The Nuts

[BB] “A good exercise for beginners to develop card sense is to figure out what the nuts are when you see the flop, and see if they change on the turn and the river. For example, what’s the nuts on a K♦8♠5♣ flop?”, Benny the Book quizzed his son, Joey the Juvenile.

[JJ] “That’s a totally dry flop. No pair and no flush or straight possible, so the answer must be three of a kind”, Joey responded after a moment’s thought.

[BB] “Right, specifically three Kings. What if the 7♣ hits on the turn?”

[JJ] “Now a straight is possible.”

[BB] “Correct again. A 9-high straight. And let’s try two different river cards, first the 8♥.”

[JJ] “That paired the board, so a full house is possible. No, wait… four Eights.”

[BB] “And what if the river is the 6♣ instead?”

[JJ] “9-high Straight flush!”

[BB] “Okay, this is already too easy for you. In another minute, you’ll realize that it comes down to just five simple rules:

  1. If three cards to a straight flush are on the board (e.g., 8♦7♦4♦), then a straight flush is the nuts (the highest one if more than one are possible).
  2. Otherwise, if the board is paired or more, then a four of a kind is the nuts (the higher denomination if two pairs or a full house are on the board).
  3. Otherwise, if the board has three of one suit, then an Ace-high flush is the nuts (add the highest missing two cards of the flush suit to the board).
  4. Otherwise, if three cards to a straight are on the board, then a straight is the nuts (the highest one if more than one are possible).
  5. Otherwise, three of a kind is the nuts (three of the highest card on the board).”1

[BB] “The two cards you hold can prevent certain nut possibilities; for example, you could hold a card that blocks the straight flush, or you could hold a card that blocks quads.”

[BB] “One oddity is that if you have a full house, it’s never the nuts if you have a pocket pair. It’s the nuts only if the board’s highest denomination is paired, and you have one of those and one of the highest other denomination on the board and no straight flush is possible. E.g., TT on T8842 board and KT on a KTT84 board are not the nuts, while KT on a KKT84 board is the nuts. Although the Ten in the second hand makes quads impossible, KK still wins (although the player with the KK doesn’t know quads are impossible).”

[BB] “On the river, the five cards on the table can only be the nuts if they form a royal flush, four of a kind with the nut kicker, or a royal straight with no flush possible.”


  1. The weakest hand that can be the nuts is QQ on a Q8732 board with no flush possible. Three Kings and three Queens are the only sets that can be the nuts as any other three of a kind makes a straight possible.

Related Links:


Table Manners

[BB] “I was going to buy you Miss Manners Guide to Etiquette at the Poker Table for your birthday, but I couldn’t find it at Amazon. Since I don’t want everyone to think we’ve raised a slob, here’s what you need to know”, Benny the Book indicated to his son Joey the Juvenile.

  • Pay attention to the action. Get your blinds in when you’re supposed to and be ready to act when it’s your turn. [This keeps the game moving. Live poker is slow enough already.]
  • Keep your cards on the table where people can see them. [This keeps players on your left from accidentally acting out of turn.]
  • Don’t act out of turn. [Besides messing things up, this could be used to angle shoot and gain an unfair advantage.]
  • Don’t reach into the muck to pull out your cards or anyone else’s. Once cards hit the muck, they’re gone forever. [This prevents people from seeing other players’ cards and avoid confusion as it may look like you’re still in the hand.]
  • Keep your chips visible at all times, preferably in stacks of the same color, with the highest denomination chips in front. Never put chips in your pocket unless you’re leaving the table. [This makes it easier for players to judge how many chips you have.]
  • Don’t splash the pot. Put your bet clearly in front of your chip stack but out of the muck. [This makes it much easier to see who’s bet what, especially after a raise.]
  • Similarly, don’t make change from the pot until the betting round is over. It’s okay to make change for someone else from your chip stack in most home games, but don’t do that in a casino. [Ditto.]
  • Don’t string bet. If you want to see how much is in the pot after you match the previous bet, say “Raise” first. Don’t emulate the old westerns and say, “I see your bet… and raise you…” Just say “Raise”. [This could be used to read an opponent’s reaction.]
  • Don’t do the opposite either. If you have a stack of chips in your hand, don’t just drop one or a few of them to the felt. When your hand moves forward, it should hold only the chips you intend to bet. [Ditto.]
  • Don’t slowroll. When it’s your turn to show your cards, flip them both over immediately without fanfare. [This is pure etiquette. Don’t prolong your opponents’ agony.]
  • Don’t ask to see someone’s hole cards, especially if you folded early. If you’re heads up, it’s okay to ask your opponent if he’ll show if you fold. [This is also mostly etiquette, as it may appear that you are accusing them of collusion. It also slows down the game.]
  • Do show your hole cards to everyone if you show them to the person on your left or right. [This is because everyone at the table is entitled to the same information.]
  • Don’t discuss the current hand until it’s over. If you’ve folded, don’t react to the flop or say that you would have flopped a straight. The one exception to this is when a hand is heads-up; either player can speak freely then. [This may seem like pure etiquette since everyone would gain the same information, but that information may be more useful to one player than another.]
  • Don’t criticize how someone is playing. If they’re making mistakes, that’s to your benefit. If it’s a friendly game, you can talk with them privately later. [This is mostly etiquette, but in a serious game, you’re also affecting other players’ profitability.]
  • Don’t complain to the dealer about your cards (or anything else). [This is pure etiquette.]
  • Follow the local customs. If rabbit hunting is standard, just help them get it over with quickly. If they cut the deck backwards (from the small blind), go with the flow. [Ditto.]

