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#Pokermath #Math and Poker #Poker Strategy #Poker Mathematics
Is poker a game of skill
or pure luck? This question resulted in 💪 extensive and profound discussions in North
America 15 years ago, because the answer directly affected the legalization process of
online 💪 poker in North American countries.
The answer lies in the math behind the poker
games. If the statistical results prove that 💪 some players have a significantly higher
probability of winning than other players, then poker is a game of skill.
Before we
💪 continue, let’s go over a few facts:
#1. In Texas Hold'em, 52 cards are used, including
4 suits and 13 points. 💪 In other words, we have clubs (♣), diamonds (♦), hearts (♥), and
spades (♠). Each suit includes an Ace, a 💪 King, Queen and Jack, while numerals range
from the Deuce (Two) to the Ten.
#2. Each player changes their relative position 💪 as
frequently as the other players. In other words, everyone will take turns playing as
the small blind, big blind, 💪 UTG, etc. Due to differences in time or other situations
such as someone leaving their seat during the game, the 💪 frequency may not be 100% equal
for everyone, but it remains roughly the same.
#3. The rules of the poker game 💪 and the
venue are not biased and every player present obeys the same set of rules.
#4.
Regardless of other factors, 💪 if all five community cards are dealt, the possibility of
winning with a leading starting hand will be much higher 💪 than that of weaker starting
hands. This has been proven through millions of computer simulations.
Why Poker Math
Matters?
It is important 💪 because the game is fair to every player, presenting everyone
with an equal chance of winning. By understanding poker math, 💪 you can improve your
chance of winning through your skills.
In the Texas Hold'em game, there are thousands
of possibilities for 💪 each hand. You only need to know that all possible results are
based on a limited combination of 52 cards.
For 💪 Example: Your starting hand is AA, and
you know that there are two Aces in the remaining 50 cards. Among 💪 the remaining 48
cards, there are 4 suits and 12 cards smaller than Aces. You don't have any information
about 💪 where these cards are before the flop, but you will gradually get more
information as the game progresses.
#Pokermath #Math and 💪 Poker #Poker Strategy #Poker
Mathematics
Moving on, when the flop shows you A44, you now have a full house. You also
💪 know that only a hand with four 4s that can beats you here. Since there are already two
4s on 💪 the table, the probability that your opponent holds the other two 4s is 1 in
1326. This probability is too 💪 low, so every time you encounter this situation, you
should treat your card as a nut hand.
How do we get 💪 the probability of 1 in 1326?
Think
this way: Get 2 cards out of 52 cards at random, and the probability 💪 of each specific
combination is 1 in 1326. The first card you get can be any of the two 4s, 💪 which is 2
out of 52, and the second card is the probability that the remaining one will appear in
💪 the remaining 51 cards, which is 1 in 51. The multiplication results in 1 in 1326,
which is our answer.
Poker 💪 Math: Basic and Practical
Many beginners have a
misunderstanding about poker mathematics, thinking that basic knowledge is the answer
or conclusion. 💪 They tend to think that they can't perform complex calculations in the
game, so they simply don't learn it, or 💪 just follow the math results to play the
game.
Let's put it this way, the basic knowledge of poker math should 💪 be the basis of
your strategy. Under the table, it should be the theoretical basis for your when you
construct 💪 or review your game strategies. The general logic is this: after you learn
about poker math, practice and verify what 💪 you learn during games then build your own
set of self-consistent strategies, execute them in the games, and keep verifying 💪 and
modifying your strategy back and forth to improve your skills.
Starting Hand This is
the most basic element in poker 💪 games. We have already said that some starting hands
are more advantageous.
This also means that in your first poker math 💪 lesson, you should
learn the starting hand first. Entering the game when you hold stronger starting hand
could win you 💪 the first advantage.
