There is no doubt that the very best poker players have actually taken matters even further into the mathematical realm. Some players analyse hands incredibly closely and make numerous in depth mathematical calculations to determine how they will play.
But not everyone needs to approach the game like that, particularly not beginners.
As the many PokerStars School courses progress, some of the mathematical aspects of the game will become more prominent. But at this stage, it is only really necessary to have a general idea of some of the core concepts.
One of the very easy calculations you should learn even at this stage in your poker career concerns counting your "outs"
WHAT ARE OUTS?We have already seen how the relative strength of a poker hand can increase or decrease as flop, turn and river is dealt. For example is a big favourite against pre-flop, but becomes a huge underdog if the flop comes .
If you have a hand that is probably losing, but has the potential to improve to a winner, (ie, a drawing hand) you need to decide whether it is worth continuing with it through the various stages of the pot.
In short, you need to identify the cards that will improve your hand - known as "outs". In later lessons you will learn about making further calculations based on your "outs", but first you need to identify what is an "out".
The best definition is simple: "outs" are the cards left in the deck that improve your hand, ideally to make it strong enough to win the pot at showdown.
Example With a Flush Draw
However if another heart appears on the turn or river, you make a flush, and unless another player has a full house or better, you will win the hand. (The board isn't paired, so none of our opponents can have a full house yet.)
There are 13 cards of each suit in the deck. You hold two of them, and another two are on the board. Four of the 13 hearts have therefore already been dealt, meaning that there are still nine hearts left in the deck.
This means there are nine cards that can improve your hand to a (probable) winner. You have nine outs.
Example With a Straight Draw
You have and the flop is . Now any ace or nine will complete your straight. There are four aces and four nines in the deck, so you have eight outs.
If one card is missing to complete a straight, you have four outs. For example, if your hole cards were and the flop was , your outs would be .
Example With a Straight Draw and Overcards
You have , and the board is . One of the four queens in the deck will make you a straight. If your opponent has a middle pocket pair, e.g. , then you have additional outs, as any king or any jack would give you a higher pair.
In this case, the number of your outs would increase to ten (four queens, three kings, and three jacks).
Example With a Set Against a Flush Draw
If you hold and hit a set on a board showing , you have a pretty strong hand. But it is not definitely a winner and could already be behind to any opponent with two spades in his hand.
However, you still have the chance here of improving your hand even further. There are seven cards that could make you a full house or better (a seven, three remaining twos and three remaining jacks), or the turn and river could be the same rank, which would also give you a full house.
Example With a Straight Draw AND a Flush Draw
You hold and the board is . You have both an open-ended straight draw and a flush draw. This means you have nine outs to make the flush and eight outs to make the straight. At the same time, you have to consider that two cards are counted twice (in this case the and the ), which have to be subtracted. Therefore you have a total of 15 outs.