Upside Down, Unexpectedly

Poker steels a person to handle the unexpected.

Those who’ve played the game even for a short while -- and who’ve paid attention enough to absorb some of the odds and probabilities and learn what is likely and what is not -- become accustomed to surprises. You know, kings cracking aces, the occasional one- or two-outer showing up on the river, or various runner-runner revelations that can make improbable winners of all-but-certain losers.

Of course, even when in possession of this knowledge, we still experience a certain level of surprise when such things happen. If we’re human, that is. Experiencing such emotion is part of what helps keep the game interesting to a lot of us. After all, in our “normal,” day-to-day lives, we rarely experience surprises, and indeed often try to map out our activities so as to avoid them.

Regardless of who you supported, the result of last night’s presidential election was more than likely not what you expected to happen.

Watching the coverage play out starting during the early evening when the first polls closed on the east coast, all the reporting emphasized the high likelihood of Hillary Clinton winning. In fact more than one outlet used a poker metaphor to describe Donald Trump’s needing to win several states in which Clinton was favored, saying his position was like “drawing to an inside straight.”

A couple of hours in, though, just after nine o’clock ET when another round of states’ polls closed and more projections and calls were delivered, the situation suddenly swung the other way. For Trump supporters, it was a delirously exciting 20-25 minutes or so; for those backing Clinton, it was a nightmarish sequence, occurring rapidly enough to make it hard to grasp fully the implications of what was happening.

The betting markets were slightly ahead of the game with their numbers last night. My friend Rich Ryan was tweeting out Pinnacle’s lines on a regular basis all night. Actually he’d been doing it for a week, with “HRC” the big favorite, climbing as high as -780 as things got going last night. In the space of an hour that figure dropped to -124, then after lingering there a while the sucker flipped to show “Trump/Other” at -122. An hour later Trump was up as high as Clinton had been, and by shortly after 11 p.m. here it already seemed all but certain there was no way Trump would lose.

I had CNN on, and sure enough Jake Tapper was revisiting that poker analogy not long after the flip had occurred. Recalling the earlier reference to Trump’s seemingly slim chances, he noted how the situation had been changed to Clinton being the one drawing not just to an inside straight, but to an inside straight flush, suggesting the need for a one-outer rather than a four-outer. (Am still hunting down the exact quote -- when I find it I’ll include it here.)

I was mentioning yesterday Nate Silver’s much-cited election forecast. He’d famously predicted 49 of 50 states plus D.C. correctly eight years ago, then got all 50 of them right along with D.C. in 2012. This time he (or his models) whiffed on five key states -- Florida, North Carolina, Pennsylvania, Wisconsin, and Michigan -- all of which he had going Clinton’s way, and all of which Trump won.

Signing off from the coverage over on FiveThirtyEight last night, Silver actually wrote he wasn’t surprised by the outcome given that the polling had indicating the possibility of a competitive race. But he also admitted that “in a broader sense... it’s the most shocking political development of my lifetime.”

Yesterday I also brought up the analogy of picking NFL games, bringing up again that Pigskin Pick’em contest I’ve enjoyed over the last several years. Sometimes when writing about the contest I’ve alluded to those “Win Probability” graphs and how wild they sometimes appear in games that end with unlikely finishes where one team snatches victory away from the other following a final, surprising twist (or two or three).

The graph tracking last night’s developments was similarly dizzying. Just below is the one from The New York Times, which is pretty much identical to the ones created by other outlets overnight:

The reasons both for Trump’s win and for the failure of so many to see it coming are going to be discussed for some time. I have my own ideas, though don’t necessarily want to try to sort them out here just yet.

When a poker hand or football game gets all twisted around at the end, it’s usually easy enough to isolate the card(s) or play(s) that caused the outcome. This one is a lot more complicated, though still can be explained.

All of that effort will have the effect of lessening the shock of experiencing that head-spinning half-hour last night. When the blue and red graph lines unexpectedly dived upon one another, crossing paths in a sudden rush that literally turned the story they were telling upside down.

I mean, really... whatta river.

Image: “Election 2016” (adapted), DonkeyHotey. CC BY 2.0.

General Eisenhower’s Calculations

In late 1943, a story regarding Dwight D. Eisenhower was circulated in the country’s newspapers. This was right about the time he was appointed Supreme Commander of the Allied Forces in Europe, beginning preparations that would lead to the invasion of Normandy six months later. A little less than a decade later, Eisenhower would be elected the United States’ 34th president.

It was a poker story, and not one usually told of Eisenhower. The more frequently shared poker-related anecdotes concerning Ike appear in his 1967 collection of autobiographical anecdotes At Ease: Stories I Tell to Friends. At least these are the ones that get repeated most often whenever Eisenhower’s poker playing is discussed.

