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1 The Bishop vaults over the Knight agreeably to Oriental usage. trifling modification will fit the position to our board, viz.-place the White Bishop on his Q. Kt. square, and put the White Knight on K. R. second square, then it makes a neat problem in which White mates in six moves.

On the Giving and Receiving of Odds.

The subject of odds is most minutely discussed by the author of the Asiatic Society's MS., of which the following is an abridged translation, viz. :-"Having now

explained the moves of the pieces, and their exchangeable value, I shall proceed, O reader! to inform you of the different degrees of odds established by the masters of old. A true Chess-player ought to play with all sorts of people, and, in order to do so, he must make himself acquainted with his adversary's strength, in order to determine what odds he may give or accept. A man who is unacquainted with the rules for giving or receiving odds is not worthy of the name of Chess-player. It is only by equalizing the strength of the combatants that both of them may reap amusement and edification; for what interest could a first-rate player, such as 'Adali, or Sūlī, or 'Ali Shatranjī, find in playing even with a man to whom they could each give the Knight or the Rook?

"The smallest degree of odds, then, is to allow the adversary the first move. The second degree is to give him the Half-Pawn, which consists in taking either Knight's Pawn off his own file and placing it on the Rook's third square. The third species of odds is the giving the Rook's Pawn; the fourth, that of the Knight; the fifth, that of the Bishop; the sixth, that of the Queen. The seventh degree of odds is to give the adversary the King's Pawn, which is the best on the board. The eighth species of odds is the King's Bishop. The ninth is the Queen's Bishop. The tenth degree of odds is the Queen. The eleventh, the Queen and a Pawn; or what is equivalent, a Knight; for though the Queen and Pawn be slightly inferior to the Knight at the beginning, yet you must take into account the probability of the Pawn becoming a second Queen. The twelfth species of odds is the Knight and Pawn. The thirteenth, the Rook. To give any odds beyond the Rook can apply only to women, children, and tyros. For instance, a man to whom even a first-class player can afford to give the odds of a Rook and

a Knight has no claim to be ranked among Chess-players. In fact, the two Rooks in Chess are like the two hands in the human body, and the two Knights, are as it were, the feet. Now, that man has very little to boast of on the score of manhood and valour who tells you that he has given a sound thrashing to another man who had only one hand and one foot.'

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There is one point in the preceding gradation of odds which I am unable at present to explain. All the MSS. agree in considering the Queen's Bishop of greater value than that of the King. The author of the Asiatic Society's MS. appears to have given the reason, but unfortunately his account breaks off suddenly at the end of fol. 25B., and the leaf that ought to follow is missing. So far as I understand him, it would appear that the Queen and her Bishop (which is necessarily of a different colour) contribute in certain situations to make a drawn game, which game with the King's Bishop would have been lost. It is possible, however, that some explanation on this point may be found in Dr. Lee's MSS. alluded to in p. 83. It would appear, also, that the Bishop's Pawn was considered to be slightly superior to that of the Knight; though, according to the author of the Mus. MS., No. 16,856, this point is undecided among the best players.

After due consideration of what we have just stated respecting the relative value of the pieces, and the laws laid down for the giving of odds, we are forced to infer that the Arabs and Persians must have been really fine players; for it is only among such that odds so small and so minutely graduated could have been established. We may further observe, that it was much more difficult to give the odds of the Knight or of the Rook, in the mediæval game, than it is in ours, for reasons that admit

of a very simple arithmetical demonstration. We have seen that assuming the Pawn as the unit of measurement, their aggregate value amounted to 8. The Bishop was worth between 1 and 2, say 12; then the sum of the two Bishops: 1 3. The Queen was between 2 and 3, say 2. Lastly, the sum of the two Knights = 8, and that of the two Rooks = 12; hence the whole amount of the forces 8 + 31⁄2 + 23 + 8 + 12 = 34. Dividing this last sum by 4, we shall find that the Knight formed between th and th part of the whole forces. Again, dividing the same sum by 6, we shall find that the Rook was something between th and 'th of the aggregate strength of the mimic army.

Let us now examine the relative value of the same pieces in our modern game. Assuming as before the Pawn as the unit of measurement, their amount will still be the same as above 8. The Queen is about= =

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I have adopted this scale of our modern game, with some modification from those given by Mr. Pratt in his edition of Philidor, 1826, and by Mr. Tomlinson in his useful little work, entitled "Amusements in Chess," London, 1845. In Tomlinson's work the value assigned to the Knight is 3·05, and the Bishop 3.50. This I hold to be erroneous, as giving an undue superiority to the Bishop over the Knight. I adopt, therefore, Mr. Pratt's scale, allowing the Knight 31, and the Bishop 31, and I much doubt whether this be not too large a distinction, for in practice the Knight and Bishop are generally admitted to be of equal value. Again I differ from both of these savans as to the value of the Queen. Pratt makes the Rook 5.55, and the Queen only 10, as much as to say that the two Rooks are worth more than a Queen and a Pawn! whereas it ought to be, as a general rule, quite the reverse, so far as the Pawn is concerned. In practice the Queen, especially in the early part of the game, is equal to two Rooks and one Pawn, as every good Chess-player knows; and it is only when the board has become somewhat cleared of the men that the two Rooks combined approximate or equal the Queen. I have set down the latter then as 11, and I rather think 12 would have been the more correct figure. I have not taken the King into account in either of the preceding scales, as he has precisely the same power in both the medieval and modern game. His value, as an attacking piece was, in the oriental game, a little more than that of the Knight, and in our game it is somewhat less, for our King is compelled to act with more caution owing to the increased power of the Queen and Bishops. In fact our final results would have been as nearly as possible the same whether we reckoned the King or not in our calculations. To conclude, then, the player who

the Rook 5, consequently the two Rooks = 11; the Knight 31, or, the two Knights together = 6; the Bishop 31, or the two Bishops = 7. Hence the aggregate value of the forces on our board is = 8 + 111⁄2 1⁄2 + 11 + 6 + 7 = 44; and dividing by 34, the nominal value of the Knight, we find that the latter is only between theth and th part of the whole forces. Dividing in like manner by 5 we have the fractional value of the Rook, which is exactly 4th of the united forces.

The Five Classes of Chess-players.

"The Arabs and Persians divided Chess-players into five classes, viz.-1st, the 'Aliyat or 'Class of Grandees,' of whom seldom three exist at the same time. It is stated in the old Arabic MS. that 'Adali for some time remained alone of his class, and that the same thing happened to Al-'Arī, a more recent Arabian player, and also to Ibn Dandan and Al-Kunaf, both of Bagdad. The second class consists of such players as are able to win only two or three games out of ten when playing even with one of the 'Aliyat; the difference between the two classes being reckoned equal, on an average, to a Pawn; that is, a player of the first-class could give to the very best of the second class a Rook's Pawn, and to the weakest of the same class the King's Pawn. The third

gave the odds