Trading and Games of Skill

We present a slightly off-topic post for president's day.

A number of people who have started out as card counters in Black Jack or as poker players have become successful traders and vice versa (e.g. hedge fund manager David Einhorn of Greenlight is a very good poker player as well).

In turn, many chess players have begun to play poker (such as e.g. German chess grandmaster Jan Gustafson or Russian grandmaster Alexander Grishuk), because there is far more money in poker than in chess. The only professional chess players that really make a lot of money with chess are the very top players, but even their earnings pale relative to those of good poker players.

There are obvious parallels with the skill sets and the basic requirements of all these activities, such as well-developed analytical skills, the ability to act rationally under pressure, and a sense for tactic and strategy. Trading and poker in addition share the money management aspect.


Black Jack and Roulette

If one plays Black Jack in 'mathematically correct' fashion, i.e., employs the optimal basic strategy that does not involve counting cards, the dealer has an advantage between 0.5% and 1% (depending on the precise game rules and the number of decks used). In short, the house is sure to win over the long term: of every $100 bet by players it takes between $0,50 to $1 – and that is assuming that all players do in fact employ mathematically correct play.

A player can improve his odds further by using a composition-dependent strategy (i.e., by considering the exact composition of his hand, depending on whether or not it contains a card valued at ten points).

Black Jack is the casino game that offers by far the best odds to players among the games played against the house.

Roulette doesn't deserve its popularity: a roulette wheel with a single zero creates an advantage of 2.70% for the casino, a double-zero wheel an advantage of 5.26%. There exist no strategies that can level these odds. 

All roulette strategies are based on the 'gambler's fallacy', also known as the 'Monte Carlo fallacy' – so named after a famous run in Monte Carlo in 1913 – black came up 26 times in a row, causing millions in losses to players trying to bet against the run. All roulette strategies betting on single chances (red/black, odd/even, hi/low) – disregarding for a moment the permanent advantage the existence of the zero gives to the house – are suffering from this fallacy. The probability that black will come up again after a run of 'N' times is in fact not decreasing – the roulette wheel has no 'memory' of what happened.

Consider the tossing of a perfectly balanced coin and the probability of it coming up 'heads' six times in a row. Prior to the first toss of the coin, this probability is 1/64, i.e., the initial ½ probability is half as high for the second toss, halves again for the third, and so forth. However, once the coin has in fact come up five times in a row, the probability of it coming up heads in the sixth toss is once again exactly ½.  Like the roulette wheel, the coin has no memory of how the previous tosses turned out.

In Black Jack, card counting and shuffle tracking are methods by which a player can turn the tables on the house and acquire a small, but persistent advantage. As a result, casinos tend to ban players who employ these skills or throw spanners into their works by other means. Such players are not doing anything 'illegal', but the house obviously doesn't like to lose. Nowadays card counters are foiled by the use of many decks, flat bet rules, frequent shuffling, exchanging the decks for new ones and so forth. A card counter's main aim in Black Jack is to find out how the cards that are valued at 10 points are distributed in the deck and adjust his play (the amounts he is betting) accordingly. One could state: if played according to basic strategy, Black Jack is a game of chance in which one is guaranteed to lose. If one plays the game employing a card counting strategy, it becomes a game of skill.


Poker and Chess

A major difference between poker and chess is that the former is a game of incomplete information: in the most popular version of the game, Texas Hold'em, one doesn't know which hole cards the opponents hold. One deals with probabilities and must try to correctly 'read' opponents. By contrast, in chess all the information about the game is always in full view. The difficulty lies in the game's complexity. As one thinks about the next move, one is forced to ponder a large amount of possible variations, which are often not necessarily obvious.

Poker appears a rather simple game by comparison, but once one studies the game more closely, it becomes evident that it actually possesses quite a lot of strategic depth. In both chess and poker tactics and strategy as well as psychological factors are important.

The analogy between poker and trading was explained by legendary trader Gary Bielfeldt in Jack Schawger's book 'Market Wizards' (Bielfeldt made a fortune trading bond futures in the early to mid 80's and apparently was also a poker fan):


„You don't just play every hand and stay through every card, because if you do, you will have a much higher probability of losing. You should play the good hands, and drop out of the poor hands, forfeiting the ante. When more of the cards are on the table and you have a very strong hand, – in other words when you feel the percentages are skewed in your favor – you raise and play that hand to the hilt.

