## Martian games

Everyone knows that a Chess Rook is worth five points and a Knight is worth three, and everyone knows that a Queen is worth more than the Rook and Knight combined (although some would disagree with that last statement). But what about Jetan? Can I sacrifice my Dwar for a Flier? Is my Padwar equal to a Warrior? And is the Panthan really the weakest piece on the board? These questions have been debated at least since the 1960's, and we still have to find an answer. This article aims to take another step towards understanding.

In the appendix to

*The Chessmen of Mars*^{1}, Edgar Rice Burroughs wrote: “The Martians ... put a price upon the head of each [Jetan] piece, according to its value, and for each piece that a player loses he pays its value to his opponent.” Burroughs, however, never specified what these “values” are.One possibility is that perhaps the number of feathers or jewels on a piece indicates its score. (The Flier has no feathers, but the exactly equal piece Odwar does have five feathers.) This is certainly possible, even though these “points” seem a bit too imprecise to be of any real use (see table at the end of this article)

In the past, there have been at least eleven other attempts to attach point scores to the eight unique Jetan pieces. Most of these are summarized in an appendix to an article about Jetan that I wrote in

*ERBzine*^{2}, Unfortunately, the scores are difficult to compare, because different rule interpretations were used for different systems, so if you compare a so-called “Free Panthan” with the standard Panthan, you are essentially comparing two different pieces. For this article, I have picked two different interpretations. These are based on the standard rules, and they were made by players that I know were experienced and whose judgement I value. The two are George Fergus^{3}and Larry Lynn Smith^{4}.
Another method is to let the computer do the work for you. The software

*Zillions of Games*^{5}has the feature to calculate a score for each piece. This is in fact the method used by Jean-Louis Cazaux and Rick Knowlton in their scoring system.^{6}The score is dependent on the piece’s position, relative the other pieces on the board, so that will have to be taken into consideration. For this article, I have made my own examination by positioning each piece close to the board’s centre.
Below is a table that shows the three different scoring systems. The figures in parentheses are for the jumping Thoat. I have cut Fergus’ scores in half in order to make them more easily comparable with Smith. For Zillions, I used Smith’s implementation, set to the variant “Chained Wild Jetan with Chained Warriors” (which corresponds to the standard rules as presented in

*AG19*^{7}). When right-clicking a piece and selecting “Properties”, Zillions gives a four- to six-figure number, which I have normalized to 1.0 for Panthan and rounded to one decimal for the others.- |
Fergus |
Smith |
Zillions |

Panthan |
1 |
1 |
1.0 |

Warrior |
1.5 |
2 |
0.9 |

Padwar |
2 |
2 |
0.8 |

Thoat |
3.5 |
3 (3) |
1.2 (2.7) |

Dwar |
5 |
4 |
2.3 |

Flier |
5 |
4 |
4.7 |

Chief |
10 |
10 |
19.1 |

Princess |
- |
0 |
2.6 |

As you can see, Fergus and Smith are fairly close, but compared with the computer only Panthan and Flier match. The humans undervalued the Chief and overvalued Warrior, Padwar, Thoat and Dwar, compared with Zillions. In order to see whether human or computer is more right, I next intend to conduct a formal evaluation of all the Jetan pieces.

No matter how you twist it, this evaluation is going to be a simplification. Many aspects will not be reflected; I just give a handful of examples here. To begin with, the Chief, with its greater reach, is on average going to be more limited by the board edges than a Padwar or a Panthan. Nor do the complexities of the different phases of the game, considering e.g. how many pieces are still on the board, come into play. Another complication is how the Panthan, for each forward step it takes, burns its bridges to one tenth of the entire board. This last problem I have chosen to address by a simplification, assuming that a Panthan is, on average, positioned on the fourth rank of the board.

For the evaluation, I have identified the following factors that would seem to be important to define the score of a Jetan piece: Reach (orthogonal and diagonal), size of footprint (number of reachable target squares), paths per target (average), jumping ability, reachable squares on the board, ability to go back, and ability to capture.

For each factor, I have determined a value between 0 and 1, where 0 is “no value” and 1 is the highest score in the game. For example, jumping is either off (0) or on (1), whereas size of footprint varies between 0.10 (5 target squares) for Panthan and 1.00 (48 target squares) for Chief and Princess.

Next we need to combine the values into one score for each piece. This cannot be done by simply adding up, because some values would then be skewed. For example, the ability to capture is much more valuable for a Chief with a footprint of 48 than for a Warrior with a footprint of 8. In order to reflect this, I added 1 to each value (to avoid zero values which would compromise the calculation) and multiplied all the values for each piece.

