Author Archives: Andre

About Andre

Hi, I'm Andre Harding, Candidate Master and National Instructor. Since 2003 I've taught chess to thousands of students in public, private, and charter schools in the New York City area, and have given countless private lessons. If you have a question about chess improvement, I can answer it. Feel free to contact me if you have any comments, questions, or suggestions.

Tournament Chess Board Options

Choosing the right tournament chess board is a topic I’ve thought about over the years, trivial as it might seem. After last Friday’s post, I decided to share my thoughts and get your opinions as well. Let’s go through different options — what is your ideal tournament surface?

I’m also assuming we’re playing in tournaments where we have to bring our own equipment. I won’t discuss square size because there aren’t a range of options here.  FIDE regulations state that the side of a square should measure 5 to 6 cm (roughly 2.0 to 2.4 in).

Here we go:

Fold-Up, Roll-Up, or Neither

By “neither,” I mean a hard, one-piece tournament chess board like the one I discussed last week. These tend to be the most aesthetically-pleasing boards, but they’re obviously not the most convenient. Choose this route only if you’re driving to a tournament, and a nice playing surface is an important part of your enjoyment of the game.

Personally, I would consider this option if I drove to a tournament and stayed in a hotel for a few days or longer. However, I rarely see players use these kinds of boards in competition.

Another seldom-chosen option is the fold-up board. I imagine the “crease” in the middle of the board is distracting, even though these boards can be very attractive otherwise.

By far the most popular choice is the roll-up board, and with good reason: these boards are cheap, compact, and easier to clean than other types.


Apparently black-and-white is not good for the eyes over a long period of time. Most players opt for a green-and-white surface, but other choices are popular as well. Next time, I might choose brown-and-white — just to be different. I’m tired of green and I’ve never been a fan of blue or burgundy.

Of course, roll-up boards are so cheap you can buy more than one and choose a color that fits your mood…


Assuming you go with a roll-up board, you still have to consider the material of your playing surface.

A vinyl roll up board.

When I first began playing chess in the 1990s, vinyl was the material of choice. I suspect it is still the most popular type of board purchased: it’s easy to clean, easy to roll or fold, and provides a decently-thick playing surface.


A mousepad board, in purple.

Recently, rubberized surfaces akin to a computer mousepad have become an option. They lay very flat, don’t move easily during play, and don’t develop creases like vinyl boards sometimes do.

The main issue with mousepad boards is they stain easily and can’t be wiped off as easily as other boards. I primarily don’t like them because of their texture.


Tournament Chess Board

A silicone roll-up board.

Another alternative is silicone boards. They can be twisted or mashed into any shape, and wipe off easily, like vinyl. It seems to me that silicone boards grip the playing surface they’re laying on better than vinyl boards do, but not as well as mousepad material.

I haven’t converted to silicone because I don’t like the thinness of the surface, and I’m not a fan of the texture. Still, I do think they will only grow in popularity in the coming years.

A tournament chess board is a very personal thing! You’re going to be spending a lot of hours with it, and I think it’s important to use a product you like. What do you like to play on during a tournament game? Is there anything I have left out? Please comment!

The English Opening: Playing 1.c4

The English Opening or …

I am by no means a specialist on openings in general, or the English Opening in particular, but I have opened with 1.c4, 1.d4, 1.e4, and 1.Nf3 in my tournament career.

As many before me have said, 1.e4 is the most straightforward first move, and 1.d4 can be very direct as well if the player intends it to be so.

A 1.Nf3 user often employs transpositional “games” against their adversary, aiming for certain openings or variations while avoiding others. Two defenses that regularly get frozen out in this way are the Nimzo-Indian and the Grünfeld, when white plays an early Nf3 and c4, but not d4.

Why 1.c4?

One of the main arguments for 1.Nf3 is that it avoids 1…e5.

In contrast, the 1.c4 player wants to play “English” positions; not just transpose into favorable d4-lines. Specifically, I’m talking about positions that arise after 1.c4 e5.

The 1.c4 player likes playing these positions since black has ceded control over the d5-square white hopes to clamp down on:

I began to like these positions after studying How to Play the English Opening (Batsford, 2007) by Anatoly Karpov. The ex-World Champion spends a lot of time covering the Four Knights Variation with 1.c4 e5 2.Nc3 Nf6 3.Nf3 Nc6 4.g3:

…mainly through his games against Garry Kasparov and other absolute top players. He also covers other choices on move 4 besides g3.