If you don't remember anything after reading this
article, at least remember this: tightening your hand range can 💪 also significantly
improve your game results. Position It is difficult to directly link the position
factor with poker math knowledge. 💪 But it is common sense that acting in later position
is more dominant in any poker game. We will talk 💪 about expected value later in the
Advanced Poker Math section. You just need to remember that the later the position, 💪 the
easier it is for you to achieve the expected value of your hand. This will make your
mathematical advantage 💪 manifest in your performance in the long term. Drawing Odds and
Outs An out refers to which of all the 💪 undistributed community cards can help you win.
This may also be the only content in the game that needs to 💪 be calculated on the spot.
You need to calculate what are the odds that you draw the cards you want, 💪 in order to
accurately know your success or failure ratio so that you are able to make a profitable
decision.
Suppose 💪 that you have KQ in your hand, J and 10 are on the table, and the
card has been dealt 💪 on the turn. Then any 9 or Ace on the river will give you a
straight. You have seen 6 💪 cards, and there are 46 cards remaining unknown. The cards
you want may be in the hands of other players, 💪 or among the undistributed community
cards. This is not important. No matter what, it is unknown to you.
In other words, 💪 if
the same situation occurs 46 times, you will hit a straight hand 8 times and miss the
other 38 💪 times.
During the game, you need to pay attention to which cards are good for
you and vice versa. Knowing the 💪 proportional relationship between these cards is very
important for you to make profitable decisions. Think About the Pot After you 💪 learn
about the outs, now you need to take the size of the pot into account and determine
whether your 💪 decision is profitable by calculating how much you can win/lose. In simple
words, calculate the odds of getting the outs, 💪 and multiply this by the total number of
chips in the pot. Base on the information, decide whether you should 💪 call or fold.
In
the previous example, you know that there are 8 cards that can help you win and you
💪 lose over the remaining 38 cards. So, your losing odds is 38 to 8, which is 4.75 to
1.
Then you 💪 think about how much you need to invest in order to win the pot. Make your
call if the odds 💪 is on your side or simply fold if it is not favorable.
Suppose that
the pot now hasR$100 and you need 💪 to callR$10, then the pot gives you a 10 to 1 chance.
If your losing odds are 4.75 to 1. 💪 Then it is appropriate to call.
On the other hand,
if the pot hasR$100, but you need to investR$40 to continue, 💪 the pot gives you a 2.5 to
1 chance. Again, your losing odds is 4. 75 to 1, therefore, it 💪 is very inappropriate to
call now and you should fold.
You cannot simply check pot odds one time during the
game. 💪 You also need to look at the following community cards. If there are still two
cards not dealt, it means 💪 you still have two chances. In the game, you don't need to
calculate very accurately, you only need to be 💪 able to roughly see the proportional
relationship.
That being said, we have prepared a sheet for you so you can have 💪 a rough
idea:
Advanced Poker Math
Upon hearing the poker math terms like “expected value”, many
beginners instinctively feel resistant. However, the 💪 truth is there is no need to
overly estimate its complexity.
After all, playing poker is not doing scientific
research. We 💪 just use mathematical knowledge to make decisions, and you don’t need to
make complicated calculations at the poker table.
All you 💪 need is to study and
understand the principles. Most of the time, you accumulate experience based on what
you learn 💪 and your poker strategies at the table until you form a subconscious
reaction.
Expected Value:
In short, it means that in hundreds 💪 of games, some result
will appear on average a certain number of times. When you know what your expected
value 💪 is, in the long run, it will be reflected in your results.
The goal of the game
is to make as 💪 many decisions with high EV as possible, while minimizing or completely
avoiding decisions with low EV.
Almost all actions in a 💪 poker game have their expected
value, and only a few elements depend on the situation.
• If most people at the 💪 table
are stronger than you, then overall this is a scenario of negative expected value.
• If
most people at the 💪 table are weaker than you, then overall this is a positive expected
value scenario and you will win a lot 💪 in the long run.
But the problem is that you
can't know who is strong and who is not, at the 💪 minute you sit down at the table.
