Horrendous Plays: There's Just No Other Way to Describe Them - Part II

In my last column, I told you of a play that truly fell into the "horrendous" category for a multitude of reasons. This time around, I shall analyze a hand that, while not played quite as horrendously as the last one, illustrates one of the most common and costly mistakes in poker – missing bets. It also illustrates the expense of "paying off" when one is clearly beaten. Since the long-term result of winning poker is achieving a positive hourly rate, every missed bet contributes a negative result to your overall hourly rate. Similar losses accrue from the inability to lay a losing hand down. Losing money in the long run is definitely horrendous, wouldn't you agree? Unlike the hand in my last column, I was not an active participant in this $20-$40 stud hand. The hand is a three-way pot on part of the journey and becomes heads up toward the end. It contains no straight or flush draws, which one might think would yield a somewhat simple analysis. As the hand progresses, we see the complexities surface quite quickly.

Third street: The No. 1 seat has a 3 doorcard, which is the low card. The suit is inconsequential in this scenario. He brings it in for $5. A queen, with a suit that is equally inconsequential, is the doorcard for the No. 3 seat, and he completes the bet to $20. The No. 5 seat has yet another "suitless" doorcard, a 7, and he calls the raise. Seats No. 6 through No. 8 fold, and the No. 1 seat reraises to $40. This is not a player who is known for being exceptionally creative, so it stands to reason that his most likely hand is pocket kings or aces. The less likely hands are rolled-up threes (since most players would adhere to perceived conventional wisdom and not reraise in this spot with such a strong starting hand) or split threes with an ace, or his raise is due to his thinking that he has the "real queens." Since the player in the No. 5 seat with the 7 for a doorcard is the one whose future mistake I am illustrating, we shall view the hand primarily from his perspective. He actually has split sevens with an ace kicker, so he should be thinking that he is most likely looking at pocket kings. The No. 3 seat with the queen calls with absolutely no hesitation (indicating probable split queens, "as advertised") and the No. 5 seat with the split sevens also calls.

Fourth street: It is totally uneventful and completely predictable. The No. 3 seat is high with the queen and he checks, the No. 5 seat also checks in turn, and, of course, the No. 1 seat with the fairly obvious premium pocket pair bets. He receives two calls, regular as clockwork.

Fifth street: The No. 1 seat pairs his 3 and nobody else improves. He is now the high hand and, naturally, bets. The No. 3 seat, who most probably has split queens, hems and haws, contemplates, and then makes the correct play by laying his hand down. However, the split sevens with the ace continues to call. There are a couple of schools of thought here. Assuming that no sevens or aces were folded, and assuming that the opponent has kings up, he is drawing to five cards with two to come. The game is full, so he has seen his own five cards, three of the No. 3 seat's cards, and five folded doorcards, and is currently looking at three of the No. 1 seat's cards; plus he can intuitively assume "seeing" the No. 1 seat's holecards as kings. That is a total of 16 seen and two quasi-seen cards. Counting only the seen cards, that leaves 36 cards in the deck.

We calculate the odds of making the hand with two cards to come (sixth and seventh streets) as: 1-(31/36 X 30/35), or 26.2 percent. Well, this is a 1-in-4 chance of making the hand, assuming the best-case scenario. However, if our intuition is incorrect and the No. 1 seat has pocket aces, the chances are very grim indeed. Let us also not forget that if the No. 1seat has kings up, he is drawing with two cards to come to a full house. His chances of filling are: 1-(32/36 X 31/35), or 21.27 percent. Computer analysis of one million theoretical hands on fifth street shows the kings up to be a 3.55-to-1 favorite, winning just over 78 percent of the time over sevens with an ace. Of course, the No. 5 seat is getting immediate pot odds to justify playing his split sevens with the ace. Currently, there is $244 in the pot for which he has to call only $40, and getting more than 6-to-1 pot odds on a 3.55-to-1 shot is profitable. But, if one factors in that a call on fifth street implies a somewhat mandatory call on sixth street (unless the No. 1 seat hits an open deadly card like another 3, for instance), it sort of becomes an $80 proposition going for $284 (the $244 currently in the pot plus the opponent's probable $40 sixth-street bet), which is barely over 3-to-1. And that assumes that he will be capable of laying down his hand on the river should it not improve or should it improve to two unacceptable pair, and not dole out another $40. This would appear to yield slightly unprofitable implied pot odds. Of course, hitting his ace on sixth street would give him ample opportunity for a raise if the kings up bet. On the other hand, making a set of sevens would cause him to lose his position, and going for a check-raise might prove costly. It's darned complicated, isn't it?

Laying the unimproved sevens down on fifth street is a somewhat viable option that some might consider, especially when it is quite possible that the opponent does have aces up, which would reduce the No. 5 seat's hand-making cards from five to three and, consequently, his chances from 26.2 percent to 16.2 percent. It is also remotely possible that the No. 1 seat has the dreaded quad threes!