Game Changers

Kosten's famous book on the English Opening

I doubt Kosten imagined the influence his small book would have on the popularity of the English Opening!

Karpov’s book is underrated, but that likely has to do with the enduring popularity of The Dynamic English (Gambit, 1999) by Tony Kosten, and the authority Mihail Marin established with The English Opening (3 Volumes, Quality Chess, 2009-2010).

Kosten and Marin recommend the move order 1.c4 e5 2.g3. Kosten’s book in particular is very system-based, which appeals to many players. But with the explosion of chess information over the past 20 years, black players are more aware than ever how to deal with his main setup, the Botvinnik System:

That doesn’t mean white should hesitate to play this way if s/he enjoys the resulting positions. The strongest ideas in chess are those that are effective even if your opponent knows they’re coming.

But the “Old” English Opening was Popular for Decades!

1.c4 e5 2.Nc3 is less predictable: both sides have freedom to choose their preferred setup — black can even try 2…Bb4. Going into lines with 2.Nc3 is something to consider for a player who has more advanced positional skills than their peers and has reasonable hopes of outplaying them — though I wouldn’t recommend the English until a player is 1600, at least.

Flank openings are more structurally fluid than 1.e4 or 1.d4, but choosing 1.c4 over 1.Nf3 takes that to another level. If you can become a specialist in “pure” English positions, there are plenty of points to be scored simply through better familiarity of the terrain.

Mark Dvoretsky: Great Chess Authors, Part 7

After mostly choosing authors for this series who geared their writings for beginners and intermediate players, let’s discuss an author on the opposite end of the spectrum.

I warn you: this post will be long.

Mark Dvoretsky (1947-2016)

Mark Dvoretsky. Photo: ChessBase.

Mark Dvoretsky. Photo: ChessBase

Muscovite Mark Dvoretsky was a very strong player, becoming an International Master in 1975. In this period he reached his peak as a player but soon became a trainer.

And what a trainer he was! He worked extensively with such players as Women’s World Championship Challenger Nana Alexandria, Valery Chekhov, Sergei Dolmatov, and Viktor Bologan, among many others.

His most prominent student was Artur Yusupov, who rose to World #3 in 1986. Dvoretsky and Yusupov would collaborate on many books for very strong (or at least very ambitious) players. These were borne out of training sessions with future stars, including Vladimir Kramnik and Peter Svidler.

NOT for Beginners!

Honestly, no other author scares me the way Mark Dvoretsky does. That’s a compliment, by the way: his books will make you work like no others that I’ve seen. A trademark of his books is very deep analysis of his own games or his students’ games. He will often discuss how well or poorly his students did in solving these training positions.

I’ve read reviews that complain about the inclusion of chapters from other trainers’, but I appreciate the different viewpoints. Dvoretsky frequently gets lost in a forest of analysis so dense you question how helpful it is to your chess development. The contributors tend to stick to one topic and cover it in very instructive fashion.

I consider my study session a success if I can get through one chapter of one of these books.

Batsford Series

These are the books that introduced the West to Mark Dvoretsky. They feature lectures at the his chess school, sometimes with chapters from other contributors like Igor Khenkin, Aleksei Kosikov, and Boris Zlotnik.

Secrets of Chess Training (1991), Secrets of Chess Tactics (1992)

I have not read these two books, unfortunately. Well, maybe I have…we’ll come back to that.

Training for the Tournament Player (1993)

Steve Colding of Chess for Children lent me this book in 1998. I remember taking notes and studying it very seriously. The problem, of course, was that I was only a 1400 player…

Opening Preparation (1994, with Artur Yusupov)

I absolutely love this book. It isn’t about opening theory, but typical maneuvers and operations in a variety of opening systems. This book forms the basis of how I play the Sicilian against the Grand Prix Attack, and helps orient me when I face King’s Indian Attack-style setups.

Technique for the Tournament Player (1995, with Artur Yusupov)

I think I got my hands on this one, but I’m not totally sure. I’ll discuss it below.

Positional Play (1996, with Artur Yusupov)

Devour this gem one bite (chapter) at a time. It discusses positional play in ways you wouldn’t expect having read other classics. The contributors each have something valuable to add — including chapters by top players Vladimir Kramnik and Evgeny Bareev!

Assiduous study of this book will vault you far ahead of other class players when it comes to positional understanding.

