A question of size :-)

Yes it will Harry, in addition for future reference use FIDE's or USCF's standard calculation (King's base divided by .78) and you will attain the correct sized playing square for any king piece base and set. Personally I would use a 2.25" playing square board for the 1.6" base of that particular Dubrovnik  3.6" King set from CB. 

What size pieces for a board I already have

I recently found myself selecting chess pieces for a 49.5 mm (1.95 in.) squares board I already had. I did of course follow the very good advice from “Loubalch” found in this forum regarding King and Pawn proportions (.765, .586, etc.). In some cases, however, I found that my bishops would bump into my bigger pieces when sliding into play. I did find a very useful video by Mr. Jonas Žnidaršič, https://youtu.be/zJeVid62NZo  which helped me in the end with the correct sizing of all my pieces

What Jonas video shows is that the bishop or the fatter of your other pieces (beside K and Q) should be able to slide between the two other bigger pieces. For example, Bishop between K and Q, or Q between K and Rook. To test Mr. Žnidaršič’s method you would need to use the dimensions (base diameter) of the three pieces with the broadest base on the set you are considering, jointly with your board dimensions.

The situation that is most common is the need to know if the pieces of a set for sale which is not yet available for you to handle is a  good fit to your board. What I did was to first apply  Loubalch’s proportions to pieces I liked, and then use the old and trusted Pythagorean formula together with some simple geometrics to make sure my pieces will not bump into each other while playing. Here is an equation illustrating the mathematical method I used in order to follow the Jonas’ method:

Max Bd ≦ c - Kd/2 - Qd/2

Max Bd = The largest diameter of the bishop base to fit to your board.

Where c = Diagonal line of your board square. Applying the Pythagoras theorem you get  c=√ (a²+b²), which in our case is also c= √ (2a²) since the sides of a square are equal.

Bd is the Bishop base diameter, or the Rook’s, or the Knight’s  (whichever has the broadest base).  In  other words you need to first find the diagonal length of one of your squares (C= √ (2A²) ) and then subtract from that half of the King’s base diameter (Kd/2) and half of the Queen’s base diameter (Qd). This is the diagonal space available between King and Queen. In actual chess playing, I have found that a clearance of at least 2 to 5 mm is practical. In other words, your Bishop’s base should be approximately 2 to 5 mm smaller than the maximum space available ( MaxBd). But, how much of a clearance you like is a matter of personal preference.

Example 1 (Choosing pieces for my 49.5 mm (1.95 in.) board):

Ideal King base: 1.95 x .765 = 1.49 in.

Ideal Pawn base: 1.95 x .586 = 1.14 in.

I looked at different chess pieces and found a Monarch Staunton 3 ¾ in. King at “House of Chess” that is the best match for my board. These were my calculations:

Monarch Set Height/Base in inches:

            King                3.75/1.46

            Queen            3.23/1.46

            Bishop           2.91/1.22

            Pawn              2.05/1.10

Testing for bishop easy sliding between K and Q:

Max Bd ≦ c - Kd/2 - Qd/2    =      (√ (2a²)) – 1.46/2 - 1.46/2

            =          (√ (2 x 1.95²))  -  0.73 + 0.73

            =          2.76 – 0.73 – 0.73

            =          1.30  is the Maximum Bishop Diameter acceptable (Max Bd)

Therefore, my set’s Bishop base of 1.22 is less than 1.30 and is acceptable with a clearance of 0.08 in (2 mm).

In the photo below my Plastic set of 3.79/1.46 King, 2.96/1.41 Queen, 2.56/1.22 Bishop fits tightly on my 1.95 in. (49.5 mm) squares board with around 2.5 mm clearance.

What size board for pieces I like (or have)

If on the other hand you need to get a board to fit pieces you already have or would like to have, you can develop a selection criteria using the Pythagorean formula as well. In this case you need to calculate the dimension of your square (A). Formula would go as follows:

First, let get the diagonal of the squares in your board (C):

c ≥ Bd + Kd/2 + Qd/2

And then you square side (A):

a ≥ √ (c²/2).

Example 2 (Choosing a board for my Chess Bazaar Reykjavik pieces):

Reykjavik Set Height/Base in inches:

            King                3.78/1.65

            Queen            3.06/1.52

            Bishop           2.72/1.38

            Pawn              1.85/1.18

c≥ Bd + Kd/2 + Qd/2           =          1.38 + 1.65/2 + 1.52/2

c ≥ 2.85         then your square sides (A) should be slightly bigger than √2.965²/2

a = square sides ≥ √4.39   A ≥ 2.0965  in.

