[RR] “Maybe we could set aside a few bucks from each of our tournaments to send someone to one of the smaller events each year”, Roderick the Rock proposed.

[LL] “I’d be in for that! But we’d need to collect $1,000 for the entry fee, and maybe another $1,000 for airfare, lodging, and spending money.”

[RR] “All the $1K events this year are No-Limit Hold ‘Em. Seven are open bracelet events, which begin on May 30, every Sunday from June 2 to June 30, and a turbo on June 19. If our winner is 50 or older, he can also do the Seniors event that starts on June 14. If the winner is a female, she can enter the June 28th Ladies Championship, which is now cleverly a $10,000 event with a $9,000 discount for women. So, of the 35 No-Limit events, 9 are $1K.”¹

[LL] “Isn’t there also a Little One for One Drop charity tournament?”

[RR] “Yes, with a $1,111 buy-in, starting on either July 3 or July 4. Just a little more expensive but they’re re-entry events, which may bum you out a little if you bust out and can’t afford to rebuy.”

[LL] “Too bad the math doesn’t work out. Just collecting from our monthly tournaments wouldn’t be enough, since that would be too steep at $200 per event. But the weeklies could work, say 40 events at $50 each.”

[RR] “Except that you don’t play in those. You’ll have to just keep dreaming.”

[LL] “Maybe when online poker comes back, I can build my bankroll to five figures…”

[RR] “Or win a buy-in through a satellite.”

[LL] “… and then parlay a decent cash in the $1K event into a Main Event buy-in! When does the Main Event start this year anyway?”

[RR] “July 6. There are three Day Ones, and they’ll play down to the final table on July 15. The November Nine will reconvene on November 4.”

[LL] “I’m really looking forward to it, even just as a distant spectator.”

[RR] “Yeah, me too.”

Footnotes:

1. Of the 62 World Series of Poker bracelet events in 2013, 40 (65%) are Hold ‘Em: 35 (56%) No-Limit, two (3%) Pot-Limit, and three (5%) Limit. Nine (15%) are Omaha, three (5%) are Seven-Card Stud, seven (11%) are mixed games, and three (5%) are Razz or Lowball. By buy-in, eleven (18%) are under $1,500, nineteen (31%) are $1,500, ten (16%) are $2,500, six (10%) are $3K, nine (15%) are $5K, four (6%) are $10K, and one each (2%) are $25K, $50K, and $111,111.

Related Links:

• Official 2013 World Series of Poker Schedule

[AA] “Well, it’s always nice to flop the nuts”, Al the Almost diverted, “but the key was extracting maximum value from his straight, which, having minraised preflop¹, he did by checking the flop, turn, and river.”

[RR] “Teddy might have bet that way with almost any two cards, but I think he had a real hand, probably a set of some sort, and quite possibly a set of Aces, as he claimed, ‘That ace could not have helped you’.”

[AA] “Since he’d been playing so aggressively, he might think that Mike could put him on almost any two cards there and call with just a pair. And Mike’s actual holding seemed pretty unlikely to Teddy, so he expected to win the hand almost every time, whether Mike folded or not.”

[RR] “As much as the movie helped fuel the Texas Hold ‘Em boom, it’s unfortunate that it also portrayed string bets, pot splashing, temper tantrums, and cheating without nearly enough discouragement of those actions from the hero.”

[AA] “It was a movie, not a training video.² I’m sure Miss Manners Guide to Etiquette at the Poker Table is a best-seller at Amazon.”

Footnotes:

1. KGB was dealing and must have called from the small blind, although that isn’t shown.
2. We covered Table Manners a few months ago.

Related Links:

• Video of the hand.