Attack and Defence (1998, with Artur Yusupov)

This one is quite good, but literally makes my head hurt! Dvoretsky keeps making you think he has revealed the answer to one of his analysis positions…only to go back and reveal a further nuance to consider. The lasting impact it has left on my play is don’t assume. The attack you think is irresistible…the defense you think is impenetrable…may not be so!

Dvoretsky’s Endgame Manual (2003, 5th edition 2020)

This is perhaps the most popular of Dvoretsky’s books, as it is not aimed towards master-level players only. It contains a lot of explanatory material and diagrams, but personally I am not a big fan. Probably I would have a different opinion if I was taking my first steps in chess.

Dvoretsky’s Analytical Manual (2008)

I have never read this book, and don’t intend to. It’s famous for its dense analysis, and is geared towards budding International Masters and Grandmasters.

Edition Olms Books

Before talking about the books, let me just say that I have never regretted purchasing an Edition Olms book, or paying their high prices. They produce gorgeous paperbacks that you never want to ruin: high-quality paper, print, and binding.

Some of these books are reprints of the Batsford books that have long been out of print.

School of Chess Excellence 1: Endgame Analysis (2003)

I have not read this one.

School of Chess Excellence 2: Tactical Play (2003)

A good mental workout! It’s not a puzzle book, but a collection of positions are discussed which feature unexpected tactical solutions. I didn’t find this book as challenging as Dvoretsky’s other works, because of I’m used to solving paradoxical “Russian” tactics.

School of Chess Excellence 3: Strategic Play (2002)

This book is original, and not a reprint of the earlier Batsford series. It’s challenging, and stresses the importance of small nuances. It’s really helpful if you play King’s English (1.c4 e5) or Reversed Closed Sicilian (1.Nf3 Nf6 2.c4 g6 3.g3 Bg7 etc.) positions from either side.

School of Chess Excellence 4: Opening Developments (2003)

I have not read this one.

School of Future Chess Champions 1: Secrets of Chess Training (2006)

This one really helped me in my coaching endeavors. It stressed to me how individual chess improvement really is, and how much of a disservice coaches can do to their students if they take a cookie-cutter approach.

I very much enjoyed the anecdotes Dvoretsky provides about his experiences as a trainer, and the frame of mind a coach should approach helping a student from. I recommend it to coaches and to anyone directing their own self-improvement.

School of Future Chess Champions 2: Secrets of Opening Preparation (2007)

I have not read this one, but I think it’s a reprint of the 1994 Batsford book.

School of Future Chess Champions 3: Secrets of Endgame Technique (2007)

I believe this one is very similar to, if not a reprint of, Technique for the Tournament Player. Since I couldn’t get that one, I got this version.

The book doesn’t really teach endgame play per se. It discusses the player’s frame of mind when dealing with endgames, and gives some advice for improving your endgame play.

School of Future Chess Champions 4: Secrets of Positional Play (2009)

This is the same book as Positional Play.

School of Future Chess Champions 5: Secrets of Creative Thinking (2009)

This is the same book as Attack and Defense.


I stopped buying Dvoretsky’s books because they require a commitment to study that I was no longer willing to give, but I might read his two autobiographical works at some point. His other titles include:

Maneuvering was the great coach’s last book, as he died in September 2016 at the age of 68. The wealth of training material he created will long outlive him.

What are your thoughts on Mark Dvoretsky’s legacy? Please share!

Chess Tactics: Van Wely — Ki. Georgiev, 1997

Loek Van Wely. Photo: FIDE

Loek Van Wely. Photo: FIDE

Loek Van Wely (b. 1972) is one of the greatest Dutch players ever, becoming Champion of the Netherlands eight times so far.

A notable tournament victory was the 1996 New York Open. He is also a fixture at the prestigious Wijk aan Zee super tournaments.

In October 2001 Van Wely achieved a career-high rating of 2714 while climbing to 10th in the world rankings, also a career high.


Van Wely wins a sparkling game against Kiril Georgiev, another former top player (=9th in the world, January 1993), and author. This game was played in the first FIDE Knockout World Championship in 1997. This tournament has since become the World Cup.

White to play. How did Van Wely punch his ticket to the Quarterfinals of the grueling knockout?

18. ?

Line Clear

Should I Withdraw from the Tournament?