Certain scenarios in the game are easier to judge the expected value, while 💪 there is
also less obvious information, unless you systematically study and observe your
opponents for a certain period of time, 💪 otherwise they remain very uncertain for
you.
If you do not have a systematic and comprehensive study and training, you would
💪 have to classify your own experiences so that next time you encounter a similar
situation, you could generally remind yourself 💪 whether the current situation is
beneficial to you.
Let me explain to you how to judge your current expectations through
a 💪 few examples.
Example 1:
You are on the turn now. Your opponent's about to bet and
you are only one card short 💪 of hitting a flush. The pot isR$400 and your opponent
betsR$100.
You can't see the river if you don't call theR$100. 💪 When you lose you
loseR$100, when you win you getR$600 back. This includes: theR$100 you called, the
originalR$400 in the 💪 pot along with theR$100 your opponent bet.
Many beginners will
confuse one thing that they think the pot still have their 💪 own input before the turn.
But whenever you face a decision, you should calculate its expected value
independently. Once all 💪 the chips are put into the pot, they don't belong to anyone,
collectively they are called "dead money."
If this situation 💪 happens multiple times,
you may win several times on average. For the convenience of calculations, we use 100
times in 💪 this example .
In this case, you can win 9 times out of 46 times. This means
that 19.56% of the 💪 winning rate, 80.44% of the probability of losing, approximately
equal to 20% and 80%.
If you investR$100, when this situation happens 💪 100 times your
cost sums up toR$10,000. You lose 80 times without any benefit. But you would win the
other 💪 20 times, in which you would get back 20 timesR$600, which comes up toR$12,000.
In other words, you makeR$2000 in 💪 total for these 100 times. An average ofR$20 each
time.
In fact, you will win more than this because we have 💪 not yet counted the river
moves. Maybe after hitting, sometimes the opponent doesn't believe it and will pay you
more.
Example 💪 2:
Assume the same situation above happens but this time you have made a
straight and your opponent is going to 💪 make a flush. The river card has been dealt, the
pot isR$600, and there are three cards of the same 💪 suit among the community cards
now.
The opponent betsR$20 this time. If he hits a flush, then he is going to 💪 win. Even
in this case you still need to call. Do you know why?
You have to call because you
cannot 💪 be 100% sure that your opponent hits a flush. They may also be bluffing or
overestimating their hands, or some 💪 strategic betting defense, while your straight hand
leads in these situations.
Let's see what poker math says.
If you do this 100 💪 times,
your total investment becomes 20 timesR$100, orR$2000.
You win and you getR$640,
including the originalR$600 in the pot,R$20 from your 💪 opponent, andR$20 from your call.
We have already wonR$1920 by winning only 3 times, covering almost all the cost of 💪 100
times.
You only need to win 4 times to start profiting. This is a positive expected
value scenario because after 💪 wining 4 times you reclaimedR$2560, you wonR$560, which
means you winR$5.6 every game.
In other words, even if your opponent bluffs 💪 only 4
times out of 100 times, and you lose 96 times out of 100, it is still profitable for
💪 you to call.
On the river, the larger your opponent's bet, the higher the probability
that you would want him to 💪 bluff. Then you need to collect relevant information about
your opponent to determine his characteristics in order to determine the 💪 positive or
negative of your current decision-making expected value.
You can try to look at all the
cards you have played 💪 in the past thinking about their expected value. It will be a bit
slow at first, but after a few 💪 times you will become more and more proficient, and you
can even see it at a glance.
To Sum Up
#Pokermath #Math 💪 and Poker #Poker Strategy
#Poker Mathematics
In the past ten years of continuous development and evolution of
Texas Hold'em game strategy, 💪 it can be said that the winning players and the losing
players are determined by poker math. Experience is important, 💪 but why not spend some
time to learn some basic poker math knowledge? It can even help you in work 💪 and life.
Hopefully this article can be a stepping stone that leads you to more advanced poker
skills.
Allen W - 💪 Mar 01 2024
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