Flash replayer version of the hand (estimated chip stacks)

Full Tilt Poker formatted version, suitable for inputting into various poker analysis tools

Full Tilt Poker Game #0000010022: Table Teddy KGB’s Place – 50/100 – No Limit Hold’em – 00:01:01 EDT – 1998/09/11

Seat 1: McDermott (41,400)

Seat 2: KGB (18,600)

McDermott posts the big blind of 100

KGB posts the small blind of 50

The button is in seat #2

*** HOLE CARDS ***

Dealt to McDermott [9s 8s]

KGB calls 50

McDermott raises to 200

KGB calls 100

*** FLOP *** [6d 7s Th]

McDermott checks

KGB bets 2,000

McDermott calls 2,000

*** TURN *** [6d 7s Th] [2c]

McDermott checks

KGB bets 4,400

McDermott calls 4,400

*** RIVER *** [6d 7s Th 2c] [As]

McDermott checks

KGB bets 12,000, and is all in

McDermott calls 12,000

*** SHOW DOWN ***

McDermott shows [9s 8s] straight, Nine high

KGB mucks

McDermott wins the pot (37,200) with straight, Nine high

*** SUMMARY ***

Total pot 37,200 | Rake 0

Board: [6d 7s Th 2c As]

Seat 1: McDermott (button) showed [9s 8s] and won (37,200) with straight, Nine high

Seat 2: KGB (big blind) mucked

[AA] “Watch it a couple dozen more times like I have, then you can really understand its brilliance”, Al insisted.

[RR] “What I certainly appreciate more now then fifteen years ago was that the poker hands weren’t over-the-top straight flush vs. four Aces hands like other in most other movies.”²

[AA] “Yep, the biggest hand they showed was only a full house. Realistic.”

[RR] “That first hand against Teddy KGB seemed far-fetched to me when I saw it in the movie theater, but now I realize that it was just an unavoidable cooler.”

[AA] “Zeebo’s Theorem.³ Especially four-handed, there’s no way Mike can fold his full house. With A♣9♣, he raised from the button preflop and got called by Teddy in the big blind. Overbet his top two pair on the A♠9♠8♣ flop to make it look like a continuation bet and steal attempt. Slowplayed by checking behind on the 9♥ turn, which gave him his boat. And then bet and reraised all in on the harmless 3♠ river, which he hoped gave Teddy a flush.”

[RR] “The betting was too big — double reverse psychology or whatnot — but there’s no way to get away from a big loss there… unless he’s spotted a reliable tell.”

[AA] “Ah yes, the tell. People complained that no pro-caliber poker player would have such a blatant tell, but we’ll call that artistic license. If all Teddy did was twitch his nose, it would have been too subtle for most viewers to notice. I forgive them for the exaggeration.”

[RR] “What was far worse than the tell was Mike showing off his cards when he could have mucked them after folding because of the tell.”

[AA] “Yeah, laying down two pairs on the flop heads-up is pretty extreme. He might as well have admitted that he’d spotted the Oreo-eating tell, and Teddy didn’t take long to figure that out and smash his cookie rack against the wall. But Mike’s narration explains his rationale, claiming that the tilt factor was worth more than the tell.”

[RR] “Except that a good poker player shouldn’t be that easy to unhinge.”

[AA] “Maybe Mike expected Teddy to realize it out on his own anyway at some point. Rather than depending on a tell that could become unreliable and cost him a lot of money, he cashed it in for what he could get right then and there.”

Footnotes:

1. Al and Rod previously discussed Rounders in The Basics of Texas Hold ‘Em.
2. For example, The Most Famous Hold ‘Em Hand.
3. See the previous discussion of Zeebo’s Theorem.

Related Links:

• Video of the hand.

Flash replayer version of the full house hand (estimated chip stacks)

Full Tilt Poker formatted version, suitable for inputting into various poker analysis tools

Full Tilt Poker Game #0000000022: Table Teddy KGB’s Place – 100/200 – No Limit Hold’em – 00:00:01 EDT – 1998/09/11

Seat 1: McDermott (50,500)

Seat 2: Player3 (21,000)

Seat 3: KGB (62,500)

Seat 4: Player4 (16,000)

Player3 posts the small blind of 100

KGB posts the big blind of 200

The button is in seat #1

*** HOLE CARDS ***

Dealt to McDermott [Ac 9c]

