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 that he liked that flop.” The word is relatively new, but the idea is simple: You assign a range of hands that 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, 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 or intermediate player who follows the starting-hand guidelines in my book Internet Texas Hold’em New Expanded Edition. My book states that a beginning player should be raising with the following range of hands: 7-7+, A-7+ suited, K-10+ suited, Q-10+ suited, J-10 suited, A-J+ offsuit, and K-Q offsuit. You hold K-Q suited on the button, and are faced with a decision.
Using the CardPlayer.com Poker Odds Calculator, you see that K-Q suited has 43 percent equity against this range. With 3.5 big blinds in the pot, you need to call only two big blinds to continue with the hand. You are effectively getting 1.75-1 pot odds to call. With those pot odds, your hand needs only 36 percent equity to break even. Of course, in limit hold’em, it pays to be aggressive, so if you are going to play your hand, you should usually reraise. In this case, you’ll be risking three big blinds to win 4.5 big blinds, which is 1.5-1 pot odds (for the sake of this example, I am ignoring reverse implied odds). Now, you need 40 percent equity to break even. Your hand has 43 percent equity and you have position, making this an easy reraise.
The flop comes J 6 2. Your opponent checks. Your hand now has 28 percent 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 that your opponent will call or raise with the following hands: 7-7+, A-J+, K-J+ suited, K-Q offsuit, Q-10+ suited, and J-10 suited. Therefore, he is folding A-10 suited, A-9 suited, A-8 suited, A-7 suited, and K-10 suited. He raised with 11.2 percent of his hands, and he will continue with 9.7 percent of his hands, so he will be folding 13 percent of the hands within his range of starting hands [(11.2 – 9.7) ÷ 11.2]. There are 7.5 big blinds in the pot, and you need to bet one big blind, so he has to fold only once in 8.5 times, or about 11 percent of the time, for you to break even on your bet. He is folding 13 percent 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 2.
Your K-Q suited now has 16 percent equity against his range of hands: 7-7+, A-J+, K-J suited, K-Q offsuit, Q-10+ suited, and J-10 suited. He checks. Before you check, you should once again determine how often your opponent might fold on the turn. If you bet, you assume that your opponent will call or raise with the following hands: 7-7+, A-J+, K-J suited, Q-J suited, and J-10 suited. Therefore, he will be folding K-Q, K-Q suited, and Q-10 suited. His flop calling range represented 9.7 percent of all hands, and his turn calling range represents 8.1 percent of all hands. Therefore, he will be folding about 16 percent of the time (1.6 ÷ 9.7). There are 4.75 big bets in the pot, so your opponent needs to fold once in 5.75 times for you to break even on a bet, which is about 17 percent of the time. Your opponent is folding almost enough for you to break even with just your fold equity, and you still have some equity with K-Q, which could end up being the best hand. You bet, and your opponent calls.
The river is the A. Based on your opponent’s narrowed-down range, you have no chance of winning the pot unless you bet and your opponent folds. If you bet, you assume that your opponent will fold 7-7 and 8-8. He is therefore calling with 7.2 percent of all hands, and folding another 11 percent of the hands with which he called on the turn. There are 6.75 big bets in the pot. Your opponent needs to fold once in 7.75 times for a bet to break even, or about 13 percent of the time. Given that he is folding only 11 percent of the time, you should check. If you feel like he would fold 7-7, 8-8, 9-9, and 10-10, now he would be folding 22 percent 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 you need to break even.
Note that this is a generalized example, as check-raises were not addressed, which would affect the hands that you might expect to be in his range.
This is just one example of the use of ranges to determine how you might play a hand. Other examples include determining whether or not you should make a value-bet, whether or not your hand has enough equity to call a bet, and so on. It’s basically a mathematical way to evaluate different scenarios in order to determine the best action to take. Use ranges to evaluate some of your hands and you might be surprised at the results.
This article first appeared in Card Player magazine.
Matthew is the owner of Dimat Enterprises, “Publishing Today’s Best Poker Books”. The Math of Hold’em by Collin Moshman and Douglas Zare is available now at pokerbooks.InternetTexasHoldem.com.