Draw Poker and Jackpots

As four-player, 20-card poque migrated up the Mississippi, it adopted a feature or two from older vying contests. English-speaking brag players liked the idea of using all 52 cards, for example, if only because more than four people would be able to play at a time. Poque had appealed to them because what they called bragging was the French game's ultimate tactic as well, though poque's narrow range of two-, three-, and four-of-a kind hands must have seemed rather limited to anyone used to drawing to flushes, runs (straights), and flush-runs. So it seems a safe bet that players raised on brag added these hands to poque's hierarchy, along with an extra round of betting and drawing, which they called "taking in," to increase their odds of hitting these long shots.



In New Orleans itself, Spanish mus players found it natural to spice up the local poque games with 52 cards and a replacement mus ("draw") to a wider range of hands. Like their Anglo counterparts, they mixed and matched rules in much the same way that their chefs were combining ingredients from Acadian, French, and African cooking.



As "Draw Poke" surged north and picked up an "r" at the end, its new rules were gradually standardized. By 1840 or so, nearly everyone agreed that after being dealt five cards each from an unstripped deck, players determined whether their hand was worth betting or "seeing" a bet with; if not, they would "throw up" their hand, or as we would say, fold it. Each remaining player then exercised his option to stand pat – that is, keep all five original cards – or turn in to the dealer facedown between one and five of them and receive an equal number, also facedown, from the top of the deck, followed by a second round of betting. If one player made a bet or a raise that the others were unwilling to see, the bettor won the "pool" without having to show his hand – though he could if he wanted to prove that he had, or hadn't, been bluffing. But if two or more players remained when the betting was over, they turned over their cards for a "show of hands," and the same hierarchy we're familiar with today determined the winner.



With more players drawing to an expanded range of hands, pools became larger and tactical skill more decisive. When holding the red kings and three other diamonds, for instance, which cards should be replaced against a raiser in early position? How often, and against which opponents, could one get away with a bluff after standing pat with "nary pair"? It was no longer simply a matter of getting lucky, or not, on the deal, then betting for value or bluffing. Draws provided hope to players dealt weak starting hands, which in turn triggered the development of tactics to deploy against overly hopeful opponents. With 52 cards in play, five contenders for the pool might remain after the draw, even more if the discards were shuffled back into the stub of the deck. Assuming the game was on the square, winning money depended on memory – how, and how much, did each opponent bet on the first round? how many cards did each draw? – as well as a knack for deducing the range of hands that each might be holding from the number of discards and the size of the second-round bet or raise, all this in light of mathematical probabilities, previous betting patterns, facial expressions, and so on.



A new wrinkle called the jackpot began to appear sometime during the Civil War. A player was required to hold at least a pair of jacks to open the betting, though no one was required to open. If no player saw the opening bet, the bettor won the small pot and was compelled to show a pair of jacks or some higher hand. If his opening bet was called, he usually drew three to his pair, though the rules permitted him to discard one paired card and draw to a straight or flush; in this case, he discarded to the side of the pile so that after the showdown he could prove he'd held at least jacks when he opened. Failure to do so would require him to contribute twice the amount of his original bet to the pot. But the key rule of jackpots was that if no one was able to open, everyone anted again, the deal rotated clockwise, and the process was repeated until one player was able and willing to "break the pot" and the hand played out as usual. In a variant known as the progressive jackpot, the second round required queens or better to open, the third round kings or better, the fourth round aces, then kings, queens, jacks, and so on.



Progressive or not, jackpots were intended to build larger pots while thwarting reckless players who made a habit of betting huge sums with weak hands. Yet such players could still call or raise the opening bet, stand pat with virtually nothing, then win the pot with a bluff.



Many Civil War soldiers preferred a 53-card version of draw they called Mistigris^[], in which the joker was wild, boosting the probability that draws to big hands would succeed, which added yet another level of reckoning and tactical prowess.



Larger pots, more diverse reckoning skills. The former attracted more blacklegs, the latter more ancestors of today's poker maestros. For the very best players, draw's extra round provided more chances to leverage probabilities or pick up a tell. But it also gave cheaters more opportunities to deal seconds, see replacement cards in a mirror, or gain other illicit advantages.



By the 1870s, as the nation tentatively recovered from the bloodiest conflict in human history, genuine and self-proclaimed experts began publishing books on the new poker variants brought home by veterans. Among the most lucid of these was math professor Henry T. Winterblossom's The Game of Draw Poker (1875). The 72-page primer begins with a brief history of cards, followed by caveats about the morality of playing for money: "Poker, unfortunately, is one of the few games that cannot be played so as to afford any pleasure, without the interchange of money. Indeed one might as well go on a gunning expedition with blank cartridges, as to play poker for 'fun.'" He puts its corrupting potential on a par with faro and betting on horse races, even warning prospective readers: "If they have never indulged in the game, they are earnestly exhorted at this point to seek no further information, but to remain happy in their innocence" – which sounds like a quaintly Victorian selling point similar to warning viewers about the Strong Sexual Content of an HBO series. "It is unnecessary to say that the game should never be permitted to enter the family circle, no matter how trifling the stake proposed may be," he tut-tuts, all part of his wobbly balancing act. "Those who have winked at [the morality of poker], and those who have denounced it, may both be in the wrong. It must be admitted, however, by its most bitter enemy that, as a source of recreation, when moderately indulged in, and stripped of its objection-able features, it presents advantages not to be obtained in any other amusement." Who, after all, could object to a game with zero objectionable features?



