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Mathematics can be used in many different situations; however, they are most commonly used when a player is on a draw such as a flush or straight draw.
If an opponent makes a bet and you are on a draw, you are faced with the decision of whether or not you should call to try and complete the draw by the next card, or fold and let your opponent take the pot.
In this situation a player that has good knowledge of poker mathematics will always know whether or not to call, whilst a player that has no knowledge of mathematics will be unsure.
Players who are unfamiliar with poker odds will make an educated guess on whether or not they should call. If the bet is large, they may feel that it is too expensive to try and catch the right card, but if the bet is small they will be more inclined to call.
On the other hand, a player that can use poker mathematics correctly will be able to work out the pot odds they are getting on the hand and act accordingly.
Pot odds take into account the amount your opponent has bet in relation to the pot, and the likelihood of completing your draw to inform you about whether or not you should call or fold.
There are other situations that incorporate mathematics a little more loosely, but still incorporate them nonetheless.
If you have no concrete evidence from the way the hand played out about whether or not your opponent has a better hand than you, you can use mathematics to determine whether or not you should call.
First of all you should estimate that probability that your opponent is bluffing and holds a worse hand than you. Lets say that:.
Let's assume your couch has four cushions. How many combinations can you arrange them in? The answer is 4! Any scientific calculator should have a factorial button, usually denoted as x!
The total number of ways to arrange 52 cards would be 52! Assume you want to form a committee of 4 people out of a pool of 10 people in your office.
How many different combinations of people are there to choose from? The answer is 10! The general case is if you have to form a committee of y people out of a pool of x then there are x!
For the example given there would be 10! You could consider the first four as the committee and the other six as the lucky ones. However you don't have to establish an order of the people in the committee or those who aren't in the committee.
There are 4! By dividing 10! The combin x,y function in Excel will tell you the number of ways you can arrange a group of y out of x. Now we can determine the number of possible five card hands out of a 52 card deck.
The answer is combin 52,5 , or 52! If you're doing this by hand because your calculator doesn't have a factorial button and you don't have a copy of Excel, then realize that all the factors of 47!
This is an area where our intuition may mislead us. But in reality, we don't even need to be a favourite in order for calling to be correct.
Call or fold? Hopefully, our instinct tells us to call this time. We don't care in the slightest that we will lose the majority of the time.
Our original question is clearly a less extreme scenario and a little more realistic, but the same principles apply. So, how often do we need to win?
So, how much of the total pot would we be investing with our call? More traditional gamblers prefer to describe pot-odds in the form of a ratio.
This format is how we are usually told our odds, assuming we went to a bookie to place a sports bet. In the above example, our odds can also be referred to as three-to-one.
Our odds are , which can be simplified to divide both numbers by 5. Most old-school poker players will describe pot-odds this way, although it's actually simpler to consider our pot-odds in percentage format.
There is no inherent advantage to using ratios or percentages. The reason we describe pot-odds as easier to calculate in percentage format is that in most cases, we will be comparing our pot-odds to our poker equity to establish whether we have a profitable call.
Therefore, the odds of getting any Ace as your first card are 1 in 13 7. For example, if you receive an Ace as your first card, only three other Aces are left among the remaining fifty-one cards.
Therefore, the odds of receiving another Ace are 3 in 51 5. Check out CORE and learn poker in the quickest and most systematic way:.
In order to find the odds of getting dealt a pair of Aces , we multiply the probabilities of receiving each card:.
Many beginners to poker overvalue certain starting hands, such as suited cards. We recommend you print the chart and use it as a source of reference.
If you do see a flop, you will also need to know what the odds are of either you or your opponent improving a hand. One common occurrence is when a player holds two suited cards and two cards of the same suit appear on the flop.
The player has four cards to a flush and needs one of the remaining nine cards of that suit to complete the hand.
The player counts the number of cards that will improve his hand, and then multiplies that number by four to calculate his probability of catching that card on either the turn or the river.