Poker Articles

Short-Handed Poker: The Overcard Quandary Part II
by Jason Pohl

In part 1 of this article, I used some fairly dense calculations to demonstrate that the best play with overcards is very often a simple fold. In the second section, we will follow-up by gauging the odds with a larger pot and multiple opponents. Then, we will answer an important question. Will folding overcards cause our opposition to run us over with bluffs?

Overcards in a Multi-Way Pot.

Scenario 4. Button has A K. Big blind has T 9. Limper has 65
Flop is 2 5 T. Big blind bets out and Limper calls. 8.5 small bets in the pot.

• Outcome 1. Ace or King on the Turn (6/43 * 10.5) = +1.465 small bets
• Outcome 2. No Ace or King (37/43 * -1) = -.861 small bets
  Total EV: .604 small bets/hand profit

The button's best hope is that all overcard outs are clean. If they are, then calling earns a considerable profit. This should be fairly obvious, since we showed a gain calling with 6 outs, one challenger, and a smaller pot size. Next, we will examine the numbers if one limper holds a kicker common to the button's overcards.

Scenario 5. Button has A K. Big blind has T 9. Limper has A 5.
Flop is 2 5 T. Big blind bets out and Limper calls. 8.5 small bets in the pot.

• Outcome 1. King on the Turn (3/43 * 10.5) = +.733 small bets
• Outcome 2. Ace on the Turn (2/43 * -5) = -.222 small bets
• Outcome 3. No Ace or King (38/43 * -1) = -.884 small bets
  Total EV: .373 small bets/hand loss

The pot size is healthier with three opponents than only two, but having one overcard cut off still represents a swing of one small bet and a significant loss. However, like the heads-up examples in Part I, the real danger is when both of the button's outs are cut off. Scenario 6 analyzes the loss when the button needs two perfect cards.

Scenario 6. Button has A K. Big blind has K T. Limper has A 2.
Flop is 2 5 T.

• Outcome 1. Running Ace/King (.0288 * 18.5) = +.5328 small bets
  The button will only win if exactly an Ace and King falls OR exactly a Jack and Queen falls. One of these combinations will transpire 2.88% of the time. To simplify, I will assume there are 4 extra big bets won if the button gets lucky enough to win.
• Outcome 2. Ace or King on Turn, Blank on River (4/43 * 38/42 * -5) = -760/1806 = -.421 small bets
• Outcome 3. Jack or Queen on Turn, Blank on River (6/43 * 34/42 * -3) = -612/1806 = -.339 small bets
  This scenario occurs because the button picks up an inside straight draw. When a complete blank falls, the button spends one extra big bet.
• Outcome 4. Jack or Queen on Turn, Ace or King on River (6/43 * 4/42 * -5) = -120/1806 = -.067 small bets
  After a Jack or Queen, if an Ace or King falls, the button will likely call down on the river, sacrificing a total of 2 big bets after the flop.
• Outcome 5. No Ace, King, Jack, or Queen on Turn (33/43 * -1) = -.767 small bets
  Total EV: (.5328 - .421 - .339 -.067 -.767) = 1.06 small bets/hand loss

Four of the five possible outcomes are quite disastrous, and even the best outcome occurs only 2.88% of the time. A similar misfortune would transpire if either opponent held a very powerful hand such as a set of 5s or 2s. Against a set, the button is drawing dead to a running Queen/Jack.

But how often can the button expect to have all 6 outs, 3 outs, or nearly zero outs? If we presume that our opposition called preflop with at least a reasonable hand, then the risk that each player holds an Ace or King to go with their pair is very significant. For example, if we assumed 22, 55, TT, AA, A2, A5, AT, K2s, K5s, KT, KK, QQ, JJ, T8, T9, JT, QT, 54s, 65s, 75s, 99, 88, 77, and 66 were all possible hands, then 25% (34 of the 136) of possible holdings would counterfeit the button's AK. If we believed for whatever reason that our bettor or limper could be holding overcards such as QJ, KQ, AQ, AJ, or weaker pairs such as 32s, 53s, T7s, 44, or 33, then the percentage of feared hands goes down to 15.2% (34 of 223). The principal sense is that each player who has called a bet increases the probability the button has 3 or fewer outs.

How often is the button drawing dead or nearly dead? On a flop like the one in Scenario 6, maybe not that often. Only a 22, 55, TT, and AA are likely dominating hands. There are only 15 combinations of these pocket pairs. Combining those deadly hands with the possibility both the Ace and King are held by an opponent, the AK is drawing nearly dead 15-20% of the time. It gets worse. A flop like {2 5 T} is abnormally non-threatening. On the other hand, a dangerous flop such as T 9 8 is prone to generate a ruinous outcome such two pair, a set, or a made straight.