If you apply the same principles of of poker strategy to trading, it increases your odds of winning significantly. I have always tried to keep the concept of patience in mind by waiting for the right trade, just like you wait for the percentage hand in poker. If a trade doesn't look right, you get out and take a small loss; it's precisely the equivalent to forfeiting the ante by dropping out of a poor hand in poker. On the other hand, when percentages seem strongly in your favor, you should be aggressive and really try to leverage the trade similar to the way you raise on the good hands in poker'


What Bielfeldt describes above is a specific style of poker play called 'tight-aggressive'. It is indeed a style preferred by many good players, and probably the style novices should strive to master at first, but it is not the only one available. The  best players tend to vary their style of play depending on their opponents, their position and other specific circumstances. A counterpart to the 'tight-aggressive' style would be the 'loose-aggressive' style. The difference between the two lies primarily in the choice of starting hands which one decides to play and raise.

For instance, Tom Dwan is certainly thought of as a loose-aggressive player, as he often raises dubious starting hand. This style relies on the players' ability to outplay the opposition after the flop. It doesn't work well with passive 'calling stations' (players who seldom raise, but will often call raises), but it may work well with weaker tight-aggressive players. The advantage of this style is that it creates a useful 'table image' – after a while, other players will also tend to play loose against a player with a loose-aggressive image, which tends to work in his favor whenever he actually catches a strong hand. On the other hand, the loose-aggressive style can lead to high bankroll volatility (Dwan's bankroll history as far as it is known confirms this).

Here is an example of Dwan bluffing an opponent out of what would have  been the winning hand with the very worst possible starting hand (which happens to be 7,2 unsuited). The special twist: before the start of the game they agreed that every time a hand was won with that particular starting hand, the winner would get an additional $10,000.

Moreover, Dwan actually tells his opponent that he holds 7 and 2 right from the get-go and that he 'just wants to steal the blinds'. His opponent doesn't believe him and ends up hopelessly outplayed:





In modern-day chess tournaments, the players are required to memorize a bewildering amount of theory in their preparation. All openings have been studied in great depth and countless books have been written about specific openings (even obscure 'irregular' openings often boast of several book-length analyses). Chess theory advances by the introduction of theoretical novelties, this is to say, new moves in a known variation that create new variations that prove to be effective. By unexpectedly straying from the 'book moves', a player usually also gains a psychological advantage: his opponent must assume that he has analyzed all the consequences of the new move in his preparation, problems the opponent confronted with the novelty must now solve over the board. Not all novelties are good, but sometimes even a sub-standard novelty can tip the scales due to this psychological effect.

There are a number of spectacular chess games such as Anderssen's 'immortal game' against Kieseritzky in 1851 (today almost nobody plays the king's gambit anymore, as it is no longer regarded a fully viable opening among high level chess players, but it made for very interesting games in its heyday) or 13 year old Bobby Fisher's win against Donald Byrne in 1956, which involved a queen and a rook sacrifice, or the famous Kasparov-Topalov game of 1999 in Wijk aan Zee (the 'Pearl of Wijk').

We recently came across an analysis of a game of a chess grandmaster who's almost forgotten today, although he once reached third place in the FIDE's world rankings in 1995 ex aequo with current world champion Vsihnavatan Anand, behind Kasparov and Kramnik. His highest ELO rating was 2715 (this was at a time when 2715 ELO points were worth more than today – a certain degree of 'ELO inflation' has occurred in the meantime).

We are referring to Valery Salov, who rather mysteriously retired from chess in 1999. Apparently (according to his own words) he was openly critical of Kasparov, whereupon he didn't get invited to many high caliber tournaments anymore. This led to his decision to call it quits, an unfortunate loss for the chess world. A write-up of Salov's career highlights and later travails can be found at Canadian GM Kevin Spragett's site.

Apparently Topalov's (another top player) manager Danailov accused Salov of playing 'boring chess' that wouldn't be attractive to spectators. Alas, as you will hopefully agree once you've seen the game discussed below, this allegedly 'boring' style actually consisted of cunning and very interesting strategic play.

