Even more guessing!

Previously, I wrote down my guesstimates how much One variant is more complex than Classical Chess, turns out a lot. Now, it's time to do the same for new, simplified variants. I'll do just Classical Chess 26, smaller variants are of lesser interest here. As for Croatian Ties variants, I haven't yet got around how to calculate complexity factor due to increased mobility; so, using previous method Croatian Ties variants would have exactly the same complexity as their Classical Chess counterparts, which doesn't feel right, but it is what it is.

If you haven't already, read blog post linked above; it explains how complexity factors are calculated, and why. So, let's start with size:

$${\mathrm{cf}}_{\mathrm{size}}=1+\ln \left(\frac{{26}^2}{8^2}\right)=1+\ln \left(\frac{676}{64}\right)=3.357310$$

Next, it's total number of pieces on the chessboards:

$${\mathrm{cf}}_{\mathrm{pieces}}=1+\ln \left(\frac{104}{32}\right)=2.178654996$$

There are no new pieces, so complexity factor for different types of pieces is one:

$${\mathrm{cf}}_{\mathrm{types}}=1+\ln \left(\frac{6}{6}\right)=1.0$$

The same applies to Croatian Ties variants, since every Knight is replaced by Pegasus, so there are the same number of different types of pieces.

There are also no new interactions, so complexity factor also goes to one (this one too applies to Croatian Chess variants):

$${\mathrm{cf}}_{\mathrm{interactions}}=1+\ln \left(\frac{3}{3}\right)=1.0$$

Our complexity $c$ is then defined as a product of all factors calculated above:

$$c_{\mathrm{regular}}={\mathrm{cf}}_{\mathrm{size}}\cdot {\mathrm{cf}}_{\mathrm{pieces}}\cdot {\mathrm{cf}}_{\mathrm{types}}\cdot {\mathrm{cf}}_{\mathrm{interactions}}=7.314420189$$

This is complexity scaling factor of regular games from Classical Chess into Classical Chess 26 variant, i.e. all games should be 7.314 times longer. For instance, the longest recorded tournament game was 538 moves (269 FIDE moves, aka cycles), which turns into 3835 moves (1968 cycles) for Classical Chess 26 variant. Average on-line match lasts about 80 moves (40 cycles), in Classical Chess 26 variant that would become 585 moves (292.5 cycles). Average tournament match lasts about 88 moves (44 cycles), which becomes 644 moves (322 cycles).

The same, however, does not apply when calculating maximal possible game length, because players will try to maximize each and every metrics available to prolong the game. So, for maximum game length we have to calculate linear scaling factors; for chessboard sizes factor becomes:

$${\mathrm{cf}}_{\mathrm{size}}=\frac{{26}^2}{8^2}=\frac{676}{64}=10.562500$$

Next, for total number of pieces on the chessboards we have:

$${\mathrm{cf}}_{\mathrm{pieces}}=\frac{104}{32}=3.25$$

Complexity number for different types of pieces is still one:

$${\mathrm{cf}}_{\mathrm{types}}=\frac{6}{6}=1.0$$

Finally, complexity factor for number of different interactions is also one:

$${\mathrm{cf}}_{\mathrm{interactions}}=\frac{3}{3}=1.0$$

Taken together, our complexity $c$ becomes:

$$c_{\mathrm{longest}}={\mathrm{cf}}_{\mathrm{size}}\cdot {\mathrm{cf}}_{\mathrm{pieces}}\cdot {\mathrm{cf}}_{\mathrm{types}}\cdot {\mathrm{cf}}_{\mathrm{interactions}}=34.328125$$

This is scaling factor for the longest possible games, i.e. the longest games should be 34.33 times longer in Classical Chess 26 variant compared to Classical Chess. For instance, previously mentioned 11797 moves (5898.5 cycles) game as the longest possible with 50-cycle rule in Classical Chess 26 variant becomes 404,968 moves (202,484 cycles) game. Even longer 17697 moves (8848.5 cycles) game with 75-cycle rule in Classical Chess 26 variant turns into 607,505 moves (303,752.5 cycles) game.