Player4 folds

McDermott raises to 500

Player3 folds

KGB calls 300

*** FLOP *** [As 9s 8c]

KGB checks

McDermott bets 2,000

KGB calls 2,000

*** TURN *** [As 9s 8c] [9h]

KGB checks

McDermott checks

*** RIVER *** [As 9s 8c 9h] [3s]

KGB bets 15,000

McDermott raises to 48,000, and is all in

KGB calls 33,000

*** SHOW DOWN ***

McDermott shows [Ac 9c] full house, Nines over Aces

KGB shows [Ad Ah] full house, Aces over Nines

KGB wins the pot (101,100) with full house, Aces over Nines

*** SUMMARY ***

Total pot 101,100 | Rake 0

Board: [As 9s 8c 9h 3s]

Seat 1: McDermott (big blind) showed [Ac 9c] and lost with full house, Nines over Aces

Seat 2: Player3 didn’t bet (folded)

Seat 3: KGB (button) showed [Ac 6h] and won (101,100) with full house, Aces over Nines

Seat 4: Player4 (small blind) didn’t bet (folded)

[FF] “I always thought a pair of Queens against Ace-King was close”, volunteered Figaro the Fish.

[HH] “I’d go with something near what you mentioned earlier”, Harriet the Hazy suggested. “Like Jack-Ten offsuit against a pair of Twos.”

[RR] “Or the Queen-Jack suited against Twos”, Roderick the Rock recommended.

[LL] “Maybe something lower like Eight-Seven suited against the same”, Leroy the Lion offered.

[EE] “Yeah, it’s probably something like that”, Elias the Eagle amended. “I’ll guess the same but against Threes.”

[TT] “Since I get to guess for free / How ’bout the suited Four-Three / Against the ultimate poo / The offsuit Seven and Two?” Tyrone the Telephone attempted.

[SS] “All excellent guesses… well, maybe not Figaro’s, which is 54% suited. Tyrone was very close to the sixth best matchup: 62o vs. 54o where the Two matches a suit (the high card or kicker value of the Six almost exactly balances the straight potential of the 54). Fifth is 73s vs. 22 in different suits, and fourth is 97o vs. 22 with four suits. Third is what you all danced around, QJo vs. a pair of double suit-dominated Threes. Roderick just missed that one. Second is T9o vs. 55 with one matching suit. All of these are 50.01% for the better hand, as is number one, which wins by a smidge: ATs vs. 33 with one matching suit, which is so close to a coin flip that if you played it out 7,075 times, you’d only expect to win one more time than your opponent (50.0071%)! In all the cases with pairs, the pair wins with more sets and boats but loses to more straights and, perhaps surprisingly, pairs (and even two pairs sometimes because of the dreaded three-pair hands).”

[RR] “Very cool, Stan”, Roderick the Rock acknowledged. “But now that you’ve given us all of these mostly non-nutritious snacks, what about the meat and potatoes of all-in heads-up matchups?”

[SS] “I was getting to that”, Stan the Stat claimed. “When I was first learning how to play Hold ‘Em, I set out to memorize all of the common odds. I thought preflop all-in percentages would be useful, but there were just way too many to remember¹. Fortunately, grouping the matchups into just eight general categories with their approximate odds is quite sufficient.”

[SS] “If neither hand is paired, there are three groups of matchups:”

[SS] “Otherwise with a pair, there are five matchup groups:”

[SS] “* Within a given category (when relevant), being suited is worth a few percent for the flushes (just being able to make a winning flush is worth half a percent), and being connected is worth a few percent for the straight possibilities. In cases where the flush or straight is one of the few ways to win, the difference for the weaker hand can be up to five percent (e.g., AA vs. AKs is 5% better than AA vs. AKo, and AA vs. T9o is 5% better than AA vs. T5o).”

[RR] “Why isn’t it always five percent?”

[SS] “All the hands where the weaker hand hits a straight or flush but would have had a winning pair, two pairs, or three of a kind anyway don’t increase the percentages. The straight or flush is superfluous in those cases. Similarly, suited connectors don’t get the full gain for both the straight and flush possibilities, more like just seven percent in the best cases.”

