• Bluffing in poker is a risky strategy that can pay off in a satisfying way. Beginning poker players often think bluffing should happen often, but it's best to be selective about when you bluff. Practice bluffing when the stakes are low to build your skill in convincing opponents that you have a good hand.
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Richard Nixon stood in a crowd of several thousand soldiers, mostly members of New Zealand’s Third Division, and watched as a plane carrying aviation hero Charles Lindbergh taxi on the tarmac on Green Island in the South Pacific. His visit was supposed to be a morale-boosting treat for the troops, but he was upstaged.

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A brown-haired, curvy nurse stepped out of the plane.

“I remember it well,” Nixon said in an interview in 1983. “In fact, Lindbergh came in the same plane as the nurse. Nobody was paying attention to him. I did. But everybody was hooting and hollering and catcalling and so forth, because, my goodness, there was this nurse. I’m telling you, she could’ve been a chimpanzee, but she was a female, and they hadn’t seen one in a long time.”

The commanding officer invited Ensign Nixon and a half-dozen or so others to have dinner with Lindbergh.

“Believe it not, I turned it down because I was the host of a poker game that night. I think back to turning down a chance to sit down with Lindbergh to have a poker game. I can’t imagine it happening. Years later, I was glad that he could be the guest at the White House when I was President.”

This was April, 1944, before Nixon became a loopy caricature for arrogance and power. He was a 30-year-old, brilliant, studious and charming man — a lawyer who graduated from Duke University before the war – and a solid poker player while serving as a Navy officer.

As a pencil-pushing passenger and cargo clerk, playing stud was the only combat Nixon would ever see.

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Nixon learned how to play five-card stud poker from fellow naval officer James Stewart. He asked Stewart to teach him poker after watching the game for a few weeks. Nixon thought the game could be beaten, so he went to who he thought was the best player and asked him for advice.

Stewart gave him some solid tips. Tight is right. Only bluff when you are quite sure. Bet when you got it. Fold when you’re beat.

Much has been made that Nixon was a Quaker, which expressively forbids gambling. Like many politicians, Nixon was as religious as necessary, and there was no way he was going to let a little thing like believing in an almighty deity get in the way of what he saw as way to kill time and make a few bucks.

“The pressure of wartime, and even the more oppressive monotony, made it an irresistible diversion. I found playing poker instructive as well as entertaining and profitable,” Nixon said.

The game they played was five-card stud. Nixon called it a five-ten game, with opening raises of $5 and $5 and a third bet capped at $10.

By all accounts, Nixon was good. He was a disciplined player with a fantastic memory, a tight player who wasn’t afraid to try to push people around if he saw the opportunity. The game came as easily to him as everything else.

“He was one of those rare individuals. He never had to work for knowledge at all. He was told something and he never forgot,” said Nixon’s former high school teacher, Mary George.

Nixon and his fellow officers had nothing but time and money, and so like thousands of other soldiers at war, they played poker, day in and day out.

“Nixon was as good a poker player as, if not better than, anyone we had ever seen,” said James Udall, a lieutenant who served with him. “He played a quiet game, but was not afraid of taking chances. He wasn’t afraid of running a bluff. Sometimes the stakes were pretty big, but Dick had daring and flair for knowing what to do. I once saw him bluff a lieutenant commander out of fifteen hundred dollars with a pair of deuces.”

As an Ensign, Nixon made around $150 a month. He definitely made more money in the Navy playing stud.

“He won more frequently than he lost and sent home to California a fair amount of money. I have no idea how much, but my estimate was between $6,000 and $7,000,” Stewart said.

The money was so much that Nixon worried what his wife Pat would think of the winnings. A former Navy buddy wrote Nixon in 1950, kidding him about his concerns.

“Your prowess in stud poker is the thing I remember with very good reason. I’ll never forget the apparent concern that troubled you because of your winnings and your expressed wish that I call Pat in Frisco to break the ice,” said a man named McCaffery, whose first name is lost.

Despite the occasional big pot, Nixon was rarely the game’s big winner, but he rarely lost. He’d usually walk away from each session a little ahead, but it added up considerably in the two years he was stationed overseas with his poker-fiend Navy friends.