These doesn't appear to be large numbers, if you recall estimates for One variant, but should not be underestimated; even "just" 7.314 times increase in complexity results in some prolonged games, especially if increase in complexity is allowed to also translate into longer time allowance per turn. So, 15 seconds per player's turn in bullet game now becomes approx. 110 seconds per turn; given that average Classical Chess 26 game length would be 585 turns, it would last for approx. 17,834 hours of gameplay time; or, 2.23 days if we assume 8-hour gameplay in a day. If we don't increase time allowance per turn, 15 second per turn bullet game would take approx. 2.438 hours of gameplay time.

In short, new Classical Chess variants does pose a challange, even if only just by scaling up. Croatian Ties builds more on top of that challenge, by replacing Knights with more mobile siblings, and also allowing Pawns to move sideways, which throws off known gameplay patterns, tactics.

New variants finished!

Well, that was surprisingly quick, but all new variants are done, including Summary. To be fair, I was  being overly cautious, thinking of what took me to finish Miranda's Veil. Turns out, simplified variants are simple, most additional stuff (in Summary) has already being done, and just needs a little edit, here and there.

Since new, simplified variants are quite a chunk, I'm also updating the book; changes include:

• fixed displacement notation examples
• fixed side-effect summary spacing
• fixed typos (thanks to @RainRat)
• new Classical Chess 14, 20, 26 variants
• new Croatian Ties 14, 20, 26 variants

The book was compiled on September 8, 2025, version is 20250908.191123, and can be found behind that red button above, or in other usual places.

New variants!

Quite some time ago I wrote that I'd like to add some enlarged, but otherwise Classical Chess variants, but dismiss them as not belonging to the book, and requiring their own, separate book which would also discuss mobility. In the meantime, I kinda warmed-up to the idea that enlarged Classical Chess variants do belong to the book presenting new variants, especially since their objective is to make playing on large chessboards more approachable to average, casual player.

Currently, I plan on adding enlarged Classical Chess and Croatian Ties variants as remarks at the very end of the book; those variants won't be fully featured, but will include images. I'm not entirely happy with this design choice, since it will disrupt the flow of the book; but it should be worth it, given that this new book on mobility and such is still very far away, if it will be written at all.

I plan on adding 3 new Classical Chess variants, those will feature only pieces found in Classical Chess, with exactly the same rules, except longer rushes and castlings. I'll also add 3 new Croatian Ties variants, those would be nearly identical to their Classical Chess counterparts, but all Knights would be upgraded to Pegasuses (Pegasi?), and all Pawns will be of side-ways variety; this is to compensate somewhat for decreased mobility of Pawns, Knights on a larger chessboards. New variants will be played on 14 x 14, 20 x 20 and finally 26 x 26 chessboards.

New variants won't bring neither any new pieces, nor any new interactions. Still, I'll have to expand Python application which generates images for the book to support all new variants; later, library will have to be expanded as well. This will take some time, given my usual tempo of writing (which is very slowly) I hope I'll have the book finished by the end of this year.

Join us at LinkedIN

As is a standard trope with older (software) engineers, I'm also bad at socializing, online and off. It's not that I'm internet illiterate, quite the opposite, but somehow casually connecting with strangers is one of my Achilles' heels. Maybe the issue is that I grew up in an disjoint world where each and every service stood only on its own, and rarely had been linked to another. Or, maybe it's that I value privacy, but data gathering and profiling is so prevalent that I have no desire to engage.

Anyway, here it is: a link to Croatian Chess group at LinkedIN; it's still a small, cozy group, with even smaller amount of posts (hey, if you join, you could improve things!). Usually I post when there is something new or relevant to Croatian Chess; usually it's about the most recent blog post. The group itself is not dedicated strictly to Croatian Chess; all posts about all chess variants, and chess in general are welcome, memes included. If you join, please avoid controversial topics like politics, religion or any other ragebaity content; there are plenty of those elsewhere.

Thank you for joining!