» How important is math to being a winning poker player?

Knowing your poker math is essential if you are to succeed in poker, especially online poker.  In live poker, some players can focus on reading a player to derive much of their profit.  When you are playing online, you can't see your opponent.  You are playing many more hands per hour and thus any mathematical edge you are giving up can be a massive drain on your profitability. Although many high level players do focus on sophisticated higher level poker math, much of the math that you need to succeed is understanding percentages and how to calculate your odds versus various hand ranges.  Understanding how to calculate pot odds (how much is in the pot versus what you have to call to continue the hand) and implied odds (how much you have to call versus what you might win if you win the hand) is vital.

Poker math is a tool. The math of poker allows a player to understand when a specific move might be profitable or not. Poker is a game that emphasizes decision making.  There are clearly right and wrong decisions to make in certain situations, based off the math.  Most of the mathematically defined decisions are based on comparing your hand odds (your odds of having or making the best hand) against the pot odds (the amount of money in the pot compared to the amount of money it costs to continue playing).  Each time you don't calculate the math properly or make the wrong decision, you are giving your opponent a statistical edge.  It is the difference in your respective decisions based off that poker math that will determine your long term success in the game.

Most players eventually memorize many of the basic math odds associated with poker. Clearly, if you know the odds of flopping a flush are 118-1, you are less likely to play a weak suited hand like 10 6. If you suspect that your opponent has a big pair and you have a small pair, you should know that they are a 80% favorite to win the hand.  If you have a pair of 10's and your opponent has A,K, you are a 52% favorite. These types of basic understandings are essential to have.

Your eventual goal is to calculate the "EV" (estimated value) of every play you make.  Assuming you play a very large sample of hands, the EV indicates what value you can expect from your hand and situation if the hand plays out.  Whether you win or lose the actual hand is immaterial to your long term expected value for playing the hand correctly and whether you played it properly or not.

Let's take a hand I recently played in a tournament.  I was dealt A's on the button.  An early position player with 9's opened for three times the big blind.  I reraised his bet with a three times raise of his bet.  It is folded around to that early position player who has to consider his decision.  If he knew I had Aces, he should fold because he is not getting the pot odds to call.  He is a 20% favorite to win the hand (4-1) and it is 6 to call a pot of 13.5, (or 2.25-1).  But he doesn't know I have Aces and if I had A,K instead he would be a favorite, so he calls against the range of possible hands that I could have in that situation. 

The flop brings Q, 8, 4 no suits.  He checks, and I continuation bet my overpair Aces $9.75 into the $19.50 pot. He is now getting 3-1 odds to call, but his hand is less than a 10-1 chance of improving by the river.  It is a mathematical error to call if he suspects my overpair.  He may incorrectly feel that I may be bluffing with a hand like A,K and call the flop bet.

This example illustrates a common math situation in poker.  One player has a made or best hand, while the second player can draw to a better hand. If you are the second player, the first step is to count your outs (the number of unseen card that will give you the best hand).  One popular poker math short cut is to multiply your improving card outs by two to give you a rough percentage of your odds of improving.  In the case above, only two nines will improve your hand on the turn, so you have roughly 5% chance to improve and thus should never call a bet that is 3-1 when your odds of improving are 20-1.  If you did call, and hit your two outer on the turn, you may win a big pot, but it was a mathematically poor decision to make.  This is where luck plays a heavy factor in the short term, as we see inferior hands outdraw superior hands all the time.  

Some common situations and the odds associated:

• If you have a flush draw, you have 9 outs to improve, which is 19% with one card to come and 35% with two cards to come.

• If you have an open ended straight draw, you have 8 outs to improve, which is 17% with one card, or 32% with two cards to come.

• If you have two overcards, you have 6 outs to improve, which is 13% with one card, or 24% with two cards to come.

• If you have an inside straight draw, you have 4 outs to improve, which is 9% with one card, and 17% with two cards to come

• One of the best situations you can find yourself when you don't have a made hand is if you have a flush draw and open straight draw or flush draw and two overcards, in those situations you have 15 outs to improve, which is 33% with one card, and 54% to improve with two cards to come.

* Remember in each math situation to only calculate your odds one card at a time. It will likely cost you to see another card, so you must calculate your odds again if they bet the turn again.

In poker, there are two types of players.  The first group are players who don't pay attention to the odds and poker math, taking many good and bad odds situations hoping they get lucky.  The second group are those that pay attention to odds and the poker math of the hands they play, and they usually take the money from the first group.