» Poker Math
While poker is very much a game of skill and psychology, there is no escaping the math. Understanding the odds and percentages associated with poker are essential to mastering the game. One needs to be able to calculate the odds of winning a hand or your opponent doing so. Even players who claim they aren’t into math have an intuitive or experiential sense of the odds of made hands versus drawing hands that they face. The basic poker math isn’t overly complicated, but does require some calculation and memorization.
In each case of poker math, you are comparing the card odds, with the pot odds and implied odds. Each of these odds are different. The card odds refer to the odds of a hand improving, whether it be yours or your opponents. The card odds come up almost every hand and the most common ones should be memorized.
For instance, if you have a flush draw, you are roughly 25% to hit it on the next card and 36% to hit it with two cards to come. The math goes like this...there are five cards in the hand that you know, your two and the three card flop. There are 47 unseen cards in the deck. There are 9 of those 47 cards that will make our flush, while 38 will not. That gives us roughly 4:1 (38:9) odds of making our flush, or roughly a bit less than 25%.
The pot odds involve the bet you are facing versus what you have to call. So if someone bets half the flop pot, you are getting 3:1. If they bet the pot, you are getting 2:1. If they bet 2/3 of the pot, you are getting the flop, you are getting 2.5:1.
The next important step is to compare the card odds to the pot odds. If the pot odds are bigger than the card odds (based on your number of outs), you should call. On example to illustrate this process of comparison: Your opponent bets 2/3 of the pot on the flop giving you pot odds of 2.5:1. You have a flush draw which is only 4:1 to hit on the next card. Your card odds are bigger than your pot odds, so you shouldn’t call unless you consider the third kind of odds, implied odds.
Implied odds involve the subjective evaluation of what money you could make if you hit your draw. It is an estimation of how much much money you can win if one of your outs hits. If more money will go into the pot on that situation, then your odds shift more in your favor. The classic example of a implied odds hand is playing a small pair. If you are against a bigger pair or top pair top kicker, your card odds to hit a set are 7.5-1. Against a bigger pair, you are a 4:1 dog - not a favorite. If they bet 3 times the pot, you don’t have the pot odds to call a raise unless there are several other callers. But if you factor in the times when do hit your disguised set and someone overplays an over pair where you might get most or all of their entire stack, consisting of 25 or more big blinds that implied odds justify a call to try to hit. Unfortunately, people tend to be too optimistic when calculating their implied odds, as when a board has three or four cards to a straight or flush, the betting will shut down. Smart players won’t overplay hands, thus not giving you much in the way of implied odds.
Another way to short cut your poker math in understanding what your percentage to improve in a hand is the rule of two. Count the number of suspected outs and multiply it by two to arrive at a rough percentage of the times you can expect to improve on the next card. So if you have two over cards to a suspected low pair, you have six outs to improve, giving you 12% on the next card or 24% if there are two cards to come.
Let’s take another example using our new found understanding of poker math. An early position raiser makes it $6 in a $1-2 game. There is one caller and you have 7,8 of hearts. Against a bigger pair, you are 4:1 and you have to call $6 to see $15 (15:6 = 2.5:1) If they have a bigger pair, you aren’t getting the pot odds to call, but if you factor in implied odds of playing your suited connector, you decide to call. The flop comes 6,9,K with two hearts. The original raiser bets $10 and the other player folds now giving you 2.5:1 pot odds. You now have a straight and flush draw giving you 15 outs (47:15 or roughly 3:1) on the next card. With two cards to come, and no made hand, you are actually a favorite in the hand to hit your card by the river 55% of the time (15 outs twice times two = 55%). While you aren’t a favorite to beat them on a single card to come, you have odds to call their bet. Your hand is disguised and you have implied odds as well as pot odds if you see the river or if they don’t bet overly large on the turn.
A common situation you will find in tournaments and cash games is what we call a flip. A flip is where someone has a big pair, like Q’s and the other player has A,K. The odds are near to 50-50, so it’s called a flip, but you always want to have the big pair, as they are usually a 52-54% favorite depending on suits.
In another article, I will discuss another type of math calculation - expected value (EV). It relates strongly to your equity or expectation of what you should win in a large sample of hands.
Understanding basic poker math will positively influence all your decisions at the poker table. An important part of considering the odds and percentages is that your opponent doesn’t ever really have an exact hand that you see, but rather a range of hands they play a certain way. Included in that range are bluffs. So that if you factor in the times they might be bluffing, it improves your odds somewhat from the pure odds you calculate.