The “¡No Más!” Tournament Withdrawal

I’m not talking about an early tournament withdrawal because of another commitment, or because you’re feeling legitimately ill. I’m also not talking about scheduling a last-round bye in advance. Let’s exclude withdrawing in order to return as a re-entry, too.

I’m talking about those cases where you could continue, but don’t want to — usually, because you’re having a bad performance and want to “stop the bleeding.”

Don’t worry, I won’t judge you. I’ve made this kind of quick escape more often than I can count. Plenty of my tournaments at the Marshall Chess Club have ended with this sequence:

  • I have a hopelessly lost position…
  • Repeatedly shake my head, make faces to no one in particular, and finally stop my clock…
  • I quickly shake my opponent’s hand and reset the pieces before others see the carnage…
  • Run to the pairing sheet…
  • Mark the win for my opponent…
  • Write OUT next to my name and circle it…
  • Race out the door without saying a word to anyone.
Tournament Withdrawal at the Pairing Sheet

How to Tournament Withdrawal: Write OUT next to your name on the yellow pairing sheet and circle it! Photo: SportzCosmos

This way no one has to see me explode or make an @$$ of myself. I do that in private…

Hypocrisy? Fake Encouragement?

Yes, I realize this “procedure” goes against my recommendation to do a post-mortem analysis with your opponent…but do as I say, not as I do, OK? Anyway, I said that step is optional!

I don’t condemn the “bruised ego tournament withdrawal” because I know it’s not easy to play your best with a sub-optimal state of mind. In fact, I don’t try to cajole my students into carrying on if they really don’t want to. That could do more harm than good.

There’s always another tournament. We can recharge and come back stronger next time.

Some parents and coaches won’t agree with my stance and will counter with platitudes like “never give up,” or “quitters never win.” My dad once threatened to never register me for a tournament again in my early years when I suggested withdrawing after a poor performance. I had to play, but didn’t learn some deep life lesson — I was just annoyed and lost badly.

Anger and disappointment can be powerful motivators. The same cannot be said of despair.

Maple and Mahogany Wooden Tournament Chess Board

In 2017 I purchased a wooden tournament chess board from USCF Sales. I wanted a hard, flat, regulation-sized surface to study chess while in bed, and a vinyl roll-up board just wouldn’t do.

At the same time, I knew I wasn’t going to use it much, and I’m not a wealthy guy, so I had to choose carefully.

I think I made a good choice.

Maple and Mahogany Wooden Tournament Chess Board

Maple and Mahogany Wooden Tournament Chess Board. Options: 2.25″ squares, with coordinates, and without a logo. Photo: USCF Sales

In my humble opinion, this is a really nice board for only $39.50 (on clearance; regular price $79.00)! You can also choose between two different bags for the board, but at an additional cost of $39.95 or $59.95, I decided to pass.

When I got it in person, it was just what I expected and I am very happy with it. The only problem is that I don’t use it nearly enough…

Warning: It’s not a DGT board, so don’t buy it expecting to use it for game broadcasts.

It will fit any standard chess set. A test to determine if a chess board and pieces are appropriately-sized for each other: four pawns should fit within one square.

If you’ve got a small chess club or run invitational tournaments, I would highly recommend this wooden tournament chess board. From a price-to-value perspective, this is one of the best chess purchases I have made in at least several years.

Should I Play Attacking Chess?

Studying tactics and checkmates is usually the first step for new chess players. Next comes classic. short attacking games: the miniatures. They’re exciting and more straightforward for inexperienced players than technical masterpieces.

What is an Attacking Style?

Sometimes, the position requires you to attack the enemy king. Even the most conservative players will launch an attack when it is clearly the right plan. Does this, then, make everyone an attacking player? Not quite.

An attacking player is one who most often chooses to attack when the best available plan is a matter of taste. In the same position, a different player might try to gain space, press a queenside initiative, or go for a promising endgame.

It’s more a question of a player’s mentality and approach to chess.

Let’s take a simple example from the Pirc Defense (1.e4 d6 2.d4 Nf6 3.Nc3 g6):

As I warned when challenging the idea that 1…e5 players need to worry about a lot of lines, while others have a much easier task: white has plenty of options against the Pirc, too.

Sedate players like Anatoly Karpov or Ulf Andersson would choose simple development with something like 4.Nf3 Bg7 5.Be2 0-0 6.0-0 and play for central control:

Another treatment is the positional 4.f4 Bg7 5.Nf3 0-0 6.Bd3 favored by, e.g., Bobby Fischer:

An attacking player would not hesitate to pursue a kingside attack, for example with 4.Be3 Bg7 5.Qd2 c6 6.f3:

This was precisely the scheme Garry Kasparov used in his famous victory against Veselin Topalov at Wijk aan Zee 1999.