[JJ] “I think you explained the rules of Hold ‘Em to me in a quarter of that time”, Joey remarked.

[BB] “Fair enough. Here’s the Reader’s Digest condensed version: Keep the game moving and be courteous. Got it?”

[JJ] “I can remember that.”

Related Links:

  • An infographic of someone else’s Top 12 Worst Poker Etiquette Mistakes
  • The International Poker Rules are now available online at (note that you can’t check the “Player” radio button in some browsers when you try to download the PDF version, but leaving it unchecked works fine). [May 21, 2013 update]


Harriet the Hazy decided to call the raise to three times the big blind. The 5♦3♣ in her hand didn’t deter her for a second because she was getting a discount from the small blind. The big blind folded, so it was heads up to a 9♠7♦2♣ flop. That felt like it hit her hand pretty hard, so Harriet led out for her standard blue chip, which was about three-quarters of the pot in this case.

[SS] Stan the Stat thought, “That couldn’t have helped her, and I probably still have the better hand, but let’s find out”, as he pushed out two blues. Harriet called with a shrug.

The turn was a harmless 7♥, and the Hazy one proffered another blue chip. Stan the Stat knew the turn hadn’t changed anything and even killed any flush possibilities, so he raised to four blues.

Now, Harriet took inventory of the hand. There were a bunch of low cards on the board and a couple more in her hand. She must be doing well, so she contributed the three additional blues.

The river was another 9, and Stan silently sat stunned. But he was confident that his opponent hadn’t noticed his reaction or wouldn’t have known how to interpret it if she had, so he carefully bet half the pot, an amount he figured would be more than enough to garner a fold from anything but a full house.

[HH] The Hazy one looked down at her chips, then at the pot, determining that the latter was quite a bit bigger than the former. “I guess I’m committed, right?”, she argued feebly as she pushed her small stack forward and flipped over her hand.

Stan looked mortified, not because she’d made such a horrible string of calls, but because she’d won the pot. He flipped over his pocket fours and conceded that her five outkicked his four.

[EE] “When is a pair not a pair?”, queried Elias the Eagle. “When it’s impaired.”

[TT] Tyrone the Telephone added, “The perilous three pair / Must be handled with care.”

Related Links:



[YY] Yuri the Young Gun lamented, “One of the things I miss the most about playing online is the four-color decks. It’s so much easier to tell the suits apart when they’re all different colors.”

[RR] Roderick the Rock reminisced, “They remind me of the Lucky Charms I used to eat as a kid with ‘Green Clovers and Blue Diamonds’.”1

[YY] “In bridge, you have majors (spades and hearts) and minors (diamonds and clubs), pointy suits (spades and diamonds) and round suits (hearts and clubs), and red suits (hearts and diamonds) and black suits (spades and clubs). These are all useful distinctions in bidding as the suits are ordered and more than a few conventions break them into one of these divisions. But in poker, the suits don’t have any use except to tell them apart, so why not use four colors to facilitate that.”

