A Sacred Cow Can Make a Tasty Dinner

A few years back, one of those brainteaser questions of the week was making the rounds, the sort of thing that gets passed around the Internet and then dissected around the office watercooler. The question was this: You're offered a part-time job with regular guaranteed raises, and the choice is yours as to how those raises are administered. Given the choice between (a) an annual raise of $1,000 or (b) a $300 raise every six months, which should you choose?



Like many a trick question, it comes with an inherent tell, since there would be little point in asking it in the first place if the correct choice was the instinctive, seemingly obvious one. Despite that tip-off, or perhaps because of it, the question effectively demonstrates the counterintuitive aspect of certain math problems, as evidenced by the many people whose resistance to "b" as the correct answer is so strong that it persists even when its explanation is laid out in simple, step-by-step detail.



It's not unusual, of course, for our guts to resist what our brains are being told; this is especially true when notions to which we've long become attached are suddenly called into question. In an age of information overload – who has time to process it all? – the sacred cow status of many beliefs may owe more to the acceptance of conventional wisdom than to any analytic process. Such sacred cows can often be spotted in the poker room, swishing their tails and grazing lazily between the tables, their flawed premises blissfully unchallenged – not because no one knows better, but because those who do are winning players who are not the least bit interested in crowding the pasture by enlightening those who don't.



One of the most popular sacred cows, a member of the Omaha family, pertains to the idea of raising in Omaha eight-or-better with nothing but the nut low. Although a few extremists regard it as a mortal sin in any context, conventional wisdom holds that it's OK in a medium to large field, but strictly forbidden with fewer than four players. This cherished bit of profit-reducing dogma has become ingrained in the heads of poor unsuspecting Omaholics from coast to coast. How did such blatant propaganda ever come to capture the public's fancy?



Well, consider a typical low-limit Omaha player who's playing in a two-chip, four-chip limit game. In a threehanded pot, someone calls a four-chip bet on the river with the nut low, and another player with the nut low raises, for a total of eight chips. As the dealer divvies up the pot, the raiser is castigated by the other nut low, and admonished by the table's Monday morning quarterbacks in conversations liberally peppered with the term "being quartered." Listen to this palaver often enough (and the Omaha player surely will) and a mathematical short circuit apparently occurs, for an astounding number of players get it in their heads that being quartered in this spot translates to a mere quarter of their last action finding its way back to their stacks (a loss of six chips!), as opposed to a quarter of the last action of all three players combined. Worse still, some players – apparently making a Pavlovian-dog-like association between the roundly vilified raise and the negative result – hazily conclude that this perceived six-chip loss (a mistake in itself) is entirely attributable to the "ill-advised" raise.



In reality, the river action costs the quartered low hands not six chips, but two (8 × 3 = 24, divided by 4 = 6, a net loss of 2 from the 8 invested) – and only one of those is attributable to the raise, since one chip was going to be lost on calling the original bet. By contrast, consider what happens when a low-hand player raises in a three-way pot and doesn't get quartered. He gains four chips (8 × 3 = 24, divided by 2 = 12, a gain of 4 from the 8 invested), two of which result from the raise. Think about that for a moment. If you lose one chip when you raise and get quartered, and gain two chips when you raise and get an even split, you can get quartered 67 percent of the time and still break even. Pick your spots any better than that – a reasonable, attainable goal – and those raises become profitable.



Appealing as that math sounds to the profit-minded player, those same numbers offer a clue as to why most players would just as soon take a pass, for a strategy that requires beating a mere 33 percent "success rate" to show a profit entails a high rate of "failure." Most players quickly become discouraged with a raising tactic that may see them quartered a majority of the time, and the "I told you so" comments and other derisive hoots and hollers that will gleefully attend all those "costly" raises are far more likely to blur than clarify the bigger picture.



One should not, of course, be indiscriminate when it comes to threehanded raises in Omaha eight-or-better; in fact, discretion is definitely recommended. For the most part, you'll want to avoid situations in which you're likely to get reraised, thereby compounding your loss when you do get quartered. To that end, you should be far more willing to consider raising into a no-pair straight board than into a no-pair flush board, since a player holding a nut straight is less likely to reraise for fear of being quartered on the high end than a player holding a nut flush, who faces no such danger. On the other hand, suppose your nut-low hand includes the ace of the same suit as the three-flush on board. Can the high hand reraise then? Of course, whether he reraises or not, you still could be quartered by the low, but clues may be available as to the likelihood of that prospect. Did the flop bring three low cards? Two? Only one? Are your opponents the types to chase nut-low draws when the flop brings two high cards? Just how many nut-low cards do you have in your hand? Has an ace on board elevated a piece of cheese to nut-low status, in which case, how likely is your opponent to have it? Are your opponents on tilt, or feeling snakebitten? These are just some of the variables that can come into play.



Were all three-way situations created equal, the no-raise rule of thumb would probably be a pretty good one. But since they're not all created equal, discriminate raising offers the potential for reward, and the inherent risks should serve as a yellow light, not a red one. The happy fact is that the board, your position, and the way the hand develops, combined with your knowledge of your opponents' tendencies, all provide clues as to when to speed and when to brake. Enjoy the drive, because the math is on your side.

Barry Mulholland may be contacted at [email protected].