Once the nervous Mr. Winterblossom finally gets down to the business of showing how mathematics can make draw poker profitable, he does a fine job all around. Employing basic algebra, he stresses "the question of percentage, believing beyond doubt that the player who will avail himself of the advantage which certain combinations give, will … have it in his favor, and must, in the long run, win." He must recall the number of replacement cards each opponent took and "endeavor to study his style of drawing," including the kinds of draws he favors, his betting patterns, facial expressions, and so on.



In the spirit of Girolamo Cardano, Winterblossom asks the reader to suppose he's been dealt four hearts and a card of another suit. "You discard the odd suit and draw a fresh card from the pack. Now, before seeing the fresh card, you wish to determine what your chance of making a flush is. You know of course that you hold four hearts in your hand, and that there are nine others among the 47 cards which remain in the pack. It is clear then that your chance is as 9 to 47, which would be 5 2/9 to 1 against your making it."



Yet what about when our opponents are holding many of those 47 unseen cards – wouldn't that alter the odds? By walking us through some slightly more complex algebra, Winterblossom proves it would not. "It may then be set down as an axiom that the number of players is a neutral element which determines nothing, and that the reasoning must be based on the five cards which you receive and the 47 which are unknown."



Such facts aren't news to most modern players, but to those who'd learned poker in the age of cold decks and mirror men, or relied exclusively on "gut feelings" and "nary pair" bluffs, Winterblossom offered what must have been eye-opening revelations. Seat-of-the-pants amateurs could suddenly calculate odds to determine the right play. If the pot offered them less than 11-2 money odds on an opponent's bet to draw to that fifth heart, for example, it was clearly a blunder to call.



What about bluffing, a more instinctual and thespian tactic? "In former days," he writes, "when the betting was unlimited, this was frequently the determining feature of a hand, no matter what the cards were; and to bluff an opponent, while holding yourself 'nary pair,' was the pinnacle of ambition at which all players aimed." In an era of limited bet sizes, however, he advises readers to "keep steadily in view the principle of conservatism." He admits that while this strategy "may perhaps to a limited degree be open to the charge of timidity, no one will regret in the end having pursued it. The most brilliant play is rarely satisfactory when it terminates in a loss."



As one of the first pokeraticians to focus on psychology, he notes that "a thorough exhibition of each individual character is revealed at every step of the game." More than that, "even the most casual observer cannot help perceiving that the commodity known as selfishness predominates to an unlimited degree, notwithstanding the various contrivances the players adopt to conceal its presence." In keeping with Adam Smith's and Alexander Hamilton's insights about market capitalism, he makes clear that poker is "not only a selfish game, but one that every subterfuge that can be brought to bear is introduced; every artifice that the laws of the game will permit, is pressed into service; and all directed at one object, viz: to win your money." In other words, playing poker well involves cunning and duplicity but no outright cheating – dishonesty, that is, while honestly abiding by an accepted set of rules.



We can infer from the growing number of such books near the end of the 19th century that a mathematical understanding of poker was gathering momentum, which in turn suggests that more and more games were being played on the square. In 1891, however, long before our national pastime finally shed its reputation as the Cheating Game, the California legislature banned gambling anywhere in the state. (Most other states had already done so.) But in 1911, California Attorney General Harold Sigel Webb exempted draw poker from the ban, arguing that it was a "Game of science rather than chance" because no cards were dealt faceup – as they were in "stud-horse poker." However faulty its logic, Webb's ruling encouraged public poker clubs to open around the state by 1930, most of them in Gardena, 15 miles south of downtown Los Angeles.



Flash forward to 1978, when Doyle Brunson's Super/System, the bible of the post-cheating era, was published by its author. Five-card draw was already on its way out, the biggest loser in a popularity contest with seven-card stud, Omaha, hold'em, high-low and low-only games. Since no cards were exposed till the showdown, if ever, draw provided less information than these newer games did. Worst of all, it allowed only two rounds of betting.



Even so, Brunson had asked "Crazy Mike" Caro, arguably the best living draw player, to write a chapter of Super/System on his specialty. Caro did himself proud – too proud, perhaps. In 76 manically brilliant pages, he broke down the minimum opening requirements for small-, medium-, and large-ante games; analyzed starting hands in terms of position, limit size, raising and sandbagging guidelines; broke new ground on bluffing strategy, tell reading, and gauging opponents' hands by how many cards they drew; and developed an elaborate count system and no fewer than 50 statistical tables showing the odds of improving one's hand.



Caro's analysis was so comprehensive, it seemed to "solve" the 150-year-old game once and for all. The only problem was that hardly anyone wanted to play it anymore. In 1983, the organizers of Binion's World Series delivered what may have been the coup de grace by dropping it from their schedule. When California legalized other forms of poker in 1987, the exodus from draw tables accelerated to the point where, except in a few longstanding home games, five-card draw jacks-or-better, poker's most popular variant for more than a century, has now gone the way of the dodo.