Salov in a recent interview pronounced his dismay with the 'computerization' of chess, which has made theoretical preparation an ever bigger part of the game. The ability to memorize countless variations has indeed become an increasingly important factor. However, computers haven't yet 'killed' the game entirely. They have so far failed to prove that it is definitely a draw (as many people suspect they one day will). Frankly, looking at the games of today's top players, no-one can really accuse them of a lack of creativity as it were. However,  Salov had his own very special style. It is not as flashy as that displayed in the games cited above – instead he is a master of the positional game, a 'long range' strategic player.


Master of the Blockade

In 1987, GM Michail Marain happened to play in the 54th Soviet championship, where Salov also played. Marain observed Salov's win against Gurevitch with the black pieces, noting that up to that point, he 'had never seen this type of chess'. Superficially, Salov appeared to come out of the opening at a slight disadvantage, which bit by bit became an overwhelming advantage as the game went on. Later in the same year, Salov played in Szirak in Hungary, where he managed two more wins with the black pieces,  comparable to that against Gurevitch.

One of these games was against Andras Adorjan, which can be replayed in its entirety here. This should probably best be done in the context of the commentary below. The comments regarding the game are largely adapted from Marain's and Salov's own analysis. As Marain remarked, Salov appeared to have fully internalized Nimzovitch's writings on the art of the blockade.


Note, we use algebraic notation below. Sometimes a move will be followed by an exclamation mark, a question mark or a combination of the two. The meaning of these is:


  • ! (good move),
  • !! (outstandingly good move),
  • !? (interesting move, but there may have been a better one),
  • ?! (dubious move),
  • ? (bad move),
  • ?? (complete blunder)


Adorjan-Salov, Szirak 1987

1.    d4,  Nf6

2.    Nf3, e6

3.    c4,  Bb4+

4.    Bd2, c5

5.    B:b4, c:b4



Position after 5)…c:b4



Black has recaptured from the center, which leads to white supremacy in the center. However, this is in the spirit of Indian openings: black tries to attack from the flanks. A longer term plan connected with this move is to get the white pawn on d4 to either move forward or capture on e5, in order to free up the square c5 as an outpost for a black knight.

6.    g3, b6

7.    Bg2, Bb7

8.    0-0, 0-0

9.    Nbd2



Position after 9) Nbd2



At this point in the game, a positive effect of the move c5:b4 becomes evident: Adorjan was unable to develop his second knight to the 'natural' square c3 (so Marain), leaving it in a somewhat passive position. Adorjan however continues to bolster his occupation of the center. 

Salov's next five moves reveal his overarching strategy: he wants to obtain control over the dark squares on the queen's side and in the center.

9.    ……………,  a5

10.                      Re1,  d6

11.                      e4,    Nfd7

This last move is a preventive measure against e4-e5, even though it is not yet clear whether it represents a serious threat. The knight is also closer to the square it ultimately strives to reach, c5.

12.                      Qc2, e5

13.                      Rad1, Nc6

14.                      Nf1, Qc7

15.                      Ne3




Position after 15) Ne3



The end of the opening phase. Adorjan has continued with development moves and brought his passive knight to a better square,  Salov has continued with his plan to take control of the dark squares. At this point, most players would probably prefer Adorjan's position at first glance. He dominates the center and has developed his rooks, something Salov has yet to do. The knight on e3 suddenly looks quite formidable as well: both d5 and f5 are potential outposts for it.  Most players would probably rate this position +/=  (white has a slight advantage).

After writing down this likely evaluation we checked it via computer, which after a fairly thorough analysis of the position comes exactly to this conclusion.  Probably the computer software lacks an eye for the subtleties of black's positioning this early in the game.

Marain makes an important observation at this point: black's position is solid, but it is also open to small, step-by-step improvements. A number of neutral and/or useful moves suggest themselves. White's position is already as good as it can be – there are no immediately obvious ways to improve it.

In other words, by standing better, Adorjan has actually managed to stand worse. This motive is one we will encounter again: the fact that he must make a move is not to his advantage.  This is indeed quite different from how one   views the 'tempo factor' most of the time in chess, especially in this fairly early phase of the game.

