ITH Poker Forum

[mchilger]

Using Ranges to Make Better Decisions
By Matthew Hilger

The newest buzz word in the poker world is range. “What range did you put him on?” “I put him on a wide range so I reraised.” “With his range, there was a good chance he liked that flop.” The word is new, but the idea is simple – you assign a range of hands your opponent is likely holding and then you start to narrow down that range as you gather more information throughout the hand. Once you assign a range of hands your opponent is likely holding, you can then select the best course of action, whether it is raise, call, check, or fold.

I am going to look at a simple Limit Hold’em hand to show how you can use ranges to help analyze your play. The idea works for both limit and no-limit, but I’ve chosen Limit as it is easier to assign “standard” ranges to an opponent.

An opponent raises first-in from middle position. He is a standard beginning to intermediate player who follows the starting hand guidelines in my book Internet Texas Hold’em New Expanded Edition. My book says a beginning player should be raising the following range of hands: 77+, A-7s+, K-Ts+, Q-Ts+, J-Ts, A-Jo+, and K-Qo. You hold K-Qs on the button and are faced with a decision.

Using the Card Player poker odds calculator, you see that K-Qs has 43% equity against this range. With 3 ½ big blinds in the pot, you need to only call two big blinds to continue with the hand. You are effectively getting 1.75 to 1 pot odds to call. With those pot odds, your hand only needs 36% equity to break-even. Of course, in limit, it pays to be aggressive so if you are going to play your hand, you should usually re-raise. In this case, you’ll be risking 3 big blinds to win 4 ½ big blinds which is 1.5 to 1 pot odds (for sake of this example I am ignoring reverse implied odds). Now you need 40% equity to break-even. Your hand has 43% equity and you have position, making this an easy re-raise.

The flop comes Jh 6s 2d rainbow. Your opponent checks. Your hand now has 28% equity against your opponent’s range of hands. However, before you check, you should determine how often your opponent might fold on the flop. If you bet, you assume your opponent will call or raise the following hands: 77+, A-J+, K-Js+, K-Qo, Q-Ts+, and J-Ts. Therefore, he is folding A-Ts, A-9s, A-8s, A-7s, and K-Ts. He raised with 11.2% of his hands, and he will continue with 9.7% of his hands, so he will be folding 13% of the hands within his range of starting hands [(11.2 – 9.7)/11.2]. There are 7 ½ big blinds in the pot and you need to bet 1 big blind, so he only has to fold 1 in 8.5 times or 11% of the time for you to break-even on your bet. He is folding 13% of the time so you make an immediate profit on your bet for the fold equity, and if he calls you still have equity with your K-Q which could end up being the best hand. You bet and your opponent calls.

The turn is the 2c.

Your hand K-Qs now has 16% equity against his range of hands: 77+, A-J+, K-Js, K-Qo, Q-Ts+, and J-Ts. He checks. Before you check, you should once again determine how often your opponent might fold on the turn. If you bet, you assume your opponent will call or raise with the following hands: 77+, A-J+, K-Js, Q-Js, and J-Ts. Therefore, he will be folding K-Q, K-Qs, and Q-Ts. His flop calling range represented 9.7% of all hands, and his turn calling range represents 8.1% of all hands. Therefore, he will be folding 16% of the time (1.6/9.7). There are 4.75 big bets in the pots so your opponent needs to fold 1 in 5.75 times for you to break-even on a bet which is 17% of the time. Your opponent is almost folding enough for you to break-even with just your folding equity, and you still have some equity with K-Q to improve to the best hand. You bet and your opponent calls.

The river is the Ac. Based on the range you’ve narrowed your opponent to, you have no chance of winning the pot unless you bet and your opponent folds. If you bet, you assume your opponent will fold 77 and 88. He is therefore calling with 7.2% of all hands and folding another 11% of the hands he called on the turn. There are 6.75 big bets in the pot. Your opponent needs to fold 1 in 7.75 times for a bet to break-even or 13% of the time. Given that he is only folding 11% of the time, you should check. If you feel like he would fold 77, 88, 99, and TT, now he would be folding 22% of the time based on the range he would call on the turn. Now you can bet and expect to turn a profit since he will be folding more than needed to break-even.
Note that the example above is a generalized example as check-raises were not addressed and would affect some of the hands you might expect in his range versus a check and call line from our opponent.
This is just one example of the use of ranges to determine how you might play a hand. Other examples are determining whether or not you should make a value bet, whether your hand has enough equity to call a bet, etcetera. It’s basically a mathematical way to evaluate different scenarios to determine the best action to take. Use ranges to evaluate some of your hands and you might be surprised at the results.

[Willem]

Very good article. The example itself is probably too simple to be practically applicable, but it's very useful for beginning/intermediate players to read.

To make it realistic, you should also take our the hands he would check-raise the flop with, for instance AJ and better. But that might make the analysis too complicated for an article.

[mchilger]

To make it realistic, you should also take our the hands he would check-raise the flop with, for instance AJ and better.

Yeah - I tried the best I could to make it as simple as possible. I did say call or raise to indicate the hands he would fold. It isn't easy when you only get 1,000 words

Matthew