Chess Variant: Alice

This is the first time I've seen the chess variant, Alice. It supposedly is inspired by Lewis Carroll's Through the Looking Glass.

There is essentially only one rule-change from orthodox chess: A second board is used, initially empty, and after a move, on either board, the moved piece is transferred to the square with the same coordinates on the other board.

Schooling

Interesting, hadn't heard of "schooling" until very recently. From the article, Schooling:

Schooling is a belittling term used to describe what loose poker players do as a defense mechanism. (Sheep flock; fish school.) If a pot is fairly small on the turn in Holdem, and the player with the best hand bets, any single player with a only gutshot draw will be making a significant mistake by calling. But now suppose several other people call too, with different gutshot draws. Because these other players are playing bad also, now the pot has grown to the point where the gutshot draws are getting better pot odds on their calls. These bad calls "school" together and miraculously become not-so-bad calls!

Schooling is part of the reason many reasonable players complain that they are unable to beat loose games. Everybody going to the river, sucking out every possible draw, how can a sensible player make a hand "hold up" and beat such a game? Well, it’s not hard really. A winning player merely wins money differently (and with higher variance) in these games. Schooling is actually profitable to good, winning players, but it does take a little analysis to see why. One column can't do justice to this topic, but maybe an example will help some people start having the right idea on how to view schooling.

Suppose you are playing $10/20 Holdem. In the big blind you have A9 (suits don’t matter here). Six people limp in, you check. The flop is AT5. Not so great, but you bet to see what happens. All six of your opponents call. Uh-oh, you start thinking about checking and mucking on the turn. But the turn card miraculously comes another Ace! You bet $20 into the $140 pot.

Via the magic of being able to make this stuff up, it turns out our six opponents have KQ, KJ, QJ, 43, 42, and 32. Of the 34 possible remaining cards in the deck, only 2 make a winner for each individual opponent. That’s 16-1 against them. When it comes to the first player, let’s say the KQ, he has to put in $20 at $160. He’s only getting 8-to-1 on a 16-to-1 draw. Bad call. But now as each subsequent player also calls, when it gets around to the 32, he has to put in $20 at a $260 pot. He’s getting 13-to-1 on his 16-to-1 draw. His call is not nearly so bad as the KQ’s call! That’s schooling, but the schooling of the other players has now also turned the KQ’s call into not nearly so bad a call -- likewise for all the other players.

But we don’t care about them, we care about our A9. If everybody had folded when we bet the turn, we get the $140. After 100 times, we’d be $14,000 ahead. But now what about when they all call? It turns out that A9 will end up winning about 65% of the time. So, after a hundred times, 65 times we get another $120 (six turn calls of $20 each), assuming nobody ever tries to bluff or calls a bet by us on the river. The 35% of the time we lose, we lose our $20 turn bet, plus any action on the river. Just to pick some numbers, I suggest we lose one bet on the river 50% of the time (when the river card is a king, queen or jack) and two bets the other 50% of the time (when the river card comes a four, three or deuce). So we lose an average of $30 on the river -- $50 total that 35% of the time the school draws out on us. What this works out to be is a decent extra profit per hand for the A9. The schooling helped our opponents, but it is still more profitable for us for them all to call -- to the tune of about $11.50 a hand. (65 wins of $260 = $16,900. 35 losses of $50 = $1750. Total profit = $15,150, or $1150 more than the $14,000. Also note that the 35 times we lose, we lose the $20 we invested in the pot to that point, or $700. However, that is not what we are analyzing here. We are looking at our situation on the turn. That $20 is already in the pot. It isn’t ours anymore. The before the flop action and flop calls by the other players have their own schooling ramifications.)

Now some people might prefer getting the $14,000 profit after 100 incidents of hands like this with everybody folding when our A9 bets the turn -- zero variance, win 100% of the time. It is about $1150 more profitable though for the A9 to live with the variance of having everybody calling. Most important, the fact that all these folks are calling/schooling is not a dramatically bad thing. A good player playing properly will do just fine against schooling opponents.

But it’s not that simple. If we change the 43 and 42 to 77 and 66, now we are going to win only 59% of the time, with that other 6% (the difference between our 65% and 59%) of the wins going to the 32. The 32 now snares a bunch of the profit in the hand, to the point that we would prefer that everybody would fold, and we just take the $140 each time. However, the A9 is still making money from people playing poorly by calling the turn bet, it just so happens that sometimes the main beneficiary of schooling is the best draw out there (the 32), not the best hand. Sometimes the second best hand benefits the most (in this case the 32 goes from a losing hand to a profitable one when everybody else calls), it all depends on the actual hands and how good their draws are, and how strong the best/most-likely-to-win hand is.

