By Tony Guerrera

A player I coach (termed Hero in this article) recently played the following hand in a 6-max $.25-$.50 no-limit hold’em game on Poker Stars:

Action is 6-handed. Hero raises to $1.50 UTG with KhQc. CO-1 calls; CO folds; B calls; SB folds; BB folds. Not accounting for rake, the pot is $5.25 going into the flop. The flop is AhQhJh, Hero leads $2.75 (just over half-pot), and both opponents call. The pot is $13.50, not accounting for the rake. The turn is the 2s, making the board AhQhJh2s. Hero checks, CO-1 checks, and B bets $5.50. Hero calls, and CO-1 folds, making the pot $24.50. The river is the Kc, making the board AhQhJh2sKc. Hero leads $13, and the button calls and shows AsJs to win the $50.50 pot.

Losing a hand isn’t synonymous with playing a hand badly, so let’s break down the action in this hand by looking at each betting round.

Preflop Analysis: 6-handed no-limit hold’em needs to be played aggressively to be played profitably. However, most aggression should happen in position. Aggression out of position shouldn’t be avoided completely, but it should be used sparingly. Because of the playability problems arising when CO-1, CO, or B enter the pot, folding KQo UTG at a 6-handed table is highly advisable. However, opening for a raise here isn’t necessarily a deadly sin, particularly if Hero hasn’t been active in the past orbit or two-recent inactivity increases the potential of winning the pot uncontested preflop. Though I take pride in being tough with the players I coach, I’m giving Hero the benefit of the doubt here and assuming that he was trying to take advantage of recent tightness.

Flop Analysis: With middle pair, an inside straight draw, and the nut flush draw, hero leads into two opponents. His UTG preflop raise represents two high cards or a pocket pair. Opponents can’t really put hero on hands like 7h6h. Outside of pocket pairs that are underpairs to the board, KJ (bottom pair + gutshot draw + possible flush draw depending on suit of king) is the worst hand that opponents can really put Hero on (perhaps there’s a chance that JT can be in Hero’s range, but given the UTG raise, it’s highly unlikely).

Meanwhile, Hero’s opponents are on distributions consisting of high unpaired cards (all the way up to AK), pocket pairs as high as TT (JJ and QQ can’t be dismissed completely; some players will call a UTG raiser with such hands instead of 3-betting), and suited connectors (most likely just in B’s calling range). Given his opponent’s ranges, Hero’s lead here is a blocking semibluff which prevents worse hands from bluffing and prevents better hands from showing aggression. Hero’s lead also has the potential to turn into an effective 3-bet semibluff because a 3-bet semibluff would put pressure on most hands in the raiser’s distribution (except for baby flushes and possibly KT). And if hands like AQ and AJ don’t back down, Hero still has 12 outs.

But opponents will tend to call or fold here (two pair type hands for pot control and baby flushes to extract value). Indeed, that’s what happens. In fact, the absence of a raise here strongly suggests that hero is not against someone holding KT.

Turn Analysis: After getting called by both opponents on the flop, Hero opts to check the turn. Given the action on the flop, there’s a good chance that hero is facing someone with AJ or AQ. AK is another possibility, as is QJ, but QJ, in particular, won’t be in all opponent’s distributions here. There’s also a remote chance that CO-1 has AT and B has AT, A9, or A8, but the chance is very remote, meaning this possibility won’t contribute much to the EV of whatever line of play we consider.

The chance that two pair folds to a lead on the turn is slim, so Hero’s check on the turn is good. At this point, Hero’s only option is checking to see what his two opponents do. Though Hero would prefer getting a free river, it’s not likely that two pair will allow a free river with such a dangerous river. B’s $5.50 bet signals AQ, AJ, QJ, with the remote possibilities of AK, AT, A9, or A8. Putting B on AQ-AJ simplifies analysis a bit and is B’s most likely distribution anyway, so we’ll work with it.

B’s bet gives Hero $19:$5.50 = $3.45:$1 pot odds. With 12 outs and 44 unknown cards (we have opponent pinned to a precise distribution), Hero is 32:12 = 2.67:1 against hitting. Hero has more than sufficient odds to call and play straight-up hit-to-win poker. The remote concern exists that B has QQ or JJ, making the 2h a card with some small reverse implied odds potential, but QQ or JJ don’t seem very likely candidates at this point in the hand given the lack of flop aggression and the small size of B’s turn bet. If the 2h falls on the river, Hero leads just over half-pot, and B goes over the top for a large raise, Hero can still be profitable if he mucks 100% of the time! Assuming that opponent folds to a $13 bet on the river on any heart or any ten (except for the 2h, on which he raises 100% of the time, inducing Hero to fold), Hero’s EV is:

Note that neither K’s nor Q’s were included as outs. With Hero’s opponent on AQ-AJ, K’s aren’t real outs, and Q’s are a big problem. If we assume that Hero check-folds any K or any Q, the passive hit-to-win line of play has an EV slightly better than +$0.33, though it’s hard to know the EV precisely (though B will most likely not turn AJ into a bluff when a queen falls, Hero’s EV ultimately depends on how often B is willing to turn AJ into a bluff). .

In the hand being considered, Hero actually used a king as a bluffing out on the river, so let’s now consider the EV of line of play that includes 3 K’s as phantom outs. (Phantom outs are scare cards that you can bluff. By themselves, phantom outs aren’t really powerful. But phantom outs have the potential to become powerful when combined with some number of real outs). Precisely, let’s find the percentage of the time that Hero’s opponent must fold to a bet when a king falls in order to make turning a king into a bluff more profitable than the straight-forward hit-to-win line of play (again pessimistically assuming that opponent raises 2h 100% of the time, forcing Hero to consider QQ or JJ as possibilities):

As long as Hero’s opponent is willing to fold to a bet more than 34.7% of the time a king falls, playing kings as phantom outs is more profitable than not playing them as phantom outs.

River Analysis:

This river is one of Hero’s three phantom outs. Hero leads with the $13 bet analyzed above. The size of this bet is small enough to extract value when Hero has hit and large enough to induce hands to fold when Hero has missed. The only hands that AQ or AJ can expect to beat are KQ or KJ that are turned into bluffs. In response to Hero’s lead, AQ and AJ are purely bluff catchers, but Hero’s opponent only needs to win at least 25.7% of the time for his call on the river to be profitable in the long run:

With AJ, Hero’s opponent can put Hero on 6 AK combinations, 6 AQ combinations, 8 AT combinations, 9 KQ combinations, and 6 KJ combinations. Against this distribution, Hero’s opponent wins 15 times and loses 20 times, putting P(Win) at 42.9%. When first discussing this hand with the player I coached, his opponent’s call seemed unreasonable. After this more thorough analysis, it looks as though my player really needed to bet more to make bluffing a king successful. The problem, is of course, the more my player bets when bluffing the king, the more often the bluff needs to work in order for the overall line of play to be more profitable than the passive, hit-to-win line of play.

In the end, the passive hit-to-win line of play may have been best in this particular hand. However, your opponents won’t always give you proper odds to play straight up fit-or-fold poker. In tougher games, incorporating phantom outs is a must if you expect to have a shot at playing your draws profitably. If you’re not considering plays like those employed by Hero in this hand, you have no shot at beating tougher competition. But simultaneously, don’t forget that folding is sometimes the best play. Maintain balance, know when to be cautious, and know when to attack!

Tony Guerrera is the author of Killer Poker by the Numbers, Killer Poker Shorthanded (with John Vorhaus), and Tournament Killer Poker by the Numbers.

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