[YY] “Why do we have these four suits anyway?”

[VV] “Once again, we can thank the French”, Vince the Veteran enthusiastically offered. “Not just any Frenchman, either. The main person responsible for our current suits was a military commander known as La Hire, Etienne Vignoles, who was Joan of Arc’s comrade-in-arms before she was captured in 1430. Not surprisingly La Hire and Joan of Arc are on the face cards of some decks, as the Jack of Hearts and the Queen of Spades (not the Queen of Hearts, as she was less than half his age, and they were not romantically linked).”

[VV] “But anyway, with his secretary, Etienne Chavalier, Vignoles designed a new set of cards to play Piquet, a new game which he may or may not have invented. He chose four easily drawn and highly recognizable symbols for the suits:

Suit Symbol Class of Society
Spades (Piques) Lance Blade (weapon) Military
Hearts (Cours) Heart (love) Church
Diamonds (Carreaux) Paving Tile2 Tradesmen
Clubs (Trefles) Clover (grazing area)3 Peasants

[VV] “Time has proven his choices to be well-considered, as the French suits have won out globally over Italian, Spanish, German, and other designs.”

[RR] “And having just two colors instead of four was to save money during mass production, I’ll bet.”


  1. Lucky Charms breakfast cereal originally had pink hearts, yellow moons, orange stars, and green clovers. General Mills added blue diamond marshmallows to the box in 1975 but removed them in 1994.
  2. An alternate explanation is that the diamonds represented wealth.
  3. An alternate explanation is that the clubs were the weapons of the peasants, who weren’t allowed to have swords.

Related Links:


The Might of the Mind

[RR] “Do you believe in psychokinetic powers?” Roderick the Rock asked Harriet the Hazy, although he figured he already knew the answer.

[HH] “No!” Harriet huffed.

[RR] “ESP?”

[HH] “That’s different”, Harriet admitted.

[RR] “What about Schroedinger’s Cat? You know, the cat in the box that’s alive and dead at the same time.”

[HH] “What does that have to do with anything?” Harriet wondered.

[RR] “Suppose we’re playing a hand of Hold ‘Em. The cards have already been shuffled and cut. The hole cards have been dealt. A burn card is now sitting at the top of the deck, followed by three cards for the flop, another burn card, the turn, another burn card, and the river. Presumably the identity of those cards is now fixed, but none of us know what they are.”

[RR] Roderick let that sink in for a few moments before he continued, “If you had the ability to change those cards, would that be telepathic or telekinetic?”

[HH] “Telekinetic. Just knowing what the card is would be ESP though.”

[YY] Yuri the Young Gun chimed in, “You know, some online poker sites determine the order of the deck like we do live, shuffling at the start of the hand. But other sites don’t pick the next card until it’s needed, presumably to make cheating harder. If I pause a fraction of a second before tapping the Call button, I can change the flop! That’s way too much pressure for me. I definitely prefer the normal shuffling technique.”

[RR] “Agreed. I was playing last night on one of the sites that randomizes each card as it’s needed, and I was trying to figure out if typing in the chat box would change what got dealt. I was all-in with J♥J♣ against K♠K♦, so naturally I was rooting for a Jack for a set on the flop. The flop came A♦Q♥10♠, giving us both inside straight draws, and suddenly I was rooting for my opponent’s King! Then the board paired with the 10♣, and I went back to rooting for my Jack again!”

[RR] “The river card was like Shroedinger’s Cat, except that it wasn’t the feline that was simultaneously alive and dead. It was my tournament life!”

[HH] “And did you hit the river?”, Harriet prodded.

[RR] “No, I mean yes, I mean no. The K♥ had barely hit the felt when I started to celebrate filling my straight, only to realize a split second later that I’d lost to my opponent’s full house.”

[HH] “If you had ESP, you could have seen that was coming and folded before the flop.”

[RR] “If I had psychokinetic powers I could have changed the river card to a Jack!”

[TT] Tyrone the Telephone hypothesized how this might affect a different card game: “When two magicians played a game of gin / Sleight of hand was their least damnable sin / With pat hands a lock / Neither would dare knock1 / And neither conjurer could ever win.”2


  1. In gin, you try to make sets and series (“straight flushes”) of three or more cards. What’s left over is your deadwood. You can knock to end the hand when your deadwood adds up to ten or lower.
  2. An opponent with the same or lower deadwood earns an undercut bonus.