[TT] “If you’re all-in, while nothing’s been fated / Know the odds, lest your hopes get inflated / It’s better not to be dominated / Or for ‘Next Bust’ you’ll be nominated”, Tyrone concluded.

Footnotes:

1. The total number of possibilities is 812,175 (52-choose-2 * 50-choose-2 / 2), but ignoring suits, there are only 14,196 (13^2-choose-2) to memorize.
2. These charts are based on the tables in John Vorhaus’s Killer Poker by the Numbers, pages 268-275, but have been modified with help from Mathematrucker. All odds are approximate, within a couple of percent except as noted in some of the following footnotes.
3. The full range is fairly wide, going from about 65% to 78%, with higher cards tending toward the upper part of the range.
4. Having alternating ranks (e.g, QTo vs. J9o) makes surprisingly little difference (the weaker hand mostly needs to pair up in either case, and having two undercards can give more straight possibilities).
5. The full range is fairly wide, going from about 58% to 71%.
6. The full range goes from about 51% to 60%.
7. The full range is fairly wide, going from 76.93% (KK vs. 54s) to 90.10% (AA vs. K2o with matching suits).
8. The full range only goes from 79.75% (33 vs. 22 of different suits) to 82.69% (TT vs. 99 with matching suits). Vorhaus listed this as 80%, probably from rounding, but it’s definitely closer to 81%.
9. The classic race, QQ vs. AKo (57%) or vs. AKs (54%), would also go here as the AK is effectively unconnected with only two Queens left in the deck to make a royal straight.

Related Links:

• Tony Guerrera’s more rounded (nearest 5%) preflop all-in chart. His “Doing Analysis Against Distributions” is a subject for a future post.

[FF] “Okay…”, Figaro responded warily.

[SS] “I’ll bet you even-money on who can roll the higher number with one of these dice”, Stan offered. “And because I like you, we’ll roll as many times as you want, and you can pick whichever die you want each time.”

[FF] After examining the dice, the Fish decided, “Okay, I’ll take this one, the only one with nines on it.”

[SS] “Very well, I choose this one with nothing higher than a seven”, the Stat countered.

[LL] Leroy the Lion chuckled, “You’re not really going to con him are you?”

[SS] “No, just for fun; we’re all friends here.”

[LL] “Fig, it doesn’t matter which die you pick, these are nontransitive dice, where each die beats one of the other two and loses to the other one.”

[FF] “How is that possible?”

[SS] “It’s like Roshambo, where rock beats scissors beats paper beats rock. The six faces on each die add up to 30, but they’re set up so you win by a little and lose by a lot, allowing the second player to win five-ninths of the matchups. C > B > A > C:”

[SS] Reaching into his right pocket and pulling out some more dice, Stan continued, “Or consider this set of four, called Efron’s dice:”

[SS] “The edge is even bigger here as the dominating die wins two-thirds of the time. G > F > E > D > G.”

[FF] “Wow, that’s amazing. Can I borrow those for the next time I go to a bar?”

[LL] “Do you really like to get beat up?”

[SS] “What’s cool is that you can do the same thing with Texas Hold ‘Em hands, although your edge is much smaller.” Having rummaged through a deck of cards and pulled out six of them, Stan continued, “For example, consider these hands: A♣K♦, J♥10♥, and 2♠2♥. Which would you prefer, Figaro?”

[FF] “Definitely the Ace-King at a full table.”

[SS] “Nope, you’re heads up.”

[FF] “I’d still take it.”

[SS] “Well, then I’d select the Twos and have a 53.0% to 47.0% edge on you. Similarly, the Jack-Ten suited has 53.7% equity against the Twos, and the Ace-King offsuit does even better against the Jack-Ten at 58.8%.”

[LL] “The Ace-King is an obvious win over the Jack-Ten, while the other two matchups are classic races. Both connectors mainly need to pair up to beat the Twos, but the Jack-Ten makes enough straights and flushes to tip the scales, while the Ace-King doesn’t.”

[FF] “Pretty cool, indeed.”