Putting it differently, from a purely static standpoint white has the advantage, but from a dynamic point of view this is actually not the case. Not even the mighty phalanx of pawns in the center can make a move, as the square c5 would then inevitably become available to black's knight.

Salov's next move parries the obvious threats emanating from the white knight on e3:

15.                      ..….., Ne7

The squares d5 and f5 are now covered.

16.                      d:e5

In Salov's own analysis that was published in Chess Informator, he proposes 16. Rd2!? as a possible alternative. Marain contends that Adorjan has proceeded logically: since he is already better developed, he unfolds active play with the aim of gaining the initiative. Moreover, he subsequently moves to  occupy the open line, which leads to the formation of a passed pawn.

16.                      ……., d:e5

17.                      Nd5




Position after 17) Nd5



17.                      …….., N:d5 (!, Marain)

Salov uses the knight on e7 to capture the white knight on d5, which at first glance is a bit unusual. Marain gives this move an exclamation mark because he notes it is actually a strategically very far-sighted choice. One would think that black would gladly exchange his light-squared bishop on b7 for the white knight, as it seems not very useful in terms of building an effective blockade. However, after 17)…..B:d5, 18) e:d5, it won't be possible for Salov to reach the optimal positioning of his knights on d6 and c5, due to the pressure against the pawn on e5 and the vulnerability of the long diagonal h1-a8. This would practically force him to play 18….Qd6 – which would make  white's later move Ng5 more effective. At the moment the bishop is also a bit of an insurance against d5-d6. Once Salov has stabilized his position, the light-squared bishop will be deployed to fresh uses.

18.                      e:d5, Rae8



Position after 18)….Rae8



Salov's development is now finished as well, and the pawn on e5 gets some over-protection. His next goals are to get the knight to c5 and the queen to d6.

19.                      Ng5

With this move, Adorjan exerts pressure on Salov's Kingside and opens the long diagonal. Salov's own analysis considers the alternative move 19) Bh3. In this case, 19)….Nc5 would run into 20) d6!, Qc6  –  21) Rd5!, f6 – 22) Bf5, leading to a strong white attack. He therefore would have countered 19) Bh3 with 19)….Nf6!, once again justifying the previous decision 17)….N:d5. 

The overarching philosophy being that first all threats are countered, while the occupation of the best squares is kept for later. This variation reveals the tactical potential harbored by this apparently 'slow' positional game.

Marain notes that Adorjan has reached a point where he should be considering  moves that retain and build out the initiative. Here or in the next move, he recommends the move d5-d6 for white.

20.                      b3

Adorjan instead protects the pawn on c4, at the same time freeing up the a1-h8 diagonal so that his queen can be brought to exert pressure on e5.

20.                      ……, Nc5 

21.                      h4?!

Salov's knight finally arrives on c5, while Adorjan misses the last chance to play d5-d6 and gain an advantage.

21.                      ……., Qd6



Position after 21)…..Qd6



At this point, the computer regards the position as either equal or to the slight advantage of black. The tables have been turned. Everything is blocked, and soon it becomes evident that only black can improve his position further.

22.                      Rd2

Adorjan should have played Ne4 here (the variation the calculation-slave also prefers), in order to preserve his chances at a draw. Apparently he did not sense any danger just yet.

22.                      …….., Bc8!

Salov's bishop returns to the game, with the idea of moving the bishop to f5, followed by f6 to force the knight back to e4, with the intention of using the bishop to capture it.

Thereafter, Adorjan would remain with a 'bad' bishop, as most of his pawns are stuck on light squares, against Salov's 'good' knight on c5.

23.                      Qd1, Kg7

Salov criticizes his own move, considering it too slow. Instead Bf5 should have been played immediately, so Salov, in order to control the square e4 and be able to capture the white knight if it moves there – following the train of thought above. There is however a danger that white could try g4 with his queen on d1. Luckily for Salov,  Adorjan leaves the knight where it is and moves his queen.

24.                      Qa1, Bf5

Now there's no longer any possibility of the Nc5 being captured. White is already in serious trouble.



Position after 24)….Bf5. Strategically, the black position is now clearly superior.