Garry Kasparov gets ready to play attacking chess against Veselin Topalov at the 1999 Wijk aan Zee tournament.

No one knew that one of the greatest games in chess history was about to begin.

Risk and Reward

Playing attacking chess in “borderline” situations increases the likelihood of a decisive result — either the aggressor breaks through or the defender repels the assault and winds up with extra material. You have to be willing to accept more losses with your wins.

There is also a greater burden on a player’s ability to calculate, even more so if they play sharp opening lines. We saw an example of this in Svidler — Vallejo-Pons. The player making the first mistake can lose outright. Some players love this kind of play, however!

What Kind of Player are You?

You have to play a lot of games and honestly assess what kinds of positions you feel more “at home” in. Does active play suit you…and how active are we talking? Do you prefer to initiate play or to play against your opponent’s ideas? Above all, don’t experiment too much in tournaments — that’s what online chess is for!

Another hint: which famous player’s games “speak” to you? It’s unlikely you’ll ever play as well as your hero, but finding a role model to emulate can be very helpful.

Don’t hesitate to keep tweaking your openings until you find a set of lines that you know how to play and actually want to play. If you would be happy to employ a line against a player rated 200 points higher than you, keep it in your repertoire!

What are your experiences? Please share!

Irving Chernev: Great Chess Authors, Part 6

After seeing my choice of Fred Reinfeld last week, today’s selection should not be a surprise. In fact, he co-authored a few books with Reinfeld.

Irving Chernev (1900-1981)

Irving Chernev. Photo: World Chess Hall of Fame.

Irving Chernev. Photo: World Chess Hall of Fame.

Born in Pryluky (part of the old Russian Empire, now Ukraine), Irving Chernev emigrated to the United States in 1920.

He wrote 20 books, including classics that have been updated to Algebraic Notation from Descriptive Notation.

While I consider Max Euwe the most instructive chess author, there is no one I enjoy reading more than Irving Chernev. His love of chess shines through on every page. Well-chosen examples, insightful comments, and easy reading.

Game Collections

I absolutely love game collections, and Chernev wrote several good ones, including Logical Chess: Move by Move (1957), The Most Instructive Games of Chess Ever Played (1965), and The Golden Dozen (1976). There is also 1000 Best Short Games of Chess (1955).

I was also gifted The Russians Play Chess (1947) by Charlie Ebbecke while I was a member of the Bronx Yonkers Chess Club in the late 1990s. I played through many of the games in this book several times!

But my favorite — and one of my top ten books — is Capablanca’s Best Chess Endings (1978).

If you have trouble making sense of endgame play, take a couple of weeks and play through the 60 games in this book. It will transform your entire outlook on chess. Chernev isolates the final phase of the games and explains in words what is going on. Brilliant stuff.


By my count there are Combinations: The Heart of Chess (1960), Practical Chess Endings (1961), and two earlier books Chernev worked on with Reinfeld: Chess Strategy and Tactics (1933), and Winning Chess (1948).


I’ve always wanted to get my hands on 200 Brilliant Chess Endgames (yes, I have a weakness for endgames!). Other titles include The Fireside Book of Chess (with Reinfeld, 1948), and The Bright Side of Chess (1948).

Final Thoughts

Irving Chernev wrote a great deal of good books for the improving and average player. His works are easy to read and you can easily spend hours on them without realizing you have done so…

Chess Tactics: Von Scheve — Teichmann, 1907

Richard Teichmann. Photo: Deutscher Schachbund.

Richard Teichmann lost sight in his right eye in the 1890s. Photo: Deutscher Schachbund.

Richard Teichmann (1868-1925) was one of the best players of the early 20th century.

The German master was nicknamed “Richard V,” as that was often his tournament placing.

Karlsbad 1911 proved to be a different story: he rose to the occasion and achieved the greatest result of his chess career.

Teichmann won the 26-player round-robin by a full point over a string of current and future top players — Akiba Rubinstein, Carl Schlechter, Frank Marshall, Aron Nimzowitsch, Savielly Tartakower, Alexander Alekhine, and Rudolf Spielmann among them.



