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.