Related Links:

• While it’s not blindingly obvious how to use it, the table at the top right of the Mathematrucker Matchups page lets you see any family of heads-up matchups (by gap and suitedness). Just tap on the proper square in the grid. In the answer cells, a pink background means the hands on the left column are winning and a blue background means the hands on the top row are ahead! Tap on the percentage to display the winning hand type breakdown on the left.

[RR] “I thought the best was something like Aces against Ace-Nine offsuit, with the Nine matching the suit of one of your Aces.”

[SS] “Close.”

[FF] “Ace-Eight?” Figaro the Fish ventured.

[SS] “Nope.”

[HH] “Ace-Seven?” Harriet the Hazy attempted.

[SS] “Nope.”

[LL] “Ace-Six?” Leroy the Lion guessed.

[SS] “And nope. Oddly, the Ace-Nine is the best of those because King-Queen-Jack-Ten is only a push, but the Ace-Six is next.”¹

[EE] “So, it’s not a pair of Aces at all! Then it must be Kings vs. King-Two”, Elias the Eagle deduced.

[SS] “Indeed, with nearly 95% equity.² With an Ace, you can’t let your opponent have anything under a Five because that would permit too many straights. With the King, no such problem. The King-Deuce does tie a few more hands, but it wins many fewer because the Six through Nine all take part in five kinds of straights while the Two only makes two. Queens vs. Queen-Two is the next best.”³

Footnotes:

1. Ace-Eight makes 12 more winning full houses than Ace-Seven, which in turn makes 12 more than Ace-Six.
2. 94.92% from 1,612,287 wins and 26,192 ties out of 1,712,304 possibilities.
3. 94.66%. Then Kings vs. King-Three (94.48%), Jacks vs. Jack-Two (94.35%), Queens vs. Queen-Three (94.22%), and finally Aces vs. Ace-Nine (94.08%), barely edging Kings vs. King-Four (94.04%) and Kings vs. King-Two with four suits (94.03%).

[FF] “The other two Aces”, Figaro the Fish observed.

[SS] “Besides that, of course.”

[RR] “I thought it was Ten-Nine suited, matching neither of the Ace’s suits”, Roderick the Rock opined.

[LL] “No, if that’s good then Nine-Eight suited has to be better. With Ten-Nine, a King-high straight is no good, since the Aces win with a royal straight”, Leroy the Lion objected.

[SS] “Both incorrect, but you’re getting warmer.”

[HH] “Eight-Seven suited”, Harriet the Hazy opted, like the next contestant on The Price is Right.

[SS] “Nope.”

[FF] “Seven-Six”, Figaro the Fish output.

[SS] “Still wrong.”

[TT] “Now it’s a cinch to derive / That it must be the Six-Five”, Tyrone the Telephone offered.

[SS] “Indeed. The Six-Five has just over 23% equity.¹ But why is it slightly better than the Seven-Six?”

[TT] “The Seven-Six gets more hits / But the Six-Five gets more splits.”

[SS] “Indeed it does. Which ones?”

[RR] “Except for my initial guess, all these suited connectors can make the same number of winning straights and flushes, so that leaves full houses.”

[LL] “No, the Seven-Six makes more winning straights. They both win if there’s a wheel straight on the board, but a 65432 board is a win for the Seven-Six and only a push for the Six-Five.”

[EE] “So the 6-high straight is some of the Six-Five’s extra pushes. The rest are on the other side: the Jack-high and Ten-high straights, which don’t happen as often for the Seven-Six.”²

[SS] “And that’s most of the difference, although there are a few full houses. 77666 down to 77222 vs. 55444 down to 55222 accounts for a few more wins for the Seven-Six and a few more ties for the Five-Four. Lastly, JT98x wins more often for the Seven-Six than 432Ax does for the Six-Five.”

[SS] “The Six-Five has enough extra straight pushes to overcome the extra wins that the Seven-Six gets.”

[TT] “When facing Aces, your prospects are wee / Even with the best hole cards you could see / Out of thirteen tries, you’ll only win three.”³

Footnotes:

1. The Six-Five suited has 23.056% equity, 0.0235% more than the Seven-Six suited (23.0325%).
2. Out of 1,712,304 possible boards, the Six-Five suited wins 55 fewer times but ties 916 more times.
3. This is an excellent estimateas three-thirteenths is the repeated decimal 0.230769.

