Full house hexagonal chess

Here's my attempt to embellish upon any number of two player 91 cell 11x11 hexagonal board variants, such as Glinski's Hexagonal Chess, by trying to find a viable and enjoyable way to fill in all cells within each side's camp for the starting position. The density of pieces to empty cells in the setup is 55%, closer to that of orthodox chess (50%) than, say, Glinski's Hexagonal Chess (40%), and a lot of the pieces are still free to move somewhere right at the start of a game.

A Game Courier preset for play is available. Note that a link for Glinski's Hexagonal Chess is provided in the Notes section further below.

Setup

Pieces

There are 13 piece types used, 6 of which are the same as for Glinski's Hexagonal Chess (which borrows from standard chess), namely the King (K), Queen (Q), Rook (R), Bishop (B), Knight (N) and Pawn (P). That leaves the 7 new types that I've added, i.e.:

Sailor (S): based on a piece from Shogi (promoted Rook, or 'Dragon', in that game) - can move like a Rook or King;

Missionary (M): based on a piece from Shogi (promoted Bishop, or 'Horse', in that game) - can move like a Bishop or King;

Thunderbird (T): can leap two hexes orthogonally or one hex diagonally - after a known fairy hexagonal board piece type, 'Witch', in Trihex, or (later) 'Warrior', in Hexagonal Iss Jetan;

Hippo (H): can move like a Thunderbird or King;

Pegasus (E): can leap three hexes orthgonally or as a Knight - could also be seen as a 'threeleaper' (fairy piece that leaps 3 cells orthogonally) that's 'knighted' (i.e. has knight move capability in addition), though as applied in the context of this variant's hexagonal board;

Hydra (Y): can move like a Pegasus or King;

Unicorn (U): can move like a Bishop or Nightrider (a Nightrider is a standard fairy chess piece that can make a move like a Knight, but then can continue to move in the same direction; thus, it can make one or more successive Knight-leaps, all in the same direction, with the condition that the spaces visited by all but the last jump must be empty).

Note that pawns may promote to any of the 7 new piece types.

Here's a diagram of all legal moves by a Sailor on an empty board:

Here's a diagram of all legal moves by a Missionary on an empty board:

Here's a diagram of all legal moves by a Thunderbird on an empty board:

Here's a diagram of all legal moves by a Hippo on an empty board:

Here's a diagram of all legal moves by a Pegasus on an empty board:

Here's a diagram of all legal moves by a Hydra on an empty board:

Here's a diagram of all legal moves by a Unicorn on an empty board (note that if placed instead on this hexagonal 91-cell board's central cell [f6], a Unicorn would only be able to take one nightrider step in any knight direction, due to going off a board edge if attempting any further knight steps in the same direction):

Rules

Except for the movements of the 7 added piece types, the rules are as for Glinski's Hexagonal Chess:

1) Pawns have an initial two-step move option.
2) En passant captures are allowed.
3) A capturing Pawn, which arrives on a friendly Pawn's starting square, regains its initial two-step move option.**
4) Pawns promote when they arrive on one of the eleven hexes that define the opposite borders of the board.
5) There is no castling.
6) Stalemate earns 3/4 points for the player delivering it and 1/4 point for the player stalemated.

**The logic here being that such a move does not place the Pawn any closer to the end rank. Moreover, the rule makes it unnecessary to keep track of which Pawns have actually moved.

Notes

I recall reading long ago that for Glinski's Hexagonal Chess (and thus also for Full House Hexagonal Chess), the relative values of the pieces were:

P=1, B=3, N=4, R=5, Q=9

I'd note that Dave McCooey has estimated rook worth seven and queen worth ten pawns, for his Hexagonal variant, which uses the same pieces and board (except for the pawns) as Glinski's variant, but one possible problem with these estimates could be that two rooks would then be worth a queen plus four whole points; here is a review of McCooey's variant:

I also recall that a chess K has a fighting value of 4 (even though it cannot be exchanged); this value in my view might be rather oddly expressed (for lack of a known formula) as

chess K = 32 x (max. # cells chess K moves to [eight]) divided by (# of cells on a chess board [sixty-four]) = 4, and similarly,

the fighting value of a Glinski's Hexagonal Chess K = 32 x (max. # cells Glinski's Hexagonal Chess K moves to [twelve]) divided by (# of cells in Glinski's Hexagonal Chess [ninety-one]) = approx. 4 too.