Schooling games give good players two main ways to win -- by either playing the best made hand or the best draw. There is more money to be made overall, but you have to make sure your game adapts to get the profit from both these ways.

You beat a schooling game the same way you beat any other game -- play smart, appropriate poker.

ChessAndPoker on Blackjack

ChessAndPoker has a basic tutorial on counting cards in blackjack.

Early Position: Sklansky & Malmuth Answer Questions Regarding Hole Cards

If you are first in, or if there is only a call to your right, what should you be prepared to play?

Those hands in the first four groups.

Group 1: AA, KK, QQ, JJ, AKs
Group 2: TT, AQs, AJs, KQs, AK
Group 3: 99, JTs, QJs, KJs, ATs, AQ
Group 4: T9s, KQ, 88, QTs, 98s, J9s, AJ, KTs
Group 5: 77, 87s, Q9s, T8s, KJ, QJ, JT, 76s, 97s, Axs, 65s
Group 6: 66, AT, 55,86s, KT, QT, 54s, K9s, J8s, 75s
Group 7: 44, J9, 64s, T9, 53s, 33, 98,43s, 22, Kxs, T7s, Q8s 1
Group 8: 87, A9, Q9, 76,42s, 32s, 96s, 85s, 58, J7s, 65, 54, 74s,K9, T8

What about a loose game if the players are not too aggressive?

You can add the Group 5 hands, especially the suited connectors.

What about a tough game?
Discard the Group 4 hands.

What do you do as the game gets more aggressive?

Discard hands such as AJ and KTs.

What do we mean when we refer to a loose game?

A game without much before-the-flop raising and with many players in most pots.

What do we mean when we say tough game?

A game with a fair amount of raising, but not many large multiway pots.

What if you are not sure which type of game you are playing?

Assume that the game is typical until you can determine otherwise.

What if the game is loose, but very aggressive?
You should not be in many pots.

What if the game is tight, but passive?

You can play a fair number of hands.

Why should you occasionally add a few hands to those you play up front?

To throw your opponents off.

Why would you play a hand like 7S 6S up front?

To stop your more observant opponents from stealing against you when "rags" flop, or if you feel that your early position raises are getting too much respect.

What if there is a raise to your right and the game is typical or
tough?

Limit your play to those hands in Groups 1 and 2.

What if the game is loose?

You can play Group 3 as well (beware of AQ).

Should you be calling many raises if no one (except the raiser)
is in?

No.

What should you be doing?

Usually folding or occasionally reraising.

Against a loose raiser, what additional hands should you play?

AQ, 99, and 88.

Assuming you play against a loose raiser, what do you do?

Reraise, except just call with AJs and KQs.

If no one has yet called, what hands do you almost always raise with?

AA, KK, QQ, AK, and AQ.

What if there have already been callers?

Usually raise with hands in Group 1 and 2, AQ, and some others at random.

What hands do you raise approximately two-thirds of the time?

AKs, AQs, AJs, and KQs.

What if you are against weak opposition?

Almost always raise with them.

What if the game is tight and most players respect your raise?

Be more inclined to limp with the big suited connectors.

When is it correct to limp with AA or KK?

When your early position raises are not getting any callers.

What if you are now raised?

Frequently, but not always, reraise.

What about a hand like T+9+ if no one has yet called?

Raise approximately one-third of the time if the game is typical or tough.

What if you are in a game with many weak opponents?

Just call.

What is proper if you call with a large suited connector and are raised?

Reraise with AKs and possibly AQs.

When can you reraise with a hand like J+T+?

If a lot of people are in the pot.

What about hands like 8S 7S?

If there are a lot of callers, but not much raising, they become playable.

What about small pairs?

They can also be played provided that you are sure that you will get a multiway pot. However, they can stand a little more action than the suited connectors.

What if the game is moderately aggressive, but features two or more players who will play virtually any ace?

Play A9s, Ah , 77, and 66 as long as the pot is not yet raised.

What if no one has opened and you have JJ?

Raise in a tight game and call in a loose game.

What if you hold JJ and the pot has been raised and reraised?