Related Links:

  • Gin is an excellent two-player card game where you can learn your opponent’s tendencies and read their hands from their pickups and discards.

Sklansky’s Fundamental Theorem of Poker

[BB] Benny the Book continued the vitally important education of Joey the Juvenile, “On pages 17-18 of his book, The Theory of Poker, the poker philosopher David Sklansky states his Fundamental Theorem of Poker: ‘Every time you play a hand differently from the way you would have played it if you could see all your opponents’ cards, they gain; and every time you play your hand the same way you would have played it if you could see all their cards, they lose. Conversely, every time opponents play their hands differently from the way they would have if they could see all your cards, you gain; and every time they play their hands the same way they would have played if they could see all your cards, you lose.'”

[JJ] “Well, get me a deck of marked cards that only I can read, and I’ll do my best”, Joey the Juvenile joked.

[BB] His dad ignored him and resumed, “Your goal isn’t to win more hands. Your goal isn’t to stack your opponents, as enjoyable as that is. Your goal is to make fewer mistakes and induce your opponents to make more mistakes. The beauty and the pain of poker is that you can play perfectly according to the Fundamental Theorem and still lose. You can play horribly and still win. But in the long run, good play is rewarded, and bad play is punished.”

[BB] “So what is perfect play? It’s maximizing your Expected Value every time you act. Suppose you have pocket Aces and raise under the gun to five times the big blind. Everybody folds and you win the blinds. Is that perfect play?”

[JJ] “Probably not, but it might save you from a bad beat.”

[BB] “You’ve virtually assured yourself of a small profit but at the expense of possibly much larger gains. (Yes, some crazies will call your big bet anyway; in that scenario, your bet may not be incorrect as you are intentionally deviating from theoretically perfect play to exploit your opponents’ less-than-optimal tendencies.)”

[BB] “Playing against weak opponents, you simply bet your good hands for value and bluff your bad hands when you think you can steal the pot. If your opponents are bad enough, you’d actually want to build the pot on the early streets before taking it down on the river, maximizing your gains.”

[BB] “If everyone folds to you on the button with 7♠2♦, what should you do?”

[JJ] “I’ll bet to steal the blinds.”

[BB] “And that might be right. But it was a trick question because I didn’t tell you who your opponents are.”

[BB] “If the blinds are both tight and willing to let you steal, then you definitely should bet. If the blinds are loose preflop but very weak postflop players, you might limp, hoping to get lucky or steal the pot later. And if the blinds are both better players than you, you should fold without regret.”

[BB] “Another example: if you have top pair and think your opponent is just on a flush draw with one card to come, should you overbet the pot so you don’t get sucked out on?”

[JJ] “I know a few people here do that, but I’m guessing that you’re going to say it’s wrong.”

[BB] “The EV1 of that overbet is the pot size, P. But your opponent has only a 20% chance of improving to a winning hand, so a half-pot bet can be a much better bet. If they fold, there’s no difference. But if they call, they’ve just made a -EV decision: 0.2 * 1.5P – 0.8 * 0.5P = -0.1P. If they’re a calling station who loves to chase draws, a three-quarter pot bet might be even better (EV = 0.2 * 1.75P – 0.8 * 0.75P = -0.25P). Maybe even a full pot-size bet (EV = 0.2 * 2.0P – 0.8P = -0.4P). Of course, you need to avoid putting any more chips into the pot if the flush card hits or the implied odds will turn the tables.”

[JJ] “But how do I know my opponent is on a flush draw in the first place? I see people paying off ‘just to see’ all the time. It’s like we’re living in Missouri.”

[BB] “If I knew the answer to that, I’d turn pro, or at least move up to a bigger game. I’d recommend you watch Elias the Eagle play. And once you’re comfortable with the basics, maybe he can help you take the next step.”

[BB] “For now, just try to stay disciplined (your favorite word, I know). If a player is representing a flush by betting, he or she probably has it. Curiosity killed the cat — old English proverb.”

[JJ] “But knowledge is power — Sir Francis Bacon.”

[BB] “Give a man a fish, and he eats for a day. Teach a man how to fish, and he eats for a lifetime — ancient Chinese proverb.”

