How to estimate your chances of winning a hand
“As far as the laws of mathematics refer to reality, they are not certain, and as far as they are certain, they do not refer to reality.” ~ Albert Einstein
Just as your table position exerts significant force upon your hand selection, so do the concepts of pot odds and outs. These are mathematical estimates you will figure out when you are weighing whether or not to play a hand. These are things you will have to do in your head on the fly. The numbers you have to deal with will rarely fit neatly into whole numbers, but that does not matter. When assessing the probability of losing, my rule is to round up. Get a stone and carve on it “Thou shall round UP.” When you’re gambling, rounding down your chance of losing is just a good way to lose more often.
The estimates you will do as a poker player will tend not to be precise, but that is because so many variables in poker are imprecise, especially in no-limit games. What you need to accomplish is a reasonable estimate of your chances of success so you can proceed intelligently or fold intelligently.
Pot odds
When you are trying to figure out pot odds, you will compare the money you are betting to the money in the pot. This ratio will be expressed as your pot odds. It is simply a determination of what odds you are getting on each of your bets. A pot is defined as the sum of all prior bets. If a pot is $10 and someone bets $5 the pot rises to a total of $15. In this situation, if you bet $5 you would therefore be looking at pot odds of 3 to 1 ($15 pot as compared to your $5 bet).
Pot odds are the pot divided by your bets.
The main goal when you figure your pot odds is to compare the value of the pot against the level of risk you are taking. The reward needs to be worth the risk. Because no one wins every pot, you need to participate in pots that will pay you in a manner that recoups your losses and supplies a profit.
The riskier your hand, the greater the pot odds need to be. If you are drawing to make a flush or straight, then estimating your pot odds is very critical so you can decide if your hand is worth the risk of playing. For hands that are more lock solid in nature, such as when you start with a super premium pair of Aces, it is not as essential that the pot odds be high. Of course, you should never mind high pot odds because it’s always nice to get good odds on your money when you can.
Implied Pot Odds
The concept of implied pot odds is when you try to figure out what your total pot odds will be at the end of the hand and you are the winner. You are basically trying to see into the future and divine how much money your opponents are going to add to the pot. This is difficult to do because you are trying to estimate unknown figures. You will be able to make guesses about implied pot odds based on how you are reading your opponents. You might know that a certain player is going to keep betting and pay you or you might know that someone is not going to put out more money. Implied pot odds is an advanced concept that you might be able to use when you know enough about the other players at the table to predict their behaviors.
Implied pot odds are easier to estimate in a limit game because you at least know what units of money can be bet. If you are playing 5-10 hold’em then you know that the subsequent bets will be $5 or $10. In no-limit games, however, trying to figure out implied pot odds will be borderline impossible because future bets can vary significantly in size. Will someone bet $20 or $200? Pot odds can jump up wildly in no-limit.
Bottom line advice on implied pot odds is that you will generally not be able to guess at it unless you know how your opponents will bet based on your experience with them.
Outs
You will hear poker players talk about their “outs” all the time. Outs are defined as how many cards that exist in the deck to make your hand fill up into a winning poker hand. Study the example below to grasp the concept of outs.
Your hand = Jack Queen
Opponent’s hand = 10 Ace
Flop = 9, 10, 6
At this point in the hand, you have an open ended straight draw. Your opponent has a pair of 10s and at this point possesses the superior hand.
You need to calculate your outs to determine how many cards exist that can make your hand the winner.
Any 8 will complete your straight, so you have 4 cards or outs.
Any King will complete your straight, so you have 4 cards or outs.
Any Jack will give you a winning pair of Jacks, so you have 3 cards or outs.
Any Queen will give you a winning pair of
After assessing how many cards exist that will give you a potentially winning hand, you see that you have a total of 14 outs.
Of course, just because your outs exist does not mean they are going to be dealt to you on the turn and the river. They might be in other people’s hands, in the muck, or the bottom of the deck, but your outs at least exist.
Once you determine your outs, you divide that figure by 47. The 47 figure is the number of cards you have not seen (52 – your 2 cards – 3 flop cards = 47). In the above example, 14/47 = .297 or 30 percent, which represents your chances of winning. So, to be conservative and lend a little more weight to the probability against winning, you should round down to 25 percent so you can use whole numbers, and then you are looking at a hand that mathematically has a 1 in 4 chance of winning. Therefore, you need to be vying for a pot that has pot odds of at least 4 to 1 but preferably higher.
Another way of doing the math is called the Four Times Rule that I read about in the book Professional No-Limit Hold’em, Volume One by Matt Flynn, Sunny Mehta, and Ed Miller. With the Four Times Rule you multiply your outs by 4 to calculate your percentage chance of winning. Applying this formula to the above example you get 4 x 14 = 56, which would be expressed as 56 percent. That is a very different and higher figure than I get with my method. Those guys writing that book are champions, so it could be worth a try, but I’m such an advocate of being conservative when you look at the numbers that 56 percent seems just too high to me.
To tell the truth I do most of my playing by feel. I count my outs and look at the pot odds, but I don’t do a lot of math beyond that. I focus primarily on my position and what I know about my opponents and what I am reading about them during any given hand. Sticking with the above example that has 14 outs, which does have a high chance of winning however you approach the math, you can sometimes do a semi-bluff if your hand has not hit for you. If you stay in the hand, people will think you hit your straight and fold. However, if you are drawing for such a hand and you have a poor position, you probably can’t put any semi-bluff moves on people. But if you have a late position you might be able to steal the pot even if one of your needed 14 outs does not arrive.
Playing poker purely by the numbers won’t work. The actual people at the table are extremely important variables that are hard to quantify (at least until you start adding their chips to your stacks). You have to get to know the players. You have to continually study them. I value the personal game more than the mathematical game. So many factors influence people’s behaviors. If you’re playing against someone under pressure, they are going to reveal their emotions.
No-limit poker more so than limit poker is the people game. The math gets fuzzy in the no-limit game because the betting is unstructured and the money is not laid out in predetermined units. In limit poker, if you have a straight draw you are trying to get people in the pot to increase the pot odds, but in no-limit you might want to make a big bet to chase players out of the pot so you don’t really have to play out the straight draw.
Bottom line advice for estimating your hand’s chances of winning: You need to estimate your pot odds and count your outs, but the rest of your attention should be applied to judging your opponents. Mathematical poker is like your long game in golf. The human aspect of poker is like your short game in golf. The math will get you on the green, but you have to know your opponents to sink the putt. Otherwise you’re just out there waving a club around.
Continue: Analyzing your playing sessions