25.                      f4, f6

This advance of the f-pawn proves harmless and the resulting simplification of the position once again favors black. 

26.                      f:e5, R:e5

27.                      R:e5, Q:e5

28.                      Q:e5, f:e5



Position after 28)….f:e5



Taking stock of the developments, we note that Adorjan has indeed ended up with the already discussed 'bad' bishop, as all his pawns are blocked and must remain on light squares. The sole exception is the pawn on d5, but it is far too late to move it profitably to d6. If it were moved to d6, it wouldn't last long.

Salov's bishop is a 'good' one. The potential threat Bf5-b1 (with the idea of B:a2) hovers like the sword of Damocles over the proceedings. If it were realized, the white position would instantly collapse.

Salov remains solidly positioned on the dark squares. His knight is clearly superior to Adorjan's, which can only hope to find a safe place on e3.  It would however require four moves for it to reach this square. Before it could possibly get there, Salov's e-pawn will already be there. Salov's knight by contrast is invulnerable on c5, can support the e-pawn's advance and curtail the activities of Adorjan's rook.

At this point white is not yet truly lost, however,  he's only a small imprecision away from getting there.

29.                      Kh2?!

This is a neutral, but dubious move, because it does nothing to better white's position. According to Salov, 29) Re2!?, Re8 – 30) Ne4, B:e4 – 31) B:e4,  was white's best chance. Apparently Adorjan didn't grasp that he could actually obtain a better position by exchanging the Ng5.

29.                      ……., h6!

30.                      Nh3, e4

This looks quite threatening. Marain notes that black could attempt to move his king toward e5 and his knight to d3, so that his king could advance into white's territory via d4 and c3.



Position after 30)….e4



31.                      d6, Rd8

It is far too late for the pawn move to d6.

32.                      Nf4, g5

33.                      Ne2, Bg4!



Position after 33)…..Bg4



Blacks minor pieces are quite effective. In case of 34) Nd4? Salov planned to play 34) e3. Since the white rook would then have been forced to move away from the d-file, the black rook would have been able to capture the pawn on d6 without being lost after Nd4-f5+.

34.                      Nc1, e3

It's difficult to stop this pawn, but Salow later thought the move should have been prepared by 34)….Kf6

35.                      Rd5, e2

36.                      Re5

With the king on f6, white would not have been able to make this move.

36.                      …….., Kf6

Salov again wanted to see this move replaced, considering 36)….R:d6 to be more precise. He offers the variation 37) Bd5, Rf6 – 38) Kg2, Rf1 – 39) N:e2, Ra1 as proof. With the fall of a2 (see also above), the white position would have been lost.

37.                      Re3, R:d6

38.                      N:e2?!



Position after 38) N:e2



Already in time trouble at this point, Adorjan didn't find 38) Bd5, which would have kept the black rook at bay. Salov planned to counter this move with 38)….b5 – 39) N:e2, b:c4 – 40) b:c4, a4. The white Bd5 would have remained 'bad' in this case, in the sense of being unable to enter the fray and the game would have been decided on the queen's side.

38.                      ……., Rd2

The entry of the black rook on the second rank has a decisive effect.

39.                      Nc1, Rd1

40.                      Ne2, Rd2

41.                      Nc1, Kg6!

White resigns. See further below as to why.



Position after Kg6 – white resigns.



The reason for Adorjan's resignation at this point was that after 42) h:g5, h:g5, every remaining legal move by white leads to a decisive loss of material (try it out and you'll see).

So we have come back to the motive we mentioned further above – no matter what move white makes after the exchange of the pawns on g5, it will perforce be a bad move. The technical term for this type of situation is 'Zugzwang'.

We hope you enjoyed this excursion into strategic chess as much as we did.



8 Responses to “Chess, Poker and Trading”

  • steve in Winnipeg:

    Nice article. On Gary Bielfeldt’s comments, I think he’s being mostly ‘tight’ than truly ‘tight-aggressive’. He just waits to play ‘good hands’. In investing you can just wait for the right set up and then play it (for awhile at least). In poker, if you only play really good hands, others will adjust to you and be less willing to play against you when you bet big. Poker, as you note, requires you to change up your style.