For the 7 new piece types added in Full House Hexagonal Chess, I'd estimate their values as follows:

S (Sailor) = 7.5 (half of all K moves are added to a R to make an S, & since Q=R+B+P in value, I'd say S=R+(K-P)/2+P in value) roughly, even though it's not at all royal.

M (Missionary) = 5.5 (half of all K moves are added to a B to make an M, & since Q=R+B+P in value, so M=B+(K-P)/2+P in value)

T (Thunderbird) = 4 (a T can have the same number of moves as an N or a K)

H (Hippo) = 6.5 (half of all K moves are added to a T to make an H, & since Q=R+B+P in value, so H=T+(K-P)/2+P in value)

E (Pegasus) = 6.5 (an E can have the same number of moves as an H; the same result for an E's value could be reached if using instead the observation that an E can have 3/2 the number of moves as an N [or a T, or a K], since just as Q=R+B+P in value, so E=N+(N-P)/2+P in value)

Y (Hydra) = 11.5 (just as Q=R+B+P in value, Y=E+K+P in value)

U (Unicorn) = 10.5 (on this game's hexagonal board a nightrider [NN] has IMHO on average about 3/2 as many moves as a N, & since Q=R+B+P in value, so U=(N+(N-P)/2+P)+B+P in value)

Some of these values may seem surprising, e.g. a sailor being worth only a pawn more than a hippo, in spite of the former's normally much greater mobility (and otherwise matching the hippo's movement capabilities in almost every other way, except for not leaping), but in this case I can imagine a hippo plus two pawns often outshining a sailor, even in an ending. Also, I suppose that in an ending with king & queen vs. king & (unicorn or hydra), with an equal number of pawns, a queen may well hold its own due to its ability to often deliver many checks, or possibly obtain a pin vs. the opposing piece against its king; thus the values I've given for the unicorn or hydra may be more appropriate for positions with more material on the board when the opponent has an unopposed queen in return.

To try to help put all of the above values into perspective, a P would normally be worth 3 tempi in an open chess position, with 4 uncompensated tempi (or 4/3rds of a P) normally enough to be decisive (in the starting position for chess, White can deliver Scholar's mate if given four free tempi, as a crude example). For no net offsetting compensation in position, 1/3rd of a P would constitute a slight edge, 2/3rds of a P would be a large advantage and an extra P alone is an almost winning advantage. This scale of small to decisive advantages might similarly be used in assessing a material or tempi advantage in Full house hexagonal chess, assuming the other side has no net offsetting compensation in position (i.e. after weighing any positive features for each side such as safer king, more solid pawn structure or control of a significant open line or hex).

Based on the above, a number of 1 for 1 piece trades could often prove equitable in Full house hexagonal chess games, i.e. H for E, M for R, or T for N. Otherwise, there are many 2 for 1, 3 for 1, or 3 for 2 trades of pieces (perhaps including pawns) possibly equitable in Full house hexagonal chess.

As in chess, pieces shouldn't be moved to cells where they are liable to be exposed to convenient attack by less valuable enemy pieces or pawns, if that then compels them to go to undesirable cells, or waste tempi due to retreating. The queens may thus take a while to activate safely, especially far from home, and that ought to hold true for many other valuable piece types in Full house hexagonal chess, which should often be more at ease once some of the correspondingly less valuable enemy pieces disappear from the board.

Here's a link for Glinski's Hexagonal Chess, as described on chessvariants.com:

The setup position of Full house hexagonal chess is admittedly not highly symmetrical, but perhaps in a way that's more endearing than ugly if one gets accustomed to it. In the setup the 7 additional pieces were placed where they are in each side's camp for a reason, with more valuable pieces generally closer to the rear. It might be the case that the powerful Hydra pieces may be exchanged for each other relatively early, and/or often, but other setups or piece types could have possible drawbacks too.