[DD] “I’m on the second to last tournament, the National Championship on the top difficulty”, Deb responded. “It’s going to be a long time before computers can beat the pros, but they’re still challenging to me.”

[NN] “Don’t be fooled. Computers will be better than the pros at Hold ‘Em sooner than you think. If IBM can conquer Jeopardy! with Watson by building a large enough information database and crafting a smart enough language parser, other programmers can certainly keep improving their Hold ‘Em algorithms until they outclass even the top poker pros. Paraphrasing The Simpsons,² Ken Jennings conceded on his Final Jeopardy answer screen, ‘I, for one, welcome our new computer overlords.’”

[DD] “How soon do you think that’s going to happen?”

[NN] “I think Black Friday set the timetable back a couple years, since the breakthroughs will probably come outside the U.S. now, but certainly within a decade.”

[NN] “Computers can do the math perfectly. They can calculate odds almost instantaneously with massive lookup tables and powerful processors. They can analyze your hand history to see how you play. All that’s really left are a few advancements in the algorithms that decide what to do with all this information. It essentially comes down to hand reading, and I don’t mean palmistry.”

[DD] “That’s what separates the pros from the amateurs.”

[NN] “The reason hand reading is so daunting to most humans is that there’s so much to keep track of on just a single hand, let alone over a session of hands with the same players. Computers don’t have the slightest problem with it. Which is why most good online players use HUDs (heads-up displays).”

[NN] “To put your opponent on a hand range even before the flop, you need to take into account his stack size; the blinds and antes; his position; the action ahead of him, including who bet what from where; the amount he called, bet, or raised; how he’s been playing recently; and his playing style, which alone can be broken down into dozens of smaller areas; and more.”

[FF] “But how am I supposed to keep track of all that?”

[NN] “To start as simply as possible, the most important element is a player’s style. In a home game, you’ll get to know the regulars quite well without even trying. You two certainly know how I play, and I know how you play. In an unfamiliar ring game or any larger tournament, you’ll have no history with your opponents, but every hand adds to your database of information about them.

• How many hands do they play (i.e., are they loose or tight preflop)?
• How often do they 3-bet? 4-bet? 5-bet? (i.e., how tight a range does each of those represent)?
• Do they correctly value position (e.g., do they play many more hands in late position than early and can you discount their bets in position vs. out of position)?
• Do they tend to call or raise (i.e., are they too passive or too aggressive)?
• Do they bluff too often or too infrequently (i.e., can you discount the strength of their bets or should you take them as real)?
• Do they call too much or can you bluff them out of pots (i.e., should you value bet them or steal from them)?
• Can they make big folds? (i.e., should you try to make a big river bluff or all-in bluff)?
• Do they like to chase draws? (i.e., should you charge them more for their draws and/or not try to bluff if you think they have a draw)?
• Will they bet if they have just a draw (i.e., could your third pair be the best hand despite their bet)?
• Do they tend to underbet the turn and river (i.e., will you get a good price to hunt for your draws)?
• Do they overbet the flop when the board is scary (e.g., can you put them on a hand like top pair or an overpair)?
• Do they adjust to their opponents (i.e., do you need to take into account what they think of your style)?
• Is their style static or can it change (i.e., once you’ve figured out how they’re playing, can you count on that always)?”
• Do they play differently when they’re shortstacked? (e.g., can you devalue a shove from them once they’re short enough on chips)?”
• Do they like to steal the blinds from the button? The cutoff? The hijack? (e.g., can you devalue all of those raises)?
• How often do they check-raise, if at all? (e.g., if they check to you, can you bluff knowing that you won’t get raised)?”

[FF] “Yikes!”

[NN] “If the event is a tournament, a few more questions are relevant:

• Are they very afraid of busting out? And do they have any rebuys left if it’s a rebuy tournament?
• Does their style change as the blinds go up?
• Are they happy just to cash or are they trying to win it all?
• Do they play more tightly near a bubble or will they attack if their stack is healthy?”