    For the really big players in investing, it’s more poker-like because of their size relative to the market. Also, over time, the market is like a good poker player adjusting to cancel out (or completely) reverse what had been good strategies (e.g. buy and hold stocks). So over time, most traders do need to adapt and change just as poker players, but its over a longer time-frame

    The one biggest thing poker taught me was to focus on the process and be emotionless on wins and losses. i.e. there are parts you can control and parts you can’t. Through poker, you can get a lot opportunities to learn that.


  • Robt:

    Just to be awkward, I’m going to propose that in the coin-tossing scenario we look at retrograde odds. Yes, the chance of tossing heads in the next toss is 1/2 and that’s the standard challenge to the argument that on the 7th toss the odds are not 1/128, but still 1/2 on the next toss and in fact remain 1/2 of all future tosses forever. But of course, intuitively we know we cannot toss heads forever, it’s just unreasonable. We have tossed 6 in a row. Yes, our chance on the next turn is 1/2 that we’ll get heads, but because we have already documented 6 heads in a row, the chances of tossing another head really are 1/128, and the next turn 1/256.
    Were we to consider each next toss as a singular event, i.e. disregard the past and the future, 1/2 would be true, and only for that next event and no others. But our series of tosses are not a singular event but a cumulative historical series, meant to be taken as a whole. Thus the fallacy of the next-toss odds of 1/2 when considered within a series: each toss is isolated as a singular event.
    Similarly, if we were to grant someone 7 tosses of a coin with the bet that he can’t toss 7 heads in a row, we realize that the probability of doing this is 1/128.
    Which is also why the legendary Monaco roulette event is in fact considered as a unique historical event, not as something as likely to be expected as say, RRBBBRRBRBBBRR etc.

  • juergenwahl:

    “When I am white, I win because I’m white [advantage of first move]. When I’m black, I win because I’m Bogoljubow [blessed by God].” – Efim Bogoljubow, Chess Grandmaster.

  • Andyc:

    Interesting article

    Here’s a pretty good free chess program

    I’m not that good at Chess so playing against this program is a bit discouraging, it doesn’t just beat me, it annihilates me.

    I wonder how the computers would fare if another row or two, maybe another two pawns and knights were added to the board?

    My thinking is that the human players might adapt more quickly to a new set up like that, of course the computers would soon catch up.

    As I understand it computers have made little headway in the game of Go and Go dans have very little trouble beating them, it would seem computers are still only good at brute force calculations and play the takes intuition is something they are not up for just yet.

    Go humans!

    : )

  • Andyc:


    As I recall the former Bill Gross at Pimpco was a card counter/Blackjack player and tried to make a living doing it in Vegas, he was successful but soon realized that he was only making a small sum per hour played and to make a reasonable amount he would need a huge stake to guard against the inevitable black swan event where you lose many hands in a row, he did not have such a stake and he also realized that if he bet at the level needed to make a living the casino would soon catch on to him and throw him out so he gave it up.

    I think he then decided that front running Greenspan in the treasury market was much the better thing and lurched off to pursue that endeavor.

    What ever happened to that guy, he still around?

    Well if he is, his treasury front running days are over, that seems certain


    : )

  • static:

    Good Game….I think the economic world, is and has been in Zugzwang for quite a while…while that is good for a trader to know, as I have for years…it has been very difficult to trade..Why?
    because normally the player in Zugzwang will soon be playing, as the immortal Tal put it, “King to ashtray”…lol (I always loved that)…but in this case the zugzwanged player and the tournament director are in cahoots….and the moral hazard clause is invoked..the rules are changed. and the game goes on…truly a sad outcome for the player/trader in the know….So what I’m looking for now…knowing all the rule changes in the world won’t win the game, rather just allow it to go on, is a stronger sense of the clock.
    got any thing for me on that Pater? will appreciate any help! lol
    by the way , I’ve been reading for quite a while and love the site, thank you for all the insights!
    thanks for the “wood”

  • FreemonSandlewould:

    You are incorrect about roulette. In fact there was a history channel show about this topic. They studied the imbalance statistics of the wheel and made out so well they ended up doing what all the card counters do. Flying all over so they will not be recognized.

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