Calculating Approximate Drawing Odds

It is vital that you are able to calculate the probabilities of success with your current hand.  For ease of use in the context of Texas Hold’em it is better to calculate the odds of success (referred to as “drawing odds”) – they can be converted into probabilities if necessary.

The first step in this process is the ability to know what cards can improve your current hand.  This is often referred to as “counting your outs” and is described in detail in the “Analysing the Flop” chapter.

When you know how many cards can improve your current hand you can then use the following method to approximate the probabilities associated with your current hand.

1)      Determine how many unseen cards there are – in the case of a calculation on the flop it will be 47 (52 – 2 pocket cards – 3 flop cards), in the case of the turn 46, and the river 45.

2)      Divide the number of cards that will not help you by the number of outs that you have determined.  This will give you your drawing odds.

Example:

Consider the case where you have 4 cards of the nut flush on the turn.

There are 46 unknown cards = 52 cards minus your 2 cards minus 4 cards on the board

9 of the unknown cards will help to give you the nut flush assuming that none of these cards will help the hands of your opponent(s).  These 9 cards are known as your “outs”.  If any of the outs will help your opponent(s) then they are referred to as “discounted outs” and should not be included in your drawing odds calculation.

37 of the unknown cards will not help your hand

Your pot odds are 37-to-9, or 4.1-to-1, which rounds approximately to 4-to-1.

Therefore, you will only bet in this situation if the pot is at least 4 times the size of the bet that you need to make to stay in the game.

Now you will have a numerical basis for making your poker decisions based on the expected value theory.  It is important to remember that the odds of getting dealt certain cards is only a probability.  It reflects the percentage of the time that you will “hit” the hand that you are drawing to – not the percentage of the time that you will win the pot.  You may not get a card that will improve your hand or another player may improve their hand to a greater degree than your hand.

There is no substitute for being able to perform the calculations quickly.  It will help improve your decision speed which can be important because sites often limit the time permitted to call, check, or raise.