, understanding mathematical concepts enables players to make informed decisions, considering factors such as pot size and opponents' betting patterns.
No equations, integrals, or logarithms are required 😅 Often, it will be enough to quickly count in mind as the hand progresses, but there are also more complex situations where you may need to use various calculators to determine chances.
Multiplying your outs by 2 and 4, gives you the chances of your hand improving on the turn and river (i.e., the likelihood of an out hitting either street). You can also easily calculate how certain actions will be theoretically beneficial. For instance, you can assess whether it's advantageous to make a call in the current game or if it's better to look for a different spot.