Fold.

What if you opened with JJ and the pot has been raised and reraised behind you?

Call.

Game Theory + Poker

Here are 2 game theory sites:

• one by the father of Chris "Jesus" Ferguson
• The University of Alberta Computer Poker Research Group

Wild Card Paradox

Ever wonder what a wild card does to a poker game?

Go Online

Cool, you can play Go online with your browser.

Essays on Go

Here is a collection of essays for beginners interested in the game of Go, including this amusing story involving Einstein:

When I first started to learn the game of go there was very little available about it in the English language. A book that was in print at that time was Dr. Edward Lasker's Modern Chess Strategy with an appendix on Go. I immediately bought it and it provided me with a beginning. Later, as I became involved in the New York City go world, I met Lasker, one of the stronger players in the area in the early 1950s.

Lasker had first learned go around 1907, when an engineering student in Berlin. His parents had wanted him to study medicine but he opted for engineering, as it provided him the opportunity to study in Berlin. His real interest at the time was chess, and Berlin offered him the chance to study and improve his game.

He first became interested in go by watching Japanese students play and, as he wrote, `with astounding perseverance and passion.' He used to visit a cafe to play chess, and one evening a Japanese gentleman left his newspaper. By looking at the game record in the paper, Lasker and his friends began to appreciate go's complexity and this started his study of the game.

After graduating, Lasker worked in England until World War I, then went to the United States. By then he was a world-class chess player and quite active in tournaments during the 1920s. Samples of his games can be found in various books discussing chess activity of the time. I believe, though am not certain, that he taught go to his cousin Emanuel Lasker, who became the World Chess Champion at 24 by beating Steinitz and losing only to Capablanca 26 years later. In any case, Emanuel Lasker became very interested in go and developed into a fairly strong player.

Edward Lasker wrote Go and Gomoku, first published in 1934 and of much interest, as it included the famous game between Junichi Karigane and Honinbo Shusai, played in 1926.

Lasker and Albert Einstein were friends. On one occasion Lasker visited Einstein in Princeton and presented him with an autographed copy of Go and Gomoku. In exchange, Einstein gave Lasker an autographed copy of one of his papers on relativity. Several years later, the autographed copy of Go and Gomoku showed up in a used bookstore in Baltimore. When told about this and asked what he thought of it, Lasker replied: `That's all right. I left his relativity paper on the subway.'

Game Theory Tutorial

Here's an interesting tutorial on Game Theory, a branch of mathematics that uses models to study interactions with formalised incentive structures ("games"). From the URL:

• Intro
• The Prisoner's Dilemma
• Zero Sum Games

Introverts vs Extroverts?

In the article, Is There an Optimal Poker Personality Profile?, Dan Mezick explores which of the 16 Meyer Briggs personality types might be good at poker. I found this observation interesting.

[I]t is well known that chess masters are often introverts. Yet the world chess champion does not win five million dollars in cash, as did the World Series of Poker Champion in 2004. The history of chess is not uniquely American, as is poker. As we all know, American society richly rewards total extroverts. The idea that introverts somehow have an big advantage in a uniquely American (and intensely competitive) game like poker has got to have a positive effect on how introverts are perceived worldwide.

Research into poker personality would likely start with a study of the current population of known long-run champions in tournament and cash games. I strongly suspect that the majority of current poker champions have the 'INTP' or 'INTJ' personality types.

INTP is short for 'Introverted iNtuitive Thinking Perceiving', and INTJ is short for 'Introverted iNtuitive Thinking Judging'. My best guess is that the INTJ type is probably the most predisposed to poker, because this type is motivated by the practical application of knowledge more so than the INTP....

Perhaps 70, 75 or even 80% of all poker champions are of these two types. If this was an verified scientific fact, what might that mean for poker worldwide? Perhaps a correct but inverse conclusion could be correctly drawn. Perhaps some specific Myers-Briggs personality types are more apt to perform poorly at poker, in the same way a narrow subset of personality types is apt to do very well.

Sklansky and Malmuth on Checkraising

Check-raising is the play of checking your hand with the intention of raising on the same round after an opponent bets. Notice that check-raising and slowplaying are two ways ofplaying a strong hand weakly to trap your opponents. However, they are not the same thing. In addition, the check-raise should often be used to exclude opponents from competing for the pot. Sometimes, in limit hold'em, this is the most desirable characteristic of check-raising. For check-raising to be correct, you usually should:

1. Think you have the best hand (though not a slowplaying hand).
2. Be quite sure that someone will bet behind you if you check.