This gives each piece a raw score, according to this table:

No matter how you twist it, this evaluation is going to be a simplification. Many aspects will not be reflected; I just give a handful of examples here. To begin with, the Chief, with its greater reach, is on average going to be more limited by the board edges than a Padwar or a Panthan. Nor do the complexities of the different phases of the game, considering e.g. how many pieces are still on the board, come into play. Another complication is how the Panthan, for each forward step it takes, burns its bridges to one tenth of the entire board. This last problem I have chosen to address by a simplification, assuming that a Panthan is, on average, positioned on the fourth rank of the board.

For the evaluation, I have identified the following factors that would seem to be important to define the score of a Jetan piece: Reach (orthogonal and diagonal), size of footprint (number of reachable target squares), paths per target (average), jumping ability, reachable squares on the board, ability to go back, and ability to capture.

For each factor, I have determined a value between 0 and 1, where 0 is “no value” and 1 is the highest score in the game. For example, jumping is either off (0) or on (1), whereas size of footprint varies between 0.10 (5 target squares) for Panthan and 1.00 (48 target squares) for Chief and Princess.

Next we need to combine the values into one score for each piece. This cannot be done by simply adding up, because some values would then be skewed. For example, the ability to capture is much more valuable for a Chief with a footprint of 48 than for a Warrior with a footprint of 8. In order to reflect this, I added 1 to each value (to avoid zero values which would compromise the calculation) and multiplied all the values for each piece.

This gives each piece a raw score, according to this table:

- |
Reach - orthogonal |
Reach - diagonal |
Footprint |
Paths average |
Squares |
Back-wards |
Royalty |
Captures |
Jumping |
Raw score |

Panthan |
1 (0.33) |
1 (0.33) |
5 (0.10) |
1 (0.14) |
70 (0.70) |
0 (0.00) |
0 (0.00) |
1 (1.00) |
0 (0.00) |
7.6 |

Warrior |
2 (0.67) |
1 (0.33) |
8 (0.17) |
1.5 (0.21) |
50 (0.50) |
1 (1.00) |
0 (0.00) |
1 (1.00) |
0 (0.00) |
18.8 |

Padwar |
2 (0.67) |
2 (0.67) |
8 (0.17) |
1.5 (0.21) |
25 (0.25) |
1 (1.00) |
0 (0.00) |
1 (1.00) |
0 (0.00) |
19.6 |

Thoat |
2 (0.67) |
1.5 (0.50) |
12 (0.25) |
1.33 (0.19) |
100 (1.00) |
1 (1.00) |
0 (0.00) |
1 (1.00) |
0 (0.00) |
27.3 |

Dwar |
3 (1.00) |
1.5 (0.50) |
16 (0.33) |
2.25 (0.31) |
100 (1.00) |
1 (1.00) |
0 (0.00) |
1 (1.00) |
0 (0.00) |
42.0 |

Flier |
3 (1.00) |
3 (1.00) |
16 (0.33) |
2.25 (0.31) |
50 (0.50) |
1 (1.00) |
0 (0.00) |
1 (1.00) |
1 (1.00) |
84.1 |

Chief |
3 (1.00) |
3 (1.00) |
48 (1.00) |
7.17 (1.00) |
100 (1.00) |
1 (1.00) |
1 (1.00) |
1 (1.00) |
0 (0.00) |
256.0 |

Princess |
3 (1.00) |
3 (1.00) |
48 (1.00) |
7.17 (1.00) |
100 (1.00) |
1 (1.00) |
1 (1.00) |
0 (0.00) |
1 (1.00) |
256.0 |

The raw scores are obviously nonsense. They give no relevant information, except roughly the order of the pieces in terms of strength. Therefore we need to add weight to all the values. This is going to be partly arbitrary, since there is no formal way to ascertain how much, for example, jumping is worth relative to a large footprint. I have used my own feel for the game and then by a trial-and-error method fiddled with the weights until I arrived at scores that seemed reasonable. Then I divided each score by the Panthan’s score in order to arrive at a baseline where than Panthan is always scored at 1.

The results are presented in the following table:

The results are presented in the following table:

- |
Reach - orthogonal |
Reach - diagonal |
Foot- |
Paths - average |
Squares |
Back-wards |
Royalty |
Captures |
Jumping |
Raw score |
Normalized score |

Weight |
1 |
1 |
1 |
0.5 |
1 |
0.5 |
1 |
2 |
0.5 |
- |
- |

Panthan |
0.33 |
0.33 |
0.10 |
0.07 |
0.70 |
0.00 |
0.00 |
2.00 |
0.00 |
10.7 |
1.0 |

Warrior |
0.67 |
0.33 |
0.17 |
0.10 |
0.50 |
0.50 |
0.00 |
2.00 |
0.00 |
19.3 |
1.8 |

Padwar |
0.67 |
0.67 |
0.17 |
0.10 |
0.25 |
0.50 |
0.00 |
2.00 |
0.00 |
20.1 |
1.9 |