Early in that book Eisenhower tells of learning poker as a young boy. He also talks about his time at West Point, and how he only attended cadet dances “now and then, preferring to devote my time to poker.” At another point he refers to the game as “my favorite indoor sport.”

He relates how when he played poker at West Point, he meticulously kept track of wins and losses. “The financial results of the games were always recorded in books with debts to be paid after graduation,” he explains, noting as well how he eventually had to stop playing with others because of their failure to pay up after he beat them.

A bit later in the book he tells of playing in a twice-a-week poker game at Camp Meade where he served under George S. Patton, where again he was a consistently winning player. That’s the setting for a much-repeated anecdote of Eisenhower winning a sum off a particularly unskilled player who paid him in war bonds, causing Ike to feel sorry for his opponent. He then conspired with others to lose on purpose to the fellow in order to get him his money back without embarrassing him.

“This was not achieved easily,” Eisenhower explains. “One of the hardest things known to man is to make a fellow win in poker who plays as if bent on losing every nickel.”

Like I say, these stories are fairly well known. There’s one other discussion in the book of a fellow named Bob Davis who served as an influence over a young Eisenhower, including teaching him about “poker percentages.”

“He dinned percentages into my head night after night around a campfire,” tells Eisenhower, “using for the lessons a greasy pack of nicked cards that must have been a dozen years old.” They played for matches, and the experience provided significant intellectual stimulation to the youth. “So thoroughly did Bob drill me on percentages that I continued to play poker until I was thirty-eight or forty and I was never able to play the game careless or wide open,” he adds. He also notes that since many of those whom he played against weren’t so knowledgeable about odds and probabilities, he was thus a consistent winner.

That episode in which the officer paid Ike with war bonds actually discouraged him from playing poker, as he eventually concluded “it was no game to play in the Army.” Especially after he had risen up the ranks, Eisenhower felt bad about beating those under him. “When I found officers around me losing more than they could afford, I stopped playing.”

However, Eisenhower still thought about the game from time to time, which brings me back to that somewhat obscure story from when Ike was well past his poker-playing days in his early 50s.

The story emanates from Naples, Italy, dated December 9, 1943. “Gen. Dwight D. Eisenhower’s popularity has skyrocketed throughout the Fifth Army as a result of one of his recent pronouncements,” it begins. But the pronouncement had nothing to do with calculating military strategy -- rather it concerned a problem involving “poker percentages.”

A soldier had written to Eisenhower, having “heard that the commander in chief has a hobby of mathematically computing odds on poker hands.” The letter writer, a GI named Simon Davis, asked him what the chances were of drawing exactly three kings and two jacks when dealt a five-card poker hand.

The article only summarizes Eisenhower’s reply, although the letter itself is quoted directly in Play the Devil: A History of Gambling in the United States from 1492 to 1955 (1960) by Henry Chafetz. Here’s what Eisenhower said:

“Although I’m afraid my power of gauging percentages in filling poker hands is a bit overrated, I do like to figure them in my spare time. I haven’t had time to go too deeply into the exact figures of your chances of drawing three kings and a pair of jacks -- but I’d say they are about 1 in 1,082,900 times. Any mathematician will prove I’m completely wrong, but, anyway, don’t count on doing it in a pinch.”

Going back to the newspaper article, we learn that “Since then doughboys through Italy have been doing heavy pencil and paper work. Scores of them wrote letters to the Stars and Stripes declaring ‘Ike’ almost hit it on the nose with his estimate.”

Clearly it was a great morale booster for Eisenhower to have answered the letter so thoughtfully. The article concludes with a quote from one “doughboy” saying “I’ve always thought a lot of the general, but now he’s tops on my list of great greats.”

Not to doubt Eisenhower, but just fiddling around a bit with this I’m pretty sure he’s a bit off with his answer, despite the support of those doughboys who checked his work.

If there are four ways to be dealt three kings and six ways to get two jacks, that would mean 24 different ways to be dealt kings full of jacks. Meanwhile there are 2,598,960 distinct five-card hands, which actually makes it 1 in 108,290 to be dealt three kings and two jacks.

In other words, I think Ike might have added an extra zero to the correct answer. I’ll be like Ike, though, and modestly invite anyone who wants to correct me to please do so.

Incidentally, while scouting about regarding this story, I ran across one attempt to summarize it that identified the GI as “Bobby” Davis (not Simon). I decided that had to have been a mistake by the author who probably conflated Eisenhower’s story of learning “poker percentages” from Bob Davis with the latter one about the GI’s letter and his question.