A situation where check-raising probably would be correct is when you flop top two pair, there are many players on the flop, and you are in an early position. This is especially true if you think that the bet will come from a late position player. (The action before the flop will frequently indicate where the bet is likely to come from.) Sometimes it is also correct to check-raise with a drawing hand. An example is when you think a player to your left will bet and two or more players will call. However, don't raise if you fear a reraise or if a reasonable chance exists that your hand won't win even if you hit it (perhaps a pair shows). Also keep in mind that a
four-flush or an open-end straight draw normally should be bet if there is any chance that you can steal the pot.

Two interesting things may happen if you check a lot of good hands on the flop. First, some of your opponents may become afraid to bet. That is, they may be more inclined to give you a free card, and this free card may win the pot for you. Second, even if a blank hits on the turn, you now may be able to steal the pot. Your opponents are not going to suspect a bluff merely because you didn't bet on the flop, as they know you might have been trying for a check-raise. In fact, some of your opponents might feel smug Check-Raising 77 when you bet, since they "escaped your trap." (When you are bluffing in this situation, never show your hand.) However, remember that if you check a lot of hands on the flop, the free card that you give occasionally may cost you the pot.

Sklansky and Malmuth on Slow Playing

Again, well put:

Slowplaying basically means to play a hand weakly on one
round of betting in order to lure people in for later bets. Hands that are correct to slowplay don't come up very often. For a slowplay to be correct the following criteria must be met:

• Your hand must be very strong.
• You probably will chase everyone out by betting, but you have a good chance of winning a large pot if you check.
• The free card that you are giving has good possibilities of making second-best hands.
• This free card has little chance of making a better hand for
  someone or even of giving him a draw to a better hand with sufficient odds to justify a call.
• The pot must not yet be very large.

Sklanksy & Marlmuth: Why Play Holdem?

Well put:

Specifically, the poorer the relationship between the expectation (win rate) and the standard deviation the larger the fluctuations that you - the skilled player - can go through. Or, put another way, the worse you can run. Consequently, you usually should prefer a poker game where your bankroll requirements when compared to the size of the game, are not too steep.

There is no question that once you have achieved expert status, hold 'em offers an excellent relationship between the expectation and the standard deviation. The reasons for this are that the best hand holds up more often in hold 'em than in any other game, and that you have the advantage of being able to see your opponent's last card which is yours as well. This means that sometimes you can throw away a hand that you would have to call with in other forms of poker, or you might be able to get in an extra bet, whereas in other games you might be forced to check. Of course, hold 'em can still be very frustrating - especially when it seems as though your opponents are always making their two- or three-out hands. However, with the trem endous growth of hold 'em, along with what we have just stated, there is no question that anyone who becomes an expert at this game will do very well indeed.

Sklansky & Malmuth's Advanced Theory of Poker

Damn, Sklansky and Malmuth's Hold'Em Poker for Advanced Players is an awesome book. (Used copies)

A PDF of the book can be found here. Unfortunately, it includes a bunch of crappy advertisements.)

Exploiting Opponents' Weaknesses

Jonny Vincent puts it well in this essay. Simply put,

"It all boils down to this: people either bet too much, call too much, or fold too much. It's your job to work out which one of these your opponent's are guilty of, and take advantage of their mistakes."

Unfortunately, he doesn't give too much info on how to individually deal with rocks, maniacs, and calling stations, and gives very broad advice:

"You absolutely must be able to determine the playing styles and quality of your opponents. After that, you can determine what strategies or adjustments to your play you need to make to beat them."

If anyone finds an article giving practical tips, please share.

Hacking Las Vegas

This Wired article gives the inside scoop of how several MIT students cleaned out several casinos.

Haven't yet read the book, but it's on my list.

Opening Holdem Hands

Here's a more mathematical (and perhaps somewhat more complicated) look at pocket cards in Holdem. From the article:

I wish to introduce some mathematical structure into the discussion....Much of the acrimonious discussion on the ranking of pre-flop hold'em hands arises from the fact some people are talking as if the 169 possible hands form a linearly ordered set. I am going to argue it is a mistake to think this way. One big problem is that the relation defining the ordering is terribly fuzzy. That is, in certain cases the notion of one hand being better than another hand is not clear-cut. In my opinion, the best thing to do for problem comparisons is simply to agree there is no order between them. In other words, treat the 169 hands as a poset.

