Turn play begins with 14 BB in the pot and 93 BB behind. Consider the BB’s initial decision point. He mostly checks, but he makes 1/5− and 1/2−pot bets with single-digit frequencies. His ranges are highly mixed, and his betting ranges have nearly the same composition as his checking range. However, he has a slight preference towards leading with strong draws (e.g., J♥-9♥) and good pairs.
Turn Play: Volatile Boards and Capture Factors
Figure 13.1: Turn starting distributions for our example on the K♣-Q♠-8♥-5♥ board.
The fact that so many hands are played with mixed strategies, despite his checking the vast majority of the time, means that almost every hand in the BB’s range is indifferent between betting and checking at equilibrium. The SB’s strategy must be finely tuned to make this true, and small devia- tions in the SB’s play will have a large effect on the BB’s best response. Knowing all this, it would be reasonable for a human player to just check his whole range for simplicity (in the absence of exploitative reads). How- ever, these results indicate that leading is also reasonable here, contrary to standard play. Does the standard approach exploit population tendencies, or is there another reason that leading (with small sizings) is rare here? Let us look at how exactly the SB’s strategy makes one of the BB’s hands indifferent to leading. This will let us see how the SB responds to a lead generally and when the BB might be able to play exploitatively. Consider the BB’s K♥-8♦. With about 93% equity at the beginning of the turn, it is the strongest made hand in his range. He will very rarely be looking to fold it, and if the EVs of taking two actions with this hand are equal, then the SB figures to be putting approximately the same amount of money in the pot on average against both. Now, the BB actually takes a number of lines on the turn with this hand. He does not just bet or check, but he bet-calls, bet-3-bets, check-calls, check-raises, etc. Let’s investigate a couple of ex-
Expert Heads Up No-Limit Hold ’em, Volume 2
treme choices: the check-call and the bet-3-bet all-in.
First, the check-call. The BB checks about 2/3 of his K-8 combinations on the turn. Facing the check, the SB frequently checks back. When he bets, he uses his 3/4-pot and full-pot options – he almost never bets half-pot or over the pot. More specifically, when the BB checks K♥-8♦:
♠
The SB checks back about 72.6% of the time, in which case we get to the river with a 14BB pot and 93BB behind. The BB expects tocapture about 1.15 times this pot on the river for an EV of about 93+(1.15×14)=109 BB.
♠
The SB bets 3/4-pot about 4.8% of the time, and we get to the river with a pot of 35BB and stacks of 82.5BB. At equilibrium, the BB’s capture factor here is about 1.20, for an EV of about82.5+(1.20×35)=124.5 BB.
♠
The SB bets full pot about 22.6% of the time, in which case we get to the river with a pot of 42 BB and 79 BB behind. At equilibrium, the BB captures 1.07 times that for an EV of about79+(1.07×42)=124 BB.
Clearly, the BB hopes to see a bet after he checks the turn with this strong hand, and when he does, he almost always just calls, keeping his strongest hand combined with other hands he plays passively. Regardless of whether a bet goes in on the turn, it expects to win a bit over the size of the pot when it sees a river. Overall, his average EV when he goes for the check-call is approximately
Now, what happens when the BB goes for the bet-3-bet all-in with his K-8 on the turn? Actually, he uses two bet sizes, but focus on the 1/2-pot lead for now. Facing this, the SB:
♠
Folds 49.0% of the time, so that the BB ends up with 107 BB.♠
Calls 40.0% of the time, in which case the BB captures 1.17 times the 28-BB pot in addition to his 86-BB stack for an expectation of 118.9 BB.Turn Play: Volatile Boards and Capture Factors
folds around 2/3 of the time (the BB’s K♥ blocks a lot of his calling range) and calls the rest, leaving our BB an average equity of 123.4 BB here.
♠
Raises to 28 BB 9.4% of the time. Facing the BB’s jam, he folds about 57% (his wider range for getting here is less affected by cardremoval) giving the BB an average EV of jamming of about 120.6 BB.
These two raise sizes correspond to half-pot and 3/4-pot raises. The SB does not use his min-raise or larger betting options when facing the lead. The BB’s average EV when he goes for the bet-3-bet is thus
This is the same as his EV when he goes for the check-call, as expected. So, the BB leads occasionally, but he mostly checks. This makes sense, judg- ing by the distributions. His average equity is quite high, simply because he always has “something” after calling the flop, but he has few very strong hands. We briefly mentioned the SB’s frequencies after the BB checks K♥-8♦, but now let’s take a closer look at his play facing the check. His three-
quarters and pot-sized bets are much smaller than the GGOP choice, since the distributions are nowhere near PvBC, but are still very large. His betting ranges are quite polar. They contain more or less no hands with equities be- tween 25% and 75% versus the BB’s checking range. His value betting cut- off (i.e., his weakest value bet) falls among his weak kings, and he has some tendency to use the larger sizing with stronger hands.
He bets everything with above about 80% equity, and as a consequence, his checking range is capped. The river can strongly affect hand values on this board, so the fact that his checking range is capped does not necessarily mean his river starting distribution is, and he simply needs to get value with his strong hands. Certainly, the BB leads the river a significant amount of the time after the SB checks back the turn, especially on “blank” rivers.
Facing a bet, the BB’s strategy includes calling, folding, and jamming. It keeps both the SB’s bluffs and various semi-bluffs more or less indifferent to betting the turn à la Section 12.8. His range for check-raising seems fairly standard: some two-pair hands and some semi-bluffs for balance.