I mean, really, what would be the odds of that?

Photo: General of the Army, February 1, 1945, public domain.

Three-Way Tie for Last

Saw an item this morning regarding last night’s episode of Jeopardy! Hear about this?

Heading into “Final Jeopardy” -- that game-ending last clue when players are allowed to wager whatever they like from their total on their response -- two players were tied for first with $13,800 apiece while the third had $6,000.

Players are told what the category for the final item is but not the clue itself before having to write down the amount they are willing to wager. I’m not sure what the category was, but the clue turned out to be a not-so-easy one: “A 1957 event led to the creation of a national historic site in this city, signed into law by a president whose library is now there too.”

Here, you can look at how it went:

That’s right -- three incorrect answers, and all three contestants went all in with their wagers, meaning a three-way tie for last. Or first. Or whatever. Each did get a consolation prize -- $2,000 each for the two players tied for first heading into “Final Jeopardy,” and $1,000 for the other player. But none gets to come back tonight.

Seems to me that when it came to calculating that final wager, the third-place player chose the only amount that was unequivocally incorrect here -- namely, to bet all $6,000. Disregarding results, anything from $0 to $5,999 would have been better, and probably equally as good. Meanwhile the decision for each of the two players tied for first was less cut-and-dry.

Remember, you only have to win by one dollar in order to take home whatever your final total turns out to be (and to come back the next night), and those finishing second and third don’t get any of the money they’ve accumulated in the show, only the consolation prizes for appearing.

Okay all you poker players (and ICM-smarties) -- what would you have recommended here for these three players when placing their wagers for “Final Jeopardy”?

Image: 3-Way Tie (For Last) (1990), The Minutemen.

High Hopes

Had a joker of a friend once named Tony who whenever the subject of pot odds came up at the home game would crack wise about the chances of him scoring a dimebag within the next day or two. Tony could be a kick in the pants sometimes.

After the shenanigans, though, Tony usually had the right answers to others' questions about poker odds, despite being half-snowed half the time. To give you an example, we had a buddy, Dobby, who from time to time would try to argue that when counting outs everyone mistakenly assumes the best-case scenario. Tony knew better, and would invariably respond to such hooey with startling clarity. Here's how Dobby's argument -- one which we all likely have entertained at some (hopefully early) point in our playing lives -- would go.

You count outs to figure your chances to win the hand, then compare them to the odds the pot are giving you. For example, you're in a 10-handed game of $1/$2 limit hold 'em. Everyone folds to you sitting left of cutoff with Qh 9h. You limp, the cutoff folds, the button folds, the SB calls, and the BB checks. There is $6 in the pot when the flop comes Kh 7c 2d. The table checks, then comes the turn, the Ah. The SB bets $2, the BB folds, and now you have to decide whether to chase the nut flush or turn tail.

Now you've had this explained to you a thousand times already. There are 46 unknown cards, 9 of which are hearts. Assuming your opponent just has a pair of kings (or some other hand that can't improve to a full house), if one of those 9 hearts comes, you're a winner. In other words, you're looking at 37-to-9 or a little worse than 4-to-1 against making your flush. The pot is $8 and you have to put in $2 to call, so the pot odds are exactly 4-to-1.

"You're dreaming if you think you really have 9 outs," Dobby would cry. "All 9 ain't left, so if you think you've got 9 ways to win you've got some high hopes."

Technically, the Dobster's right about it being unlikely to have 9 ways to win. Here 24 cards have been dealt (the 10 hands plus the 4 on the board), and so only 28 remain in the deck. On average, only 5 or 6 of those 28 cards will be hearts, with the other 3 or 4 having been dealt and folded. According to Dobby, since we only likely have 5 or 6 winners left, our odds are down (to 8-to-1 or thereabouts). That's where Dobby's line of reasoning goes haywire, of course. You compare the (let's say) 6 hearts left to the 23 other cards left in the deck, not to the total number of other unseen cards (41). Thus the odds remain about 4-to-1; in fact, if 6 hearts are left your odds are slightly better than average here (with about 21.5% of the possible river cards being hearts).

If all 9 hearts are improbably still in the deck, you're about 2-to-1 to hit the flush. If only one is left, you're down to 27-to-1. And if none are left well then you're whistling in the dark like usual.

None of this matters, of course. Unless you're in some kind of bizarro game where all hands are played face up, you have no way of knowing what cards are spent and what cards remain. So note your outs (making sure they really are outs) and the odds of spiking one, figger your pot odds, and make your play.

Or, as Tony would explain with a glassy-eyed twinkle and dismissive shake of the head, "Pass the Doritos."