[FF] “My head is spinning.”

[NN] “I know it’s overwhelming at first, so start by just watching the player on your immediate left or right or the most active player at the table, and note only a few of those pieces of information. As you get comfortable, add more information and more players. You can do it. You just have to try.”

Footnotes:

1. See “A New Game in Town – THETA Poker Pro”.
2. You can watch the segment from the “Deep Space Homer” episode.

[BB] “Poker is a funny game in this respect. You want to think deeper than your opponent, but don’t want to think too much deeper than your opponent. A seasoned pro and a complete neophyte might make the same exact bet for completely different reasons, so you need to determine how deeply your opponent thinks to know how to play against them. You want to be thinking exactly one level deeper than your opponent.”

[BB] “Beginners think at the first level: what cards do I have and how good is my hand? Some beginners are able to adjust for the texture of the board, but most won’t think to devalue their nut flush if the board is paired.”

[BB] “Intermediate players think at the second level: what does my opponent seem to have? But they only have a vague notion of your hand strength: strong, fair, or weak. Sometimes intermediate players prematurely and inaccurately try to place you a specific hand, but that usually doesn’t work out well for them.”

[BB] “Advanced players also think at the second level, but they start you on a fairly wide hand range and try to narrow it as the hand progresses. When they’ve deduced correctly, they can cause you major problems.”

[BB] “Expert players think at the third level: what does my opponent think I have? That’s as far as anyone goes in the games we’re playing in. Which means that if you can go to the fourth level (what does my opponent think that I think they have), you’ll dominate here.”

[BB] “Do you remember the battle of wits scene in The Princess Bride?”¹

[JJ] “Of course!” Joey the Juvenile confirmed.

[BB] “Westley, then referred to anonymously as the man in black, shows Vizzini some poisonous iocane powder, turns his back for a moment, then says, ‘All right. Where is the poison? The battle of wits has begun. It ends when you decide, and we both drink and find out who is right… and who is dead.’”

[BB] “Vizzini tries to deduce which glass to pick, reasoning, ‘Now, a clever man would put the poison into his own goblet, because he would know that only a great fool would reach for what he was given. I’m not a great fool, so I can clearly not choose the wine in front of you. But you must have known I was not a great fool; you would have counted on it, so I can clearly not choose the wine in front of me.’”

[BB] “Vizzini is thinking at level three, considering what his opponent, the man in black would think he thinks.”

[BB] “Vizzini apparently solves the dilemma by switching the glasses while his enemy isn’t looking. The man in black doesn’t hesitate to drink from his own goblet, so it must have originally been the safe one. Because of the swap, Vizzini therefore has the drink that’s safe to imbibe, which he does.”

[JJ] “But Westley was thinking at level four!”

[BB] “Right. Although Vizzini did momentarily come close to the right answer, he spent most of his time considering the wrong data. Of course, a wise man wouldn’t ever consider drinking from a glass if there were a 50% chance that it would be fatal, not unlike a coin flip for your tournament life.”

[BB] “Wallace Shawn’s villain character flopped the nut flush draw and concluded that his Ace was good anyway. But he really had no outs as his opponent already had a full house. Both glasses were poisoned, and Cary Elwes’s hero character had spent years building up his immunity to iocane.”

[BB] “So make sure you use the appropriate level of thinking for your opponent. Against Figaro the Fish, there’s no need to go beyond level two. If you explain his actions with any deeper logic, you’ll end up making the wrong move. Against Vince the Veteran, level three is good. He’ll try to put you on a hand, so a little deception will go a long way. And against Deb the Duchess, level four would be right, although I still aspire to that.”

Footnotes:

1. If you prefer, here is the transcript of the battle of wits.

[JJ] “Miss Cleo?”,¹ Joey the Juvenile offered facetiously.

[BB] “Sherlock Holmes! Sir Arthur Conan Doyle’s great detective once said, ‘It is my business to know what other people don’t know’.”²

[BB] “You’ve now played a few tournaments with us, so you should have an idea of how people play. Preflop, who’s the loosest player in the group?”