Then remember to add a minimum clearance of around 2 mm (.0787 in.), then your board size should have squares of at least 2.0965 + .0787 = 2.175 inches, or around 55 mm of squares. But if you prefer a little more working space (I do) then, a 2.25 in (57 mm) square is better.

 In the photo below my Reykjavik bishop fits tightly between K and Q, with just 2 mm clearance on a 2.17 (55 mm) board.

Finally if this entire math is a bore to you, I am more than willing to do the calculations for you. Just send me a note with your dimensions (board or pieces). Thank you for reading.

@plctrees: man, that's really great. Can you help me this set (https://www.chessbazaar.com/the-reproduction-1950-dubrovnik-bobby-fischer-chess-set-in-stained-crimson-box-wood-3-6-king.html) and the mentioned diameters...on my 55 mm square DGT Bluetooth chess board? Thank you so much! Harry

I have seen the thing about the B being able to slide between the K & Q - what I read was the B needs to go between them to marry them.

I use that one and the 4 pawns. I like them to overhang just a tad when I put 4 of them on a square. Between the B sliding through with just a little clearance and the 4 pawns on a square the set fits the way I prefer.

Thank you synthesechess. Here are the calculations for your 55 mm squares (calculations also given for a 57.15 mm board) and the Chess Bazaar Dubrovnik (SKU D1097). Actually the Dubro pieces diameters are the same as my Reykjavik (K 42, Q 39, B 35).  

Therefore you will have a clearance of 2.3 mm with a 55 mm board. A bit tight. See photo below:

If I were to buy a new board for this set, I will go with the 57.15 mm (2.25 in.) board. The bigger board would provide a nice 5.3 mm clearance for the Bishop sliding between K and Q. But my 55 mm board is perefctly fit for the set. I just would have prefer the extra clearance.

plctrees,

I'm glad you found my formulas useful.

What started me on my journey was buying a set based on "acceptable" guidelines (i.e. the king approximately 75% of the square and 4 pawns to a square), only to find that although the king fit nicely on the board, the pawns looked like Munchkins! I realized then and there that the accepted dogma would not necessarily yield an aesthetically pleasing chess set. So I did some experimenting. I began by replacing the pawns with progressively wider ones until I found some that just looked right (to me). As it turned out, two of these pawns would fit perfectly when placed diagonally inside the square. When I did the math, the ideal diameter turned out to be 58.6% the width of the square.

When I worked out the calculations on my scientific calculator, I sat staring at a 10-digit number that rounded off to .586; for some unknown reason, I pushed the square root key and came up with another 10-digit number that rounded off to .765, or 76.5%. A light bulb went off, that's very close to the 75% guideline for the diameter of the king. Perhaps the mathematical relationship between these two numbers was nature's way of pointing out an interesting relationship between circles, squares, and a sense of balance and proportion. Well, it was either that or a flash forward from all the mind altering substances I ingested back in the 60s, either way, it worked for me.

Why? Because it was a sizing scheme that considered the diameters of both the king and the pawn, the largest and smallest pieces on the board. It just made sense. If you're trying to fit a set of anything inside of something else, you have to make sure that the largest piece is not too large and the smallest piece is not too small. It was a scheme that guaranteed that the two extremes were balanced. The assumption being that the designers scaled the remaining pieces to fit proportionally between the two.

At this point, I realized the new guidelines enabled me to 1) define the parameters of a balanced chess set, one where all the pieces were proportionally balanced, and 2) provide me with the approximate sized board that would best fit that set. Because of other variables such as piece height and width have a bearing on aesthetics, I never intended this system to be a "one size fits all" solution.

As I saw it, I was identifying a "Goldilocks Zone", a range of three adjacent board sizes wherein you pick the board that best fits your preference. The system finds the Mama board so to speak, if it's too crowded then move up 1/8" to the larger Papa board; if the board's too spacious then move down 1/8" to the smaller Baby board.

Is it a perfect system? No. Is it a helpful guideline? Well, it works for me, but then again, I designed it that way. So, if my system can work for you, GREAT! If not, "Scusi. Mille regretti."

Size doesn't matter, it's what you do with it.  I have a big, hard bishop (actually, two) as do many of you, but what sets me apart is my ability to make it penetrate the area around my opponent's king in preparation for mating, and unlike so many of you, I will use the entire five minutes allotted to me to maximize our mutual pleasure.  There will never be a letdown in the afterglow as the thin blue curl of my cigar smoke rises above your prostrate pieces.