Against a fairly non-threatening flop, we can estimate that the button has all 6 outs about 40% of the time, only 3 outs 40% of the time, and virtually no outs 20% of the time:
Overall EV: (.604 * .4) - (.373 * .4) - (1.06 * .2) = .2416 - .1492 - .212 = 0.12 small bets/hand loss

If we measured a more dangerous flop, our numbers might look closer to the following:
Overall EV: (.604 * .2) - (.373 * .5) - (1.06 * .3) = .1208 - .1865 - .318 = 0.297 small bets/hand loss

The lesson here is that the bigger pot goes a long way towards adding profitability to a call with overcards, but as the chance for a catastrophe increases (due to a dangerous flop or a high number of players), the profit with overcards turns into a definite loss. For that reason, solid play of overcards is so often associated with excellent or world class players. Remember, the rewards earned by calling at the correct times with overcards are relatively marginal. The losses faced when misplaying overcards can be huge. So, stick with a conservative approach. Call with overcards only against one opponent (and not even then if the pot is small) unless you have a very strong understanding of your opponent's play and their possible holdings.

Overcards against a Habitual Bluffer.

There are two last situations I'd like to briefly examine. Occasionally, a shorthanded player will find himself against a habitual bluffer or semibluffer. A habitual bluffer will consistently bet the whole way with no pair, sometimes with overcards or ace-high but also with far less. It frequently makes sense to call with the intention of showing down ace-high. Other times, taking a card off is the best play, if implied odds are good or it sets up future plays (slowplaying a big hand.)

Scenario 7. Button has A Q. Big blind has K J.
Flop is 2 5 T. Big blind bets out. 5.5 small bets in pot.

With a hand like AQ, I will call the entire way against a known bluffer. Here's why.
If the bluffer has no pair (e.g. KJ), the AQ will win about 75% of the time.
If the bluffer actually has a pair (e.g. T9), the AQ will still win about 25% of the time.

Even with only 5.5 small bets in the pot, the button can call down and remain a winner if the big blind is semibluffing with no pair 20% of the time or more. The combined potential of the AQ as a bluff-catcher and 6-out draw makes a calldown profitable. If the big blind will only bluff on the flop, the button should call even more often. In such a case, the big blind's check on the turn could indicate weakness, and the button has the option to take a free card or to semibluff back at the big blind.

In my experience, facing habitual bluffers is the exception rather than the rule. Most players in the big blind do not bet out as a bluff, and most players would not stop betting until at least the river. If you find yourself against either type of bluffer, your calling standards (and in fact, the whole way you would play a legitimate hand) should be adjusted to overcome their style.

Won't My Opponents Begin Bluffing More?

With no pair against all but the most aggressive competition, overcards are a loser. It is better to dump them quickly and move on to the next hand. But good players will be quick to point out one possible impact of such a strategy. If a preflop raiser plays fairly tight and will fold on the flop without a made hand, doesn't this leave a huge gap that good players can exploit? Namely, wouldn't a bluff on the flop from the big blind become incredibly profitable? The answer is 'yes.' However, there are two reasons that we shouldn't worry so much about it.

First, most players are unobservant, especially at lower limits. Online I have found lack of observation skills to be further in the norm, since many players try to compete at two or more tables simultaneously. To have one's tightness countered effectively, a player must observe the button folding multiple times in similar situations, and then they must be advanced enough to know how to use this information. While I would not always expect your opponents to be oblivious to your folds, it is far worse to expect your opponents to "guess" your cards. Don't sweat it until you find yourself the victim of excessive aggression from one player. When you do, switch gears and adjust your play to punish their bluffing.

Second, you will still have a hand often enough to camoflage how tight you are playing. Realize that in all seven scenarios in this article, the highest card on the flop is a Ten. Such flops are atypical. A hand like AKo will flop a pair or better 1/3rd of the time. AKo will also flop a decent draw (and overcards) somewhat regularly. On the other hand, the solid preflop raiser is more vulnerable when the flop contains three small cards. When the button doesn't hold a pocket pair, a bluff from the big blind will likely be profitable. For this reason, it is important to carefully observe the frequency of bets on those ragged flops (and flops such as QQx or AA4), since those are the types of flops that bluffers target. All in all, my suggestion to fold quickly on the flop without a pair is dangerous if the bluffer faces no consequences. So, it's your job to remain vigilant, identify a player's attempts to steal pots, and effectively counter.

Let me reiterate one last time. Losing players almost always lose because they call too much. Until you reach middle limit and high limit games (and very often then too), a winning strategy entails abandoning fancy plays, big bluffs, and even some semibluffs. Straightforward play takes the money, and showing down a strong hand is required. Overcards don't qualify as a "strong hand." Instead, they are a weak draw not playable except as a semibluff or in exceptional circumstances against exceptional players.

I hope you are enjoying the new year. If you would like to email me with a question or comment, you can reach me at Jason@PokerPages.com. Until next article, good luck!!!