The other school of thought is what would prevail in most players' minds in this situation: Assume that the most likely hand is kings up and play these marginal odds. In my opinion, neither decision would constitute a horrendous play, yet. Let's move on to sixth street.

Sixth street: Sure enough, the No. 5 seat hits his magic ace, and the No. 1 seat with open threes impulsively bets out without considering what that ace likely means. Of course, he gets raised, and in simply calling, he has virtually turned his hand over, quasi-exposing a pocket pair that is of little consequence, since anything he has will not beat aces and sevens, including aces in the pocket! Ironically, aces in the pocket would now be the hand the No. 5 seat would want him to have instead of kings in the pocket. As it turned out, kings up was the hand.

Temporarily shifting our perspective to the No. 1 seat, should he have called the No. 5 seat's sixth-street raise? Let us briefly analyze this scenario, as it is simply a variation of a core stud situation that is common enough to warrant some study. At this point, he simply has to give his opponent at least split aces up, and in doing so, he knows his six cards, the five folded doorcards, and the No. 3 seat's folded upcards, and can safely eliminate six more of his opponent's cards as not being directly relevant to his hand. That leaves 32 cards, of which he can hit only four to make his hand. That's precisely a 1-in-8 shot, or 12.5 percent. The pot at this exact moment has $404 in it, and he needs to call only $40, so he is getting more than 10-to-1 on his money on a 7-to-1 shot. Well, that sounds profitable, right? On the surface, it is correct to call, but if the opponent bets on the river, can he release his sure-to-lose kings up? If he is one of those all-too-common players who will think that he has "come this far" and cannot resist the compulsion to call the river since he called the sixth-street raise, he is not getting correct odds to continue playing past this point. Also, we are not factoring in his equal chance to fill up. Further confusion arises due to the staggered arrangement of the pair ranks, in that the No. 5 seat's high pair and low pair are both higher than the No. 1 seat's, respectively. Should the No. 1 seat fill the threes and proceed with a check-raise on the river only to be met with a three-bet, it will get very costly. What is worse, filling the kings could yield the same result, and a three-bet on the No. 5 seat's part could be indicative of aces full just as likely as it could mean sevens full. This is just one of "those" hands. Of course, the likelihood of both parties filling up on the river is fairly remote, 1.56 percent, so playing the hand to the end is fine if he has mentally prepared himself to release the unimproved hand if his opponent bets the river. Calling the probable bet on seventh street with unimproved kings up is tantamount to throwing money out of the window.

What should also be of great concern to the No. 1 seat is the very real possibility that the sixth-street raise is not aces up, but is indicative of any one of four sets (slow-played rolled-up sevens; a pocket pair making trips on fourth or fifth street, although I would say that fifth-street trips would be the least likely possibility, as most players would reactively raise their opponent's fifth-street bet coupled with the paired doorcard in that proverbial "Oh, yeah? Take that!" kind of way; or, he may have slow-played pocket aces and thought he had the sole option of calling on fifth street due to his opponent's open pair, but now could raise on sixth street with virtual impunity with trip aces). If it is three aces at this point, kings up is in serious trouble. Of course, all of this conjecture, while necessary during the hand in contemplating all possibilities and correct decision-making, is moot now, as the omniscience of hindsight analysis of the hand from multiple viewpoints tells us that on sixth street, the hands are, in point of fact, kings and threes against aces and sevens.

Seventh street: Here, the most serious mistake occurs. The No. 1 seat predictably checks, and the man with aces up checks the river behind him! This is a very costly mistake. Since kings up had precisely a 12.5 percent chance to fill up on the river, aces up is going to be a good hand a whopping 87.5 percent of the time. Of that 87.5 percent, I would conservatively estimate (it's probably more) that at least 80 percent of players with kings up would incorrectly call a bet, yielding at least 70 percent. Well, give me a 7-to-3 favorite position on an even-money bet and I will take it all day long! Assuming that the No. 1 seat had kings up going to the river, a check on the river by the No. 5 seat is a very bad play. But what if the No. 1 seat has pocket aces and the No. 5 seat truly "sucked out" on sixth street by catching that case ace? It's possible, albeit less likely than kings up. In this scenario, the No. 1 seat's chances of filling are cut in half, to a mere 6.25 percent. That's 15-to-1! To clarify, I'm stating categorically that checking in either scenario is tantamount to the aforementioned "throwing money out of the window." In fact, it is an even worse mistake to refrain from betting than it would be for your opponent to call a bet. In the unlikely event that you do encounter the unfortunate check-raise, you can always opt to be the better player and lay your hand down. There is no law that says you have to call at that point. If you bet and get raised, your opponent is full. The few players in the world who could put a profoundly sophisticated read on your ability to lay down obvious aces up (or better) in the face of a river check-raise, and who would have the temerity to do so in that spot without having made their hand, are an exceptionally small fraternity, and not one whose membership you'll likely contend with except in very high-limit games. Play the percentages. Bet your hand.