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Learning No-Limit From Scratch ­- Analyzing How to Play

by Roy Cooke |  Published: Jul 08, 2015


Roy CookeI enjoy solving the poker quizzes on Facebook’s “The Poker Forum.” John Rackham, the group’s leader, posts hands he has played online, and anyone can comment on how they think the hand should be played. The debates on how to play often get lively, and it’s interesting to read others’ thought processes, even those I know aren’t correct. Reading these posts gives me a lot of insight into others’ thinking.

One interesting quiz was: You’re in a $5-$10 no-limit hold’em full-ring cash game with a $1,000 stack. A very tight, inexperienced player with $1,000 makes a standard raise from early position to $40. You are on the button with 9Heart Suit 9Spade Suit and call the raise. The blinds fold. The flop is ASpade Suit KDiamond Suit 9Club Suit. The villain bets $60, you raise to $200, and he reraises to $500. What should you do?

Let’s go step by step how I would solve this equation. First, I put my opponent on a range of hands that he would play in this manner. Since he’s both tight and inexperienced, I don’t think he’s three-bet bluffing, and the board is flush-drawless. So, I’m going to give him a range of A-A, K-K, or A-K, hands that a player with his tendencies would play this way. Then I calculate the odds of his holding each hand by comparing the mathematical odds of each holding to the other holdings.

There are six preflop combinations of every pair, and 16 combinations of all non-paired hands, of which four are suited. Then, you must adjust the number of potential combinations your opponent may hold based on seen cards. In this case, since an ace and a king are on the board, it removes three of the possible combinations of each pair. Additionally, it reduces the number of A-K combinations he may hold from 16 to nine.

Nine combinations of A-K are available, and three each of A-A and K-K. So, with three nines, I’m 9-6 to have the best hand, or 60 percent. But that fact alone doesn’t dictate how I should play the hand. I must also assess how my hand plays against each portion of that range. Since my opponent has four wins the 60 percent of the time I have him beat and I have only one win the 40 percent of the time he has me beat, I must adjust my expected value (EV).

Since I’m incapable of doing the exact math in my head, I do some “rough justice” at the table and make an approximate mathematical finding. In this case I adjust it a 50-50 proposition (You’re actually a 51-49 percent favorite).

So now we have the equation defined. We’re approximately 50-50, and the money already in the pot is laying us a price to call. But is calling the right play? If he will call with A-K, is a shove in order since we’re going to the river anyway?

But I shouldn’t just calculate the current mathematical odds of the play and formulate a decision based on those odds. I also need to calculate how the hand will play out and if there are any ways in which I can strengthen my odds by playing my hand differently.
In this case, a call is better than a shove. That’s because it removes any chance of his folding the A-K, a hand that your opponent would be losing EV by putting in the remainder of his money. And if you call and an A or a K comes on the turn, you can safely fold your hand thereby saving the remainder of your money and increasing your EV.

This hand is a great example of how to calculate the correct play. It’s a very simple example; most poker equations will have bigger ranges and more complicated equations. But the concepts remain the same. When I’m analyzing wider ranges, I compartmentalize my opponents’ ranges into those I’m beaten by, those I beat, and those that are draws. Then I estimate how my hand will play against each of those ranges and determine the best forward course of action.

I determine the value by the EV of the blend of all the plausible scenarios, not the odds of my hand being good at the current moment. Your hand can be a favorite to be good and have negative EV, such as the times in which you are beat you are virtually dead, but the times that your ahead you’re not a big enough of a favorite to make up the EV lost when you’re virtually dead.

The hand is also an example of how you can play your hand in a manner to decrease your loss in a few select scenarios, thereby increasing your overall EV. The converse can also be true, where you increase either your win or your odds of winning in a few scenarios and improve your EV by playing your hand more effectively. That can be accomplished by pushing players out of the pot, increasing your bet sizes, trapping, waiting for a later street to raise, and so on. The potential plays are endless and mostly a function of your opponent’s tendencies. You need to think in terms of how you can either lower your assumption of risk or maximize your gain. In this case, flatting the three-bet lowered your assumption of risk by allowing you to get away from the hand if an ace or king came.

Going through poker exercises like this is good for your mind and game. Doing it on a forum where you can read and relate to others players ways of thinking also adds value to your poker thought process. If you want to join the forum, go on Facebook and go to “the Poker Forum”, anyone can join and the range of expertise is from beginner to expert.
It’s fun and it will help your game! ♠

Roy Cooke played poker professionally in Las Vegas for 16 years prior to becoming a successful Las Vegas Real Estate Broker/Salesman. Should you wish any information about Real Estate matters-including purchase, sale or mortgage his office number is 702-376-1515 or Roy’s e-mail is His website is You can also find him on Facebook or Twitter @RealRoyCooke