Poker Math Page

While googling for "math" and "poker," I stumbled across Brian Alspach's mathematics and poker page.

Check out his articles, as well as his computational section:

• 3-Card Poker Hands
  
• 4-Card Poker Hands
  
• 5-Card Poker Hands
  
• 6-Card Poker Hands
  
• 7-Card Poker Hands
  
• 7-Card Poker Hands with Joker
  
• Sousem Hands
  
• Mambo Poker
  
• Low Board Probability
  
• Flushing Boards: I
  
• Flushing Boards: II
  
• Flushing Boards and Random Hands
  
• Computations for Losing Flushes
  
• Overcards in Hold'Em
  
• Straight Completion
  
• 7-Card Stud Flush Completion
  
• Suit and Rank Distributions for Boards
  
• Bad Beat Jackpots: Omaha
  
• Multiple Pocket Pairs
  
• Rank Sets and Straights
  
• Pai Gow Poker Computations
  
• Flop Sums
  
• Enumerating Starting Poker Hands
  
• Probabilities for Successive Memorable Hands
  
• Online Bad-Beat Jackpot Computations

Shorthand vs Full Rings Holdem Games

From an article on some of the differences between full ring nad shorthand no limit Holdem games:

1) Top pair on the flop is almost always worth something. In full ring NL, you learn to distrust a lone top pair, especially if it is a 10 or below; in a short No Limit game, especially in an unraised pot, top pair on a relatively safe board is frequently the best hand and should be bet as such.

2) You can be more aggressive with your draws, even the non-nut ones. A smaller field on the flop means a greater chance that someone will try to pick up the pot just by betting position - leaving you with a great situation to checkraise your draws with the confidence that your misses will be covered or exceeded by your opponent's folds on the flop. You can also feel more comfortable overbetting your draws on the flop because of the reduced likelihood that someone will have a hand strong enough to call, let alone to come over the top of you with. To boil this concept down to a simple idea: to bet and raise draws profitably, you have to be reasonably sure that you frequently can take down the pot with a bet. The less players in the hand, the better your chances.

3) You can steal and semi steal a whole lot more from the last position. If you're playing against average players who aren't sharp enough to keep you in line with resteals here and there, you should abuse position to pick up pots fairly often. Also, the semi-steal with middle or bottom pair often is actually a value bet in shorthanded no limit. For example, in a full ring game if you hold 6h7h last to act with this flop:

If five or more players check to you, it's hard to believe you're betting the hand for value. But as the number of players in the hand drops down to 3 or so [as it commonly does in 6 handed games], bottom pair is often good and should be bet as such.

4) Preflop position just isn't as important. Calling loose UTG in a full ring is scary because preflop, 9 players behind you could still raise and once the flop hits, as many as seven players are between you and the button. Obviously in short handed there's a smaller chance of a raise behind, but there's also a really good chance in a tight game that UTG preflop will be the button or one off once the flop hits, as there are only 3 players in between you and the button. Raising UTG with a variety of hands is also a workable strategy, since the chances of someone waking up behind you with a re-raising hand are greatly diminished. Bottom line: you don't have to play as tight UTG because the risks of loose play are lower.

5) It's a little easier to target individual players and 'set them up'. Shorthanded, you're just going to butt heads with any given player more often than you would in a full ring. This makes it easier for you to make setup plays, as you can establish patterns quicker and have a greater certainty that a player notices [and gets pissed at / confused by] your patterns. For example, in a full ring you might checkraise player A with a draw and show when he folds, planning to checkraise the next time you have a lock hand, but the next time you're going to be in a heads up confrontation with that player in a full ring is potentially a long ways off. By the time it comes up again, the player may have a) forgotten your 'play', b) not seen you do it enough to form a strong conclusion about what your particular bets mean, or [most likely] c) his ego has healed a bit with the passing of time and he's no longer looking to 'get you back'.

Amarillo Slim Quotes

"Poker is a game of people... It's not the hand I hold, it's the people that I play with."

"Look around the table. If you don't see a sucker, get up, because you're the sucker."

"Nobody is always a winner, and anybody who says he is, is either a liar or doesn't play poker."

"They anticipate losing when they sit down and I try my darndest not to disappoint one of them.