[JJ] “William the Whale. He makes big bets all the time.”

[BB] “‘You see, but you do not observe. The distinction is clear”³, Benny quoted. “William likes to make you think he’s incredibly loose, but that’s only because you notice his big bets when he’s in a hand.”

[JJ] “Well, Carlos the Crazy then.”

[BB] “You’re getting warmer. He’s probably in second.”

[JJ] “I don’t know.”

[BB] “Tyrone the Telephone. He’s a total calling station. He flies under the radar because he mostly just calls, but he definitely sees more flops than anyone.”

[BB] “Who sees the fewest flops?”

[JJ] “Either Mildred the Mouse or Roderick the Rock.”

[BB] “Right! Roderick loosens up a bit in the cash game, which Mildred never plays in, but they’re both super-afraid of busting out of the tournament. They pretty much stick to premium hands and will fold a dozen times in a row, no sweat.”

[BB] “You’ve already touched on this, but who are the most aggressive players besides William and Carlos?”

[JJ] “Deb the Duchess, Elias the Eagle, and Yuri the Young Gun.”

[BB] “Excellent. If you were sitting at a table with those five, I don’t think you’d ever see a flop where everyone limped.”

[BB] “Who really loves suited connectors, even the awful Four-Three and Three-Two?”

[JJ] “I have no idea.”

[BB] “That would be Harriet the Hazy, who always thinks she can hit a lucky flop.”

[BB] “Who will play any pair, even facing a big preflop raise out of position?”

[JJ] “Most of us.”

[BB] “Not too inaccurate, but I was thinking of Figaro the Fish. You saw him last month when he almost won the tournament after hitting so many sets.”⁴

[BB] “Holmes also insisted, ‘It is a capital mistake to theorize before one has data. Insensibly one begins to twist facts to suit theories, instead of theories to suit facts.’⁵ Every hand leaves a trail of data to be collected. You go into each hand with what you already know about your opponents. That’s like the case file for each criminal. You add that to the checks, bets, raises, and calls on each street. Those are your clues from the current crime (well, they’re trying to steal your chips, right?). With all the evidence you have, you can then decide what the best action to take is.”

[BB] “Now, I don’t even really know the answers to these questions, but it would really help your play if you could notice… Who will play any Ace? Any pair? Who will play any two cards from the button? Who defends their blinds too much because they don’t correctly value position? Who will call almost any bet to chase a draw? Who will bet when all they have is a draw? Who will bluff a four-flush on the board without a flush? Who will represent an Ace on the board without it?”

[JJ] “Wow, I guess I need to start paying more attention.”

[BB] “Exactly. Especially when you’re not in a hand, since that should be more often than when you’re in a hand. After each hand, try to mentally review what just happened and update your images of each active player.”

[BB] “If you can do that, you’ll be a better player than me very soon.”

[JJ] “I can’t wait! But didn’t Holmes also claim, ‘There is nothing more deceptive than an obvious fact’?”⁶

[BB] “Well, you also need to figure out who the deceptive players are. Against the better players, you won’t be able to pinpoint their two hole cards. ‘We balance probabilities and choose the most likely. It is the scientific use of the imagination.’”⁷

[BB] “Ultimately, if you pay more attention, you’ll have more information. If you have more information, you’ll make better decisions. If you make better decisions, you’ll win more.”

[JJ] “Elementary!”⁸

Footnotes:

1. Youree Dell Harris portrayed Miss Cleo in television ads for the Psychic Readers Network from 1997 to 2003.
2. Sir Arthur Conan Doyle, The Adventure of the Blue Carbuncle, page 254.
3. A Scandal in Bohemia, page 162.
4. See Sets Education.
5. A Scandal in Bohemia, page 163.
6. The Bascombe Valley Mystery, page 204.
7. The Hound of the Baskervilles, page 687.
8. Doyle never had Sherlock Holmes say, “Elementary, my dear Watson.” The catchphrase was popularized by the many movies made from his stories.