“Dick never lost, but he was never a big winner. He seemed always to end up a game somewhere between $30 and $60 ahead. That didn’t look like showy winnings, but when you multiplied it day after day, I’d say he did all right,” said old friend Lester Wroble.

Nixon said he took what he learned playing profitable poker home with him and his new set of skills helped him with his political career. Here’s what historian Stephen Ambrose wrote about Nixon and poker in Nixon, Vol: The Education of a Politician 1913-1962:

“Poker gave Nixon the financial stake he needed to launch his political career. It also gave him invaluable lessons that were crucial to his political career. He learned how to take the measure of his opponents, to recognize the exact moment to strike, to realize when he could bluff the man with the strongest hand into an ignominious retreat, to know when to fold his own hand and quietly withdraw from the game.”

Nixon used $5,000 of the winnings on his first congressional run in 1946, which he was victorious. He also wrote about dealing with stressful situations in his 1962 book Six Crises and it sure sounds like he knows how it feels bluffing the big stack at the table with nada.

“When a man has been through even a minor crisis, he learns not to worry when his muscles tense up, his breathing comes faster, his nerves tingle, his stomach churns. He recognizes such symptoms as natural and healthy signs that his system is keyed-up for battle.”

Frank Gannon, who conducted 38 hours of interviews with Nixon on video in 1983, asked him, “Do you subscribe to the theory that a great President must be a great poker player?”

“It helps,” Nixon said. “The Russians of course, are chess players. I never understood chess, it’s much more complicated, much more complex. But many of the things you do in poker are very useful in politics, and are very useful in foreign affairs.”

“One of the problems you see in foreign affairs, particularly, especially dealing with great leaders abroad — particularly those who are adversaries — is the almost insatiable tendency of American politicians to put everything on the table, their inability to know when to bluff, when to call, and, above everything else, to be unpredictable.”

“Unpredictably is the greatest asset or weapon that a leader could have of a major country. Unless he’s unpredictable, he’s going to find, he loses a great deal of his power.”

Ten years before, Nixon boarded a helicopter that took him away from the White House for the last time. He had tried to run over too many people, ran more than one too many bluffs. All of the skills that got him in the Oval Office – including his poker skills – had failed him and he was out.

There’s little written about Nixon playing poker in office. What there is comes from Tip O’Neill, who played with him in the ‘50s when Nixon was vice-president to Eisenhower. According to The Arrogance of Power: The Secret World of Richard Nixon, O’Neill said:

“Nixon thought of himself as a good poker player, but he talked too much and didn’t follow the cards. Moreover, he used the fact that he was the highest-ranking person at the game to his advantage.”

Now, that sounds more like the Nixon we all know and don’t really love.

But poker players have to love the strangeness of a hand that Nixon would never forget, a hand every poker player should be lucky enough to get at least one time in their lifetimes. He told Gannon about it 40-plus years after it happened, and here it is, in his own words:

“I must say though, my greatest experience, I could remember the cards to these days, a game of five card stud. The deal was made, six of us in the game, and I was dealt ace of diamonds in the hole – the card that was down.”

“And then in order – there were no wild cards in the game – in order, I got the king of diamonds, the queen of diamonds, the jack of diamonds, the 10 of diamonds. Two of the other players had a pair showing by the time we got to the fourth card. That’s very good in a five card stud game, so they kept betting. I did not raise. I couldn’t be sure. On the other hand, it would’ve been a pretty good hand to bluff on because they thought I might have doubled up the king or doubled up the queen, or what have you. So, when finally I got the 10, I didn’t make any gesture or whatever to show my excitement. I thought, my gosh, this couldn’t happen, understand that it’s a 650,000-1 shot.

“So, the first fellow with the first pair bets, and of course, he bet the $5. The game was what we called a 5-10 game. You opened with $5, you can raise $5, third bet is $10. That’s all. So, he bet $5, the next fellow raised him, so that made it $10, and it finally came around to me, and so I did, I bet the $10, the maximum.

“Unfortunately, I had established my credibility too well with all the small pots. Nobody called. So I raked in the chips – it was a pretty good pot – and then, and although you should never let people see your card unless they call you, they got to pay their money to see your card, I flipped over the ace. Everybody yelled. They never saw anything like that before that, and won’t see anything like that again, probably.”

