With few practical exceptions, river strategy is based on the players’ start- ing distributions and the stack and pot sizes only. The details of early- street play are only relevant insofar as they affect those things. That said, we will take advantage of this opportunity to put in a little hand-reading practice to show how we arrive at the river starting ranges. This will help us to see how different types of equity distributions can arise in the course of real play. For hand-reading purposes, we assume the players are gener- ally thinking and competent, perhaps such as those that can be found playing mid-stakes games online.
For each of these example hands, we will go through the early-street play to make an estimate of the hands with which each player might arrive at the river. Then we will discuss the equity distributions induced by the players’ river starting ranges. Keep in mind that the BB’s equity distribu- tion on the river is essentially just the complement of the SB’s and can be visualized by flipping the graph as discussed in Section 5.3.
As always, it is good to think about how certain points might change if these hands were played by players with other tendencies. In particular, for each hand example and position, try to imagine your own range for getting to the river this way against an unknown opponent in your games or against a particular opponent with whom you have a lot of experience. You should try to do this very precisely. Understanding one’s own ranges is a very important skill which is neglected by many players.
7.1.1 Example 1
Effective stacks: 25 BB Preflop:
SB raises to 2BB, BB calls 1BB Flop: 9♥-2♠-9♦ (4BB)
BB checks, SB bets 2BB, BB calls Turn: A♠ (8BB)
BB checks, SB bets 4BB, BB calls River: 6♥ (16BB)
This flop is very absolutely weak for both players. In particular, there are 1,326 hand combinations in the deck and 192 of them contain a 9. How- ever, after the 9♦-2♠-9♥ flop, there are 1,176 possible holdings left in the deck, only 95 of which contain a 9. The SB will thus hold a 9 about 8 per- cent of the time if he is playing any-two-cards preflop. How likely is the BB to have hit the 9? Besides that, no draws are possible and many deuces and pocket pairs may be discounted from the players’ ranges since they would have played differently preflop.
Since neither player has an absolutely strong holding very often, the SB is prone to c-betting with most of his hands to try to take down the pot. After the flop action, his range still contains almost anything while the BB is ei- ther slow-playing a strong hand, has weak showdown value (a high card or the rare deuce), or has an even weaker hand which will often try to win without a showdown on a later street. Many aggressive players, however, do not slow-play here often since a raise can look very bluffy and induce action.
The A♠ turn is interesting. If the starting stacks were a bit deeper, A-high would make up a lot of BB’s range to call preflop and check-call the flop. As it is, most aces will be 3-bet preflop. As for the SB, he may or may not c-bet A-high on this flop. Without further information, however, the A is gener- ally a strong card for the SB, but of course he still has a lot of pure bluffs in his range as well. After calling again on the turn, the BB’s range is still composed of bluff-catchers and the occasional slow-play. The SB can have continued to bet most hands two-pair or better for value, and he is proba- bly frequently bluffing as well.
Thus, at the beginning of river play, we can give the BB a lot of K-high, the rare high-card hand that called the flop and turned a spade draw, and the occasional slow-played nine. We give the SB some deuces, all better made hands, and many pure bluffs. The SB’s equity distribution is shown in Fig- ure 7.2a. It has a simple structure. A fair fraction of his hands have no eq- uity at all and the rest are quite well off. This will often be the case on the river when one player has taken a very aggressive line and the other re- sponded passively. The aggressive player has either a particularly good hand or a particularly bad one, and his opponent’s holding is a mediocre one which was not strong enough to raise or weak enough to fold.
7.1.2 Example 2
Effective stacks: 50 BB Preflop:
Flop: Q♠-9♠-6♥ (4BB)
BB checks, SB bets 2BB, BB calls Turn: 2♥ (8BB)
BB checks, SB bets 6BB, BB calls River: 6♣ (20BB)
Let us assume that the SB gets to the river in this hand with most two- heart and two-spade hands (some may not have bet twice) as well as J-10, K-J, 10-8, 8-7 and any made-hand pair of queens or better. Slow-plays on his part will be rare due to the drawy nature of the board, but it may also be perceived as a relatively poor spot to make many pure bluffs since the offsuit deuce on the turn is unlikely to scare many hands that called the flop bet. The BB can also have missed flush and straight draws, although they may be discounted since he would have played them more aggres- sively sometimes and may have folded two hearts on the flop. Additionally, weaker queens, many nines, and the occasional stubborn six are in his range for getting to the river. We will suppose he can slow-play earlier streets occasionally, as well, and gets to the river with
9♣9♦, 9♣9♥, KJs, K♥T♥, K♠T♠, K♠6♠, K♠5♠, K♠4♠, K♠3♠, K♠2♠, QTs-Q9s,
Q♠6♠, JTs, J♠8♠, J♠7♠, T8s, 87s, KJo, QTo-Q7o, JTo, T8o
The players’ equity distributions are shown in Figure 7.2b. The SB is some- what polar here, having taken an aggressive line. However, as compared to the previous example, much more of the SB’s range has at least a little showdown value, and the BB’s range is not nearly as narrowly defined. Of course, these two observations are connected. Since we assumed the BB played a number of draws passively, some of the SB’s bluffs actually end up with the best hand on the river. In fact, some players in the BB will check-call the flop in this hand with many unpaired holdings which have some way to improve and otherwise plan on bluff-leading the river. This tendency incentivizes the SB to continue betting on the turn with many more high-card “bluffs” (such as K-J) than he might otherwise.
7.1.3 Example 3
Effective stacks: 100 BB Preflop:
SB raises to 3BB, BB calls 2BB Flop: K♣-Q♠-8♥ (6BB)
BB checks, SB bets 4BB, BB calls Turn: 5♥ (14BB)
BB checks, SB checks River: 5♣ (14BB)
This flop is fairly static and strong for the BB. The SB might often stab once with air hands to try to fold out two cards below the Q, but he is unlikely to barrel since one call from the BB often represents a K or Q, high paired hands that will be unwilling to fold on later streets. He may have barrelled the turn with some draws, but these all missed on the river. Either way, the SB can therefore make it to the river this way with almost all the unpaired holdings. He also probably plays almost all rivered 3-of-a-kind hands this way, but these make up a small part of his overall range. Finally, the SB can have some queens and eights, although these could have played differ- ently on earlier streets, and the occasional king, although these will often have bet on the turn.
The BB, on the other hand, probably has all the queens and eights that are in his preflop range, weaker kings that did not check-raise the flop, and, say, A-10, J-10, and J-9s. For this hand’s discussion, we will assume that this is all the BB gets to the river with this way. It is probably about right for many players.
However, it is worth noting how play could differ in this spot. In particular, from the discussion so far, this BB range is almost certainly too tight. No- tice that he always has something when he gets to the river – even his missed straight draws are high cards that are ahead of a significant part of the SB’s range. Anticipating this, we assumed earlier that the SB was going