Note that the positions of Glinski's Hexagonal Chess' 36 pieces are kept in the setup position for Full house hexagonal chess, except each side's king takes the place of one bishop, which is now positioned three cells forward on the same file. This is with the hope of maximizing a king's initial safety. Next, each side's unicorn starts where it is so that its nightrider capability in particular might affect the play relatively soon, aside from putting such a valuable piece initially in the rear. Then, each side's sailor is positioned so that as a result there is just one piece with rook movement capability placed on every other file in their camp, and also there is just one such piece placed on each 'rank' in their camp (at least the term 'rank' does apply to the White camp, given the board's co-ordinate system). Each pegasus is positioned so it may influence early play in the centre or on either wing (which a thunderbird or hippo couldn't from the same cell). The hydra is placed deeper on the other wing, where it may elect to eventually influence play there with its own pegasus movement capabilty. It may become a target of the enemy unicorn even in its own camp, though. The lightweight thunderbird goes where it might eventually leap out of the way of the queen. The missionary goes where not doubled on a diagonal at a possible target in the enemy camp. The hippo goes where it at the least guards a R.

Note that on his first turn, White can attack Black's sailor by moving his pegasus to the cell that is three hexes in front of it. However, this may not be one of the most incisive first moves for White to play, since if nothing else Black can counterattack White's sailor with his pegasus in reply, which can lead to exchanges that may be objectively unhelpful for White.

One may ask, how did I decide upon the 7 new piece types for Full house hexagonal chess? First, I wanted to add the Thunderbird as a piece type, which has a precident (and might be considered a standard option for hexagonal variants at some point). I also wished to add the Pegasus (a kind of 'augmented knight' that hexagonal chess terrain permits). Next I decided to 'crown' (i.e. add king move capability to) both of the above (plus Glinski's 6) piece types if applicable, except for pawn and knight. That's as a knight if crowned (i.e. the standard fairy piece centaur) would have moves arguably slightly harder to visualize on the game's hexagonal board than if crowning this variant's 'augmented knight' (Pegasus) to produce the new Hydra piece type, and so I decided just to use the Hydra.

Thus, I came up with a total of 4 crowned pieces that I decided to use. Note that a centaur fairy piece type, if included, would have been a completely inferior version of a Hydra in terms of movement capability on this game's hexagonal board, and arguably & aesthetically, far less different in comparison to a Hydra than, say, a queen is to an amazon fairy piece type. Moreover, a centaur is the compound of a piece (fairy piece type mann) with the movement capability of a previously selected piece for this variant (i.e. a king) that's also been knighted. If a centaur were to be included, that could be viewed as beginning to pursue a theme that I didn't wish to, as explained in the next paragraph.

All this accounts for 6 of my new piece types, and I needed just one more to fill a given side's camp (in the start position of Glinski's Hexagonal Chess). Thus any thought of the additional theme of having many previously selected pieces of this variant that would be knighted was out (or even just having, as a commonplace variant piece pair, both of the standard archbishop [aka cardinal] & chancellor [aka marshall] fairy piece types).

I decided the remaining piece should be special, in some other way, so it came down to a Unicorn. That's if only due to my fancy for the name, and since having a mere nightrider instead would not ever permit one to quadruple on a diagonal with unpromoted pieces of one's own, like one already (at this point in my creative process) might quadruple on a file with all one's unpromoted pieces having rook-like movement capability. Being able to pile up along a file or a diagonal an equal number of times seemed pleasing to me somehow.

Selecting a Unicorn might be seen as beginning a -rider theme, however. Before tackling this possible objection to my selection, first note that a cardinalrider (aka Unicorn) is not (simply) a knighted version of a previously selected piece for this variant (in this case, a bishop). It would have been a similar story for, say, an amazonrider vis-a-vis a queen, if I had selected that -rider instead. Getting to my personal justification for selecting a Unicorn as my one & only -rider, in case of instead selecting just an amazonrider as a -rider, one might in that case quintuple on a rank with all one's unpromoted pieces having rook-like movement capability, but merely quadruple on a diagonal.

If I somehow had room for more piece(s), e.g. -rider(s), in each player's camp, I might have alternatively selected an amazonrider in addition to selecting a Unicorn, so as to allow one to quintuple on both a file or a diagonal. However even if I had room for more piece(s), I would have rejected selecting an amazonrider, which IMHO would generally be way too powerful a piece on the 91 cell hexagonal board. Thus went my rather involved, but hopefully entertaining, selection process for the 7 new piece types added in Full house hexagonal chess.

Last revised by Kevin Pacey.