Here is a brevity against Theodor von Scheve, played at the Berlin Jubilee Tournament of 1907.

Black to play. How did Teichmann conclude the game in short order?


Don’t abandon your castled king

How to Calculate Cash Prizes

Experienced players can skip this post, but it might be helpful to newer players and to parents.

I would also encourage Organizers to keep in mind the following advice given to me by the late Mike Anders at the 2008 National High School Championship:

How do you split $100 three ways? Give each player $35 and thank them for coming!Associate National TD Mike Anders (1955-2013)

Important: US tournaments almost never apply tiebreaks for cash prizes, unlike with trophies! Every player’s points count the same.

Well, what are the prizes, anyway?

Guaranteed Prizes

Fully-guaranteed prizes are as advertized: they do not increase or decrease.

One possibility is to guarantee some of the prizes, say 1st and 2nd place, and calculate the rest based on entries, as we’ll see next.

The organizer could also guarantee a certain percentage of the prize fund, say, 70%. In that case he or she would be on the hook for at least 70% of each prize, assuming there is at least one player eligible to win it.

Based-on Prizes

It’s best to show an example. The Tournament Life Announcement (TLA) in Chess Life says:

$480 based on 32 entries

The event is unlikely to get exactly 32 entries, so the prizes will probably be higher or lower than advertised.

20 entries? Prize fund is $480 x (20 ÷ 32) = $300.

42 entries? Prize fund is $480 x (42 ÷ 32) = $630.

Each prize in the total prize fund is calculated the same way.

Now that we are sure what the actual prizes are, there are two magic words to prize calculation:

Add and Split

Let’s take the basic example of three prizes:

1st Place: $100

2nd Place: $50

3rd Place: $25

There is no issue if the top three places have different scores (for example, 4-0, 3½-½, and 3-1 in a four-round tournament). This seems to happen rarely, however!

Scenario 1
Player A and Player B both score 3½-½. Player C scores 3-1.

Players A and B do not both receive $100, and Player C $50! A player once got upset with me at the World Open when I explained that all players tying for 4th place do not get a full 4th place prize!

Players A and B share 1st and 2nd place equally: $100 + $50 = $150. $150 ÷ 2 = $75 each.

Player C receives $25.

Scenario 2
Player A scores 4-0. Players B, C, and D each score 3-1.

This time Player A receives $100. Players B, C, and D share the next three prizes, if they exist. There are only two prizes, so those two prizes are split three ways:

Players B, C, and D share 2nd and 3rd place equally: $50 + $25 = $75. $75 ÷ 3 = $25 each.

Class Prizes and Under Prizes

Open tournaments often feature additional prizes beyond “place” prizes. This is to give lower-rated players a chance to win something for their efforts as well.

Compare the following prizes:

Class A: $35

1800-1999: $35

Under 2000: $35

The first two prizes are synonymous, because Class A is defined as 1800-1999. A tournament ad could use either wording.

The third prize is not the same as the first two! It’s available to any rated player Under 2000, so a 1680 who has a good event can win this prize for himself or herself. If the Organizer wants to make unrated players eligible for this prize, it should read like this:

Under 2000/Unr: $35

Note: One cash prize per player. A player can only win the highest prize available to them, not multiple cash prizes. So if they go 4-0 they get 1st Place (using $100 as before), and someone else gets the Class or Under Prize.

It is possible to win a cash prize plus other prizes such as a trophy, plaque, qualification, or free tournament entries.

One Last Example


1st Place: $150

2nd Place: $100

3rd Place: $50

Under 1800: $50

Under 1600: $40

Final Standings:

Amy (2231): 4½

Bob (2174): 3½

Charlie (2071): 3

Diana (1993): 3

Edward (1770): 3

Frank (1692): 2½

Gabby (1575): 2½



How are the prizes calculated?



Amy gets 1st Place ($150), and Bob gets 2nd Place ($100).

Charlie and Diana are only eligible for 3rd Place, but Edward is eligible for 3rd Place and Under 1800. We figure out which prize is larger for Edward: either 3rd Place + Under 1800 divided by three players, or Under 1800 alone. Clearly, it’s the latter. Therefore:

Charlie and Diana share 3rd Place ($50) and receive $25 each.

Edward gets Under 1800 ($50).

Gabby gets Under 1600 ($40).

This is by no means an exhaustive treatment, but I hope it demystifies prize-giving for those new to tournament play! Good luck!