Mathematics can be used in poker to work out the probability of certain cards being dealt at any point during the hand. If we are able to work out the probabilities, we can then determine whether or not it is worth calling a bet to chase after a draw. So obviously if we can work out that a certain draw is unlikely to be completed by the river, we will be less inclined to call big bets to try and catch those cards. Using the probability of completing a draw along with the amount you have to call in relation to the pot to figure out whether it is profitable to chase after a draw is called pot odds.
Pot odds can be worked out calculating the number of outs in relation to the number of cards left in the deck as well as the bet amount we have to call in relation to the size of the pot, then these number are compared to work out if a call is profitable. For example, if we are on the flop and we have a flush draw, there are 9 cards left in the deck to complete our hand. There are 47 cards in total left in the deck, 38 of which will not make our draw, so by putting these numbers together we get a ratio of 38:9, or put more simply, 4:1 odds of making our flush by the next card. Therefore, for every 4 cards that will not make our hand, the other 1 card will. If you find this method difficult, you can use poker odds charts to help you quickly figure the odds out.
The next step is to work out the ratio between the size of the bet we have to call and the total amount in the pot. So if the size of the pot is $50 and we have to call $10 to try and hit our flush, the odds we are being given are 50:10, or put more simply, 5:1. Now when comparing the two ratios, we have 4:1 odds of completing our hand with 5:1 odds to try and hit our hand. This means that the odds are in our favour because the odds we are getting from the pot are greater than the odds we are getting from the cards. Therefore if we make the call, this will be a profitable call in the long run.
As mentioned, mathematics is all about poker in the long run. Just because you are able to work out the pot odds for each individual hand, it does not mean that you are more likely to win the hand. You may lose many hands in a row, but as long as you have the correct pot odds to call each time, in the long run you will come out on top as a winner. Poker mathematics is a great weapon to add to your poker arsenal, and it is good to know when you should and should not call bets for each drawing situation.
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