Thoat |
0.67 |
0.50 |
0.25 |
0.19 |
1.00 |
0.50 |
0.00 |
2.00 |
0.00 |
30.7 |
2.9 |

Dwar |
1.00 |
0.50 |
0.33 |
0.16 |
1.00 |
0.50 |
0.00 |
2.00 |
0.00 |
41.7 |
3.9 |

Flier |
1.00 |
1.00 |
0.33 |
0.16 |
0.50 |
0.50 |
0.00 |
2.00 |
0.50 |
62.5 |
5.8 |

Chief |
1.00 |
1.00 |
1.00 |
0.50 |
1.00 |
0.50 |
1.00 |
2.00 |
0.00 |
216.0 |
20.2 |

Princess |
1.00 |
1.00 |
1.00 |
0.50 |
1.00 |
0.50 |
1.00 |
0.00 |
0.50 |
108.0 |
10.1 |

Comparing this with the older scoring systems, we find that my method lands us pretty close to Fergus and Smith for the Warrior, Padwar, Thoat and Dwar, whereas the Chief is closer to the results from Zillions. The Flier is higher than any of the previous estimates.

Boiling down all of the above is still not going to help us to a perfect scoring system for Jetan. To achieve that, we need many more recorded and analysed games than currently exist. But I will try to present a tentative result that can be used for now, until someone comes up with a better suggestion.

The Panthan, being the closest equivalent to the chess pawn, should always score 1, in order to simplify comparisons.

The Warrior and Padwar are both weak pieces. The former is particularly weak because of its slow diagonal move (augmented by its starting positions in the corners, which I did not consider in my analysis). The latter has the problem that it can only access one fourth of the board’s squares (in fact, no Padwar can ever capture another Padwar). When compared one on one, each is nevertheless stronger than the Panthan, due to the latter’s slow move and inability to move backwards. This may change when several Panthans are strung together. A chain of four connected Panthans may well be more than double the strength of a pair of Warriors, which do not operate terribly well together. But a basic scoring system must do away with complex situations and assume the simplest pretext. Thus, the Warrior and Padwar are stronger than the Panthan, but not terribly much stronger. Unlike Fergus, I assume that they are of equal strength, and put them at 1.5 each.

The Thoat is stronger than either Warrior or Padwar since its footprint is twelve squares, 50% more than the other two-steppers. Also, it can reach any square of the board. I value it at 3 points, or 4 for the jumping variety.

The Dwar has a footstep that is very similar to the Thoat’s, except the Dwar has four extra squares at its orthogonal extremes. It also has greater maoeuverability, with more ways on average to reach its target squares. It scores at 4 points.

The Flier has the same number of squares as the Dwar in its footstep, but it has two great advantages. One is that it is very fast on the diagonals, double the speed of the Dwar. The other advantage is its jumping ability. The setback is that it is bound to squares of one colour. Even so, it has to be worth more than the Dwar, and I place it at 5 points.

The Chief is almost ridiculously strong, and I therefore feel that Fergus and Smith undervalued it at 10 points. My own calculated estimate, as well as the Zillions score, seems more reasonable. Some others who set scores for Jetan gave no value to the Chief, but I feel that this is not a good approach. For one thing, a score helps to evaluate whether it is worth the effort to try to block a piece, either to block the Chief itself, or to use the Chief as part of a blockade. The high score is also necessary to discourage deliberately forcing a draw if the game is played with wagers. The Chief should be worth 20 points.

The Princess, finally, is essentially impossible to put a score on. While the Princess can also be used to block other pieces (but cannot be blocked itself), the piece’s inability to be used in any kind of attack means that nothing is lost by binding it in a blockade. Even so, I feel that Smith’s score of 0 is not right. If that was its true value, then it could be freely captured by the other side. Therefore, Fergus’ idea of no score at all wins my favour.

Summing up, the following table gives all the scores that have been dealt with in this article:

Boiling down all of the above is still not going to help us to a perfect scoring system for Jetan. To achieve that, we need many more recorded and analysed games than currently exist. But I will try to present a tentative result that can be used for now, until someone comes up with a better suggestion.

The Panthan, being the closest equivalent to the chess pawn, should always score 1, in order to simplify comparisons.

The Warrior and Padwar are both weak pieces. The former is particularly weak because of its slow diagonal move (augmented by its starting positions in the corners, which I did not consider in my analysis). The latter has the problem that it can only access one fourth of the board’s squares (in fact, no Padwar can ever capture another Padwar). When compared one on one, each is nevertheless stronger than the Panthan, due to the latter’s slow move and inability to move backwards. This may change when several Panthans are strung together. A chain of four connected Panthans may well be more than double the strength of a pair of Warriors, which do not operate terribly well together. But a basic scoring system must do away with complex situations and assume the simplest pretext. Thus, the Warrior and Padwar are stronger than the Panthan, but not terribly much stronger. Unlike Fergus, I assume that they are of equal strength, and put them at 1.5 each.