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In the card game of poker, a bluff is a bet or raise made with a hand which is not thought to be the best hand. To bluff is to make such a bet. The objective of a bluff is to induce a fold by at least one opponent who holds a better hand. The size and frequency of a bluff determines its profitability to the bluffer. By extension, the phrase 'calling somebody's bluff' is often used outside the context of poker to describe situations where one person demands that another proves a claim, or proves that they are not being deceptive.^[1]

Pure bluff[edit]

A pure bluff, or stone-cold bluff, is a bet or raise with an inferior hand that has little or no chance of improving. A player making a pure bluff believes they can win the pot only if all opponents fold. The pot odds for a bluff are the ratio of the size of the bluff to the pot. A pure bluff has a positive expectation (will be profitable in the long run) when the probability of being called by an opponent is lower than the pot odds for the bluff.

For example, suppose that after all the cards are out, a player holding a busteddrawing hand decides that the only way to win the pot is to make a pure bluff. If the player bets the size of the pot on a pure bluff, the bluff will have a positive expectation if the probability of being called is less than 50%. Note, however, that the opponent may also consider the pot odds when deciding whether to call. In this example, the opponent will be facing 2-to-1 pot odds for the call. The opponent will have a positive expectation for calling the bluff if the opponent believes the probability the player is bluffing is at least 33%.

Semi-bluff[edit]

In games with multiple betting rounds, to bluff on one round with an inferior or drawing hand that might improve in a later round is called a semi-bluff. A player making a semi-bluff can win the pot two different ways: by all opponents folding immediately or by catching a card to improve the player's hand. In some cases a player may be on a draw but with odds strong enough that they are favored to win the hand. In this case their bet is not classified as a semi-bluff even though their bet may force opponents to fold hands with better current strength.

For example, a player in a stud poker game with four spade-suited cards showing (but none among their downcards) on the penultimate round might raise, hoping that their opponents believe the player already has a flush. If their bluff fails and they are called, the player still might be dealt a spade on the final card and win the showdown (or they might be dealt another non-spade and try to bluff again, in which case it is a pure bluff on the final round rather than a semi-bluff).

Bluffing circumstances[edit]

Bluffing may be more effective in some circumstances than others. Bluffs have a higher expectation when the probability of being called decreases. Several game circumstances may decrease the probability of being called (and increase the profitability of the bluff):

• Fewer opponents who must fold to the bluff.
• The bluff provides less favorable pot odds to opponents for a call.
• A scare card comes that increases the number of superior hands that the player may be perceived to have.
• The player's betting pattern in the hand has been consistent with the superior hand they are representing with the bluff.
• The opponent's betting pattern suggests the opponent may have a marginal hand that is vulnerable to a greater number of potential superior hands.
• The opponent's betting pattern suggests the opponent may have a drawing hand and the bluff provides unfavorable pot odds to the opponent for chasing the draw.
• Opponents are not irrationally committed to the pot (see sunk cost fallacy).
• Opponents are sufficiently skilled and paying sufficient attention.

The opponent's current state of mind should be taken into consideration when bluffing. Under certain circumstances external pressures or events can significantly impact an opponent's decision making skills.

Optimal bluffing frequency[edit]

If a player bluffs too infrequently, observant opponents will recognize that the player is betting for value and will call with very strong hands or with drawing hands only when they are receiving favorable pot odds. If a player bluffs too frequently, observant opponents snap off their bluffs by calling or re-raising. Occasional bluffing disguises not just the hands a player is bluffing with, but also their legitimate hands that opponents may think they may be bluffing with. David Sklansky, in his book The Theory of Poker, states 'Mathematically, the optimal bluffing strategy is to bluff in such a way that the chances against your bluffing are identical to the pot odds your opponent is getting.'

Optimal bluffing also requires that the bluffs must be performed in such a manner that opponents cannot tell when a player is bluffing or not. To prevent bluffs from occurring in a predictable pattern, game theory suggests the use of a randomizing agent to determine whether to bluff. For example, a player might use the colors of their hidden cards, the second hand on their watch, or some other unpredictable mechanism to determine whether to bluff.

Example (Texas Hold'em)[edit]

Here is an example for the game of Texas Hold'em, from The Theory of Poker:

when I bet my $100, creating a $300 pot, my opponent was getting 3-to-1 oddsfrom the pot. Therefore my optimum strategy was ... [to make] the odds againstmy bluffing 3-to-1.

Since the dealer will always bet with (nut hands) in this situation, they should bluff with (their) 'Weakest hands/bluffing range' 1/3 of the time in order to make the odds 3-to-1 against a bluff.^[2]

Ex:On the last betting round (river), Worm has been betting a 'semi-bluff' drawing hand with: A♠ K♠ on the board:

10♠ 9♣ 2♠ 4♣against Mike's A♣ 10♦ hand.

The river comes out:

2♣

The pot is currently 30 dollars, and Worm is contemplating a 30-dollar bluff on the river. If Worm does bluff in this situation, they are giving Mike 2-to-1 pot odds to call with their two pair (10's and 2's).

In these hypothetical circumstances, Worm will have the nuts 50% of the time, and be on a busted draw 50% of the time. Worm will bet the nuts 100% of the time, and bet with a bluffing hand (using mixed optimal strategies):

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${\displaystyle x=s/(1+s)}$^[3]

Where s is equal to the percentage of the pot that Worm is bluff betting with and x is equal to the percentage of busted draws Worm should be bluffing with to bluff optimally.

Pot = 30 dollars.Bluff bet = 30 dollars.

s = 30(pot) / 30(bluff bet) = 1.

Worm should be bluffing with their busted draws:

${\displaystyle x=1/(1+s)=50\mathrm{\%}}$ Where s = 1

Assuming four trials, Worm has the nuts two times, and has a busted draw two times. (EV = expected value)

Under the circumstances of this example: Worm will bet their nut hand two times, for every one time they bluff against Mike's hand (assuming Mike's hand would lose to the nuts and beat a bluff). This means that (if Mike called all three bets) Mike would win one time, and lose two times, and would break even against 2-to-1 pot odds. This also means that Worm's odds against bluffing is also 2-to-1 (since they will value bet twice, and bluff once).

Say in this example, Worm decides to use the second hand of their watch to determine when to bluff (50% of the time). If the second hand of the watch is between 1 and 30 seconds, Worm will check their hand down (not bluff). If the second hand of the watch is between 31 and 60 seconds, Worm will bluff their hand. Worm looks down at their watch, and the second hand is at 45 seconds, so Worm decides to bluff. Mike folds his two pair saying, 'the way you've been betting your hand, I don't think my two pair on the board will hold up against your hand.' Worm takes the pot by using optimal bluffing frequencies.

This example is meant to illustrate how optimal bluffing frequencies work. Because it was an example, we assumed that Worm had the nuts 50% of the time, and a busted draw 50% of the time. In real game situations, this is not usually the case.

The purpose of optimal bluffing frequencies is to make the opponent (mathematically) indifferent between calling and folding. Optimal bluffing frequencies are based upon game theory and the Nash equilibrium, and assist the player using these strategies to become unexploitable. By bluffing in optimal frequencies, you will typically end up breaking even on your bluffs (in other words, optimal bluffing frequencies are not meant to generate positive expected value from the bluffs alone). Rather, optimal bluffing frequencies allow you to gain more value from your value bets, because your opponent is indifferent between calling or folding when you bet (regardless of whether it's a value bet or a bluff bet).^[3]

Bluffing in other games[edit]

Although bluffing is most often considered a poker term, similar tactics are useful in other games as well. In these situations, a player makes a play that should not be profitable unless an opponent misjudges it as being made from a position capable of justifying it. Since a successful bluff requires deceiving one's opponent, it occurs only in games in which the players conceal information from each other. In games like chess and backgammon, both players can see the same board and so should simply make the best legal move available. Examples include:

• Contract Bridge: Psychic bids and falsecards are attempts to mislead the opponents about the distribution of the cards. A risk (common to all bluffing in partnership games) is that a bluff may also confuse the bluffer's partner. Psychic bids serve to make it harder for the opponents to find a good contract or to accurately place the key missing cards with a defender. Falsecarding (a tactic available in most trick taking card games) is playing a card that would naturally be played from a different hand distribution in hopes that an opponent will wrongly assume that the falsecarder made a natural play from a different hand and misplay a later trick on that assumption.
• Stratego: Much of the strategy in Stratego revolves around identifying the ranks of the opposing pieces. Therefore depriving your opponent of this information is valuable. In particular, the 'Shoreline Bluff' involves placing the flag in an unnecessarily-vulnerable location in the hope that the opponent will not look for it there. It is also common to bluff an attack that one would never actually make by initiating pursuit of a piece known to be strong, with an as-yet unidentified but weaker piece. Until the true rank of the pursuing piece is revealed, the player with the stronger piece might retreat if their opponent does not pursue them with a weaker piece. That might buy time for the bluffer to bring in a faraway piece that can actually defend against the bluffed piece.
• Spades: In late game situations, it is useful to bid a nil even if it cannot succeed.^[4] If the third seat bidder sees that making a natural bid would allow the fourth seat bidder to make an uncontestable bid for game, they may bid nil even if it has no chance of success. The last bidder then must choose whether to make their natural bid (and lose the game if the nil succeeds) or to respect the nil by making a riskier bid that allows their side to win even if the doomed nil is successful. If the player chooses wrong and both teams miss their bids, the game continues.
• Scrabble: Scrabble players will sometimes deliberately play a phony word in the hope the opponent does not challenge it. Bluffing in Scrabble is a bit different from the other examples. Scrabble players conceal their tiles but have little opportunity to make significant deductions about their opponent's tiles (except in the endgame) and even less opportunity to spread disinformation about them. Bluffing by playing a phony is instead based on assuming players have imperfect knowledge of the acceptable word list.^{[citation needed]}

Artificial intelligence[edit]

Evan Hurwitz and Tshilidzi Marwala developed a software agent that bluffed while playing a poker-like game.^[5][6] They used intelligent agents to design agent outlooks. The agent was able to learn to predict its opponents' reactions based on its own cards and the actions of others. By using reinforcement neural networks, the agents were able to learn to bluff without prompting.

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Economic theory[edit]

In economics, bluffing has been explained as rational equilibrium behavior in games with information asymmetries. For instance, consider the hold-up problem, a central ingredient of the theory of incomplete contracts. There are two players. Today player A can make an investment; tomorrow player B offers how to divide the returns of the investment. If player A rejects the offer, they can realize only a fraction x<1 of these returns on their own. Suppose player A has private information about x. Goldlücke and Schmitz (2014) have shown that player A might make a large investment even if player A is weak (i.e., when they know that x is small). The reason is that a large investment may lead player B to believe that player A is strong (i.e., x is large), so that player B will make a generous offer. Hence, bluffing can be a profitable strategy for player A.^[7]

See also[edit]

References[edit]

1. ^'call bluff'. The Free Dictionary by Farlex. Retrieved October 22, 2020.
2. ^Game Theory and Poker
3. ^ ^abThe Mathematics of Poker, Bill Chen and Jerrod Ankenman
4. ^[1]Archived December 28, 2009, at the Wayback Machine
5. ^Marwala, Tshilidzi; Hurwitz, Evan (May 7, 2007). 'Learning to bluff'. arXiv:0705.0693 [cs.AI].
6. ^'Software learns when it pays to deceive'. New Scientist. May 30, 2007.
7. ^Goldlücke, Susanne; Schmitz, Patrick W. (2014). 'Investments as signals of outside options'. Journal of Economic Theory. 150: 683–708. doi:10.1016/j.jet.2013.12.001. ISSN0022-0531.

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General references[edit]

• David Sklansky (1987). The Theory of Poker. Two Plus Two Publications. ISBN1-880685-00-0.
• David Sklansky (2001). Tournament Poker for Advanced Players. Two Plus Two Publications. ISBN1-880685-28-0.
• David Sklansky and Mason Malmuth (1988). Hold 'em Poker for Advanced Players. Two Plus Two Publications. ISBN1-880685-22-1.
• Dan Harrington and Bill Robertie (2004). Harrington on Hold'em: Expert Strategy For No-Limit Tournaments; Volume I: Strategic Play. Two Plus Two Publications. ISBN1-880685-33-7.
• Dan Harrington and Bill Robertie (2005). Harrington on Hold'em: Expert Strategy For No-Limit Tournaments; Volume II: The Endgame. Two Plus Two Publications. ISBN1-880685-35-3.
• Bill Chen, Jerrod Ankenman. The Mathematics of Poker.