[BB] “Teach a man how not to be a fish, and he eats well for a lifetime.”

[JJ] “Who said that?”

[BB] “I just did. Your mom and I really do hope you’ll move out of the house after college.”


  1. Yesterday’s post was all about EV (Expected Value).

Expected Value

[BB] “Every action you take in a poker game has an expected value, which is the average amount of chips or money that action will win or lose in the long run”, Benny the Book explained to his son.

EV of Folding

[BB] “Folding has an expected value, or EV, of 0, since you aren’t gaining or losing any more chips. Remember that the chips in the pot are no longer yours, so they don’t factor in when you fold. Whether there are 10 chips or 10,000 chips in the pot, folding will change your chip stack by the same amount, zero.”

EV of Calling

[BB] “Following up on our discussion of pot odds, the EV of calling is calculated as the odds of winning times the pot size minus the odds of losing times the call size. For example, suppose the pot is P and you call a half-pot all-in bet on the turn when you’re sure you need to hit a flush on the river. Since 9 outs is about 20%1, the EV of the call is 0.2 * 1.5P – 0.8 * 0.5P = -0.1P2. You’ll lose just over a tenth of the original pot size on average by making this bad call. If you also had a straight draw, you have 15 outs, about 32.5%, which we can call 1/3, and (1/3)*1.5P – (2/3)*0.5P = 1/6P3. You’ll win almost a sixth of a pot on average.”

EV of Raising

[BB] “This is impossible to calculate without knowing how often your opponent is going to fold, call, or reraise, but we can lay out the general formula. For simplicity, let’s say we’re on the river, the pot is P, your opponent bets B, you raise R, and you have the better hand N% of the time (all percentages should be divided by 100 to give a number between 0.0 and 1.0). When your opponent folds, you win P+B. When your opponent calls you win P+B+R if your hand is better and lose B+R if your hand is worse. Let’s ignore the possibility of your opponent reraising for now. Your overall EV is (opp fold %) * (P+B) + (opp call %) * ((N * (P+B+R)) – ((1-N) * (B+R))).”

[JJ] “You expect me to crunch all that at the table?”, Joey the Juvenile objected.

[BB] “No, but it’s useful in postgame analysis. The important thing to note is that your raise wins some of the time by folding your opponent and some of the time when you have the best hand. Whenever you raise, you want to think about both of those possibilities to determine how much to bet. Against calling stations, you should expect fewer folds, so you should bet more for value. Against tight players who haven’t shown any strength, you can bluff more.”

[BB] Seeing his son smiling much too broadly, Benny regretfully wondered, “Why do I feel like I’m training a maniac?”


  1. This was covered a few days ago in Counting Outs.
  2. The exact calculation is 9/46 * 1.5P – 37/46 * 0.5P equals about 0.29P – 0.40P = -0.11P.
  3. The exact calculation is 15/46 * 1.5P – 31/46 * 0.5P equals about 0.49 – 0.34 = +0.15P.

Related Links:

  • Bobby Crosby’s PG-13 +EV comic follows the life of an addicted online poker player, who views everything in life in terms of Expected Value. Sometimes funny, sometimes sad. Always depraved.

Implied Odds

[BB] Benny the Book resumed explaining to his son, “Pot odds are pretty straightforward, but here’s the tricky part; implied odds are when you take into account additional chips that you could win if you hit your draw. If you or your opponent is all-in, the implied odds are the same as the pot odds. But if you both have more chips, you need to factor that in. There’s no clearcut formula for implied odds, unfortunately. You need to take into account the playing style of your opponent and even how they view you. Some players will frequently pay you off, while others will be very suspicious every time a possible draw fills.”

[JJ] “Are you implying that I need to use my excellent judgment here?”, Joey the Juvenile offered.

[BB] “Yes on the ‘judgment’ part; not sure about the ‘excellent’ part. Let’s say it’s early in a tournament so both you and your opponent have deep stacks. You’re facing a half-pot turn bet with nothing but a flush draw. Should you call?”