The Thoat is stronger than either Warrior or Padwar since its footprint is twelve squares, 50% more than the other two-steppers. Also, it can reach any square of the board. I value it at 3 points, or 4 for the jumping variety.

The Dwar has a footstep that is very similar to the Thoat’s, except the Dwar has four extra squares at its orthogonal extremes. It also has greater maoeuverability, with more ways on average to reach its target squares. It scores at 4 points.

The Flier has the same number of squares as the Dwar in its footstep, but it has two great advantages. One is that it is very fast on the diagonals, double the speed of the Dwar. The other advantage is its jumping ability. The setback is that it is bound to squares of one colour. Even so, it has to be worth more than the Dwar, and I place it at 5 points.

The Chief is almost ridiculously strong, and I therefore feel that Fergus and Smith undervalued it at 10 points. My own calculated estimate, as well as the Zillions score, seems more reasonable. Some others who set scores for Jetan gave no value to the Chief, but I feel that this is not a good approach. For one thing, a score helps to evaluate whether it is worth the effort to try to block a piece, either to block the Chief itself, or to use the Chief as part of a blockade. The high score is also necessary to discourage deliberately forcing a draw if the game is played with wagers. The Chief should be worth 20 points.

The Princess, finally, is essentially impossible to put a score on. While the Princess can also be used to block other pieces (but cannot be blocked itself), the piece’s inability to be used in any kind of attack means that nothing is lost by binding it in a blockade. Even so, I feel that Smith’s score of 0 is not right. If that was its true value, then it could be freely captured by the other side. Therefore, Fergus’ idea of no score at all wins my favour.

Summing up, the following table gives all the scores that have been dealt with in this article:

- |
Burroughs |
Fergus |
Smith |
Zillions |
Ekman calculated |
Ekman |

Panthan |
1 |
1 |
1 |
1.0 |
1.0 |
1 |

Warrior |
2 |
1.5 |
2 |
0.9 |
1.8 |
1.5 |

Padwar |
2 |
2 |
2 |
0.8 |
1.9 |
1.5 |

Thoat |
2 |
3.5 |
3 |
1.2 |
2.9 |
3 |

Thoat (jumping) |
3 |
NA |
3 |
2.7 |
4.3 |
4 |

Dwar |
3 |
5 |
4 |
2.3 |
3.9 |
4 |

Flier |
5 |
5 |
4 |
4.7 |
5.8 |
5 |

Chief |
10 |
10 |
10 |
19.1 |
20.2 |
20 |

Princess |
(1) |
- |
0 |
2.6 |
10.1 |
- |

I sincerely hope that this text is not the final word on the subject of Jetan scoring. But I also hope that while we are waiting for something better to come along, the above figures give the Jetan player a tool to use when playing the game. Then with increased experience, the player can form his or her own opinion.

A possible next step to refine this system would be to play a lot of endgames with selected combinations of pieces set against one another. That would give one possible perspective on the usefulness of the figures. ◾️

Header image: Edgar Rice Burroughs (1922).

L. Lynn Smith’s Zillions implementation of Jetan is here.

A possible next step to refine this system would be to play a lot of endgames with selected combinations of pieces set against one another. That would give one possible perspective on the usefulness of the figures. ◾️

**References**Header image: Edgar Rice Burroughs (1922).

*The Chessmen of Mars.*A. C. McClug. [front cover], painted by J. Allen St. John.L. Lynn Smith’s Zillions implementation of Jetan is here.

- Edgar Rice Burroughs,
*The Chessmen of Mars*, Gutenberg edition, Appendix (in the Gutenberg e-text, the Appendix is appended to the end of Chapter 22, rather than as a separate segment) - Fredrik Ekman, “Exploring Jetan”,
*ERBzine*, 2019 (cited on 2021-01-01) - George Fergus, “Jetan (Martian Chess)”,
*The Gamesman*#1, The Games Bureau, circa 1965 - L. Lynn Smith, "The Game of Jetan or Martian Chess," (referenced on 2021-01-01)
- Jeff Mallett & Mark Lefler,
*Zillions of Games*[computer software], ver. 2.0.1p, 1998 – 2003 (registration is required to play the Jetan add-ons) - Jean-Louis Cazaux and Rick Knowlton,
*A World of Chess: Its Development and Variations Through Centuries and Civilizations*; McFarland & Company; 2017, p. 379 - Fredrik Ekman, ”Jetan re-evaluated”,
*Abstract Games*#19, pp. 28 – 31.