[JJ] “Well, the flush draw is 9 outs, which is 9 * 2 + 1.5 = 19.5%”, Joey responded then thought for a bit. “The half-pot bet means 25%, so my pot odds aren’t good enough. I can call if my opponent will call a small bet on a flush river card though, since my odds are only off by a little.”-

[BB] “Right, so it matters quite a bit whether you have suited or unsuited hole cards. In the latter case, that river put four cards to a flush on the board, and it doesn’t take Albert Einstein to find that fold. In the former case, it’s easier to believe that you don’t have the flush. The same thing is true with straight draws. The obvious straights are just as obvious as 4-flushes. If the board has King-Queen-Jack-Ten, everyone’s going to worry that you have the Ace, or even the Nine, for the straight. But the less obvious straight draws can be very well disguised. If the board has Queen-Ten-Three-Two, and an Eight hits on the river, will your opponent think you have the Jack-Nine? Your implied odds are barely better than your pot odds for obvious draws and significantly better for less likely draws.”

[JJ] “I’m usually on an unlikely draw.”

[BB] “Two undercards isn’t considered to be a draw.”

[BB] “Anyway, before you go too crazy and stick around even more because of your implied odds, keep in mind a couple caveats. First, if you’re not drawing to the nuts, you can still be beat. A classic case is when you have a suited King. The flop puts two of your suit and an Ace of another suit on the board. Every once in a while, your opponent has the nut flush draw, and you’re practically drawing dead.”

[BB] “Second, if you hit your draw on the turn, your opponent may have redraws to beat you on the river. This commonly happens when you hit your straight or flush but your opponent has three of a kind. They then have ten outs on the river; any card that puts a pair on the board gives them the boat or four of a kind. Another case is when you hit a straight but your opponent has a flush draw. Then they have the usual nine outs to win.”

[BB] “Sufficiently warned?”

[JJ] “Sufficiently armed!”


The Buss Stops Here









Related Links:


Pot Odds

[BB] “Do you know what pot odds are?”, Benny the Book asked his son.

[JJ] Joey the Juvenile jested, “Would that be the chance that the police discover that the pointy little plants in your garden are marijuana?”

[BB] With a scornful look, Benny chided his son, “In poker, the pot odds are the current odds that you are getting to make a call. If you don’t know what odds you’re facing, you can’t make an informed decision. If you aren’t making informed decisions, you’re making mistakes. If you’re making mistakes, you’re…”

[JJ] “Okay, okay. I get it”, Joey interrupted.

[BB] “If you’re ahead in a hand, it’s good to know what your opponent’s odds are of catching you, so you charge him enough for his draw. But let’s focus on the flip side.”

[BB] “If you’re behind, it’s even more important to know what your odds are. If you’re chasing draws with bad odds all day, you’re just asking to lose. We just covered what your odds are of hitting your draws. Next you need to look at what odds the pot is giving you. If there’s 1,000 in the pot, and you need 250 to call, then you’re getting 1,000-to-250, or 4-to-1 odds. So if you can hit your draw once for every four times you miss, which is 20%, then you’ll break even on pure pot odds.”

[JJ] “Why is 4-to-1 20% instead of 25%?”

[BB] “Oh, I should have explained that last time. 4-to-1 means 4-misses-to-1-hit, which is the same as 1-in-5 (1 hit in 5 attempts), which is 20%. Even I get 4-to-1 versus 1-in-5 confused occasionally, so I prefer to work in percentages all the time.”

[BB] “To summarize, your pot odds are the amount that’s in the pot to the amount you need to call. Reversed, it’s the amount that you need to call in the pot size, so the percentage is the amount you need to call divided by new total pot (times 100% unless you want to keep it as a decimal). Let’s stick with this last equation from here on out.”

[BB] “If the pot is 250 and your opponent bets 500 on the turn, what are your pot odds for calling?”

[JJ] “That’d be 500 divided by (250 + 500 + 500) equals 40%. You’d need like 19 outs to make that a good call.”

[BB] “Exactly. Overbetting the pot makes almost all draws unprofitable for one street.”

[BB] “If the pot is 2,000 and your opponent moves all-in on the flop for 1,500, how many outs do you need to make it a good call if he never bluffs?”

[JJ] “1,500 divided by 5,000 is 30%. You’d need about 14 outs… no, that’s one street… you’d need 7 or 8 outs.”

[BB] “Excellent! I think you’ve already got it.”

[JJ] “Thanks. And you know those pointy green things in my bedroom? They’re buckeye leaves ;-).”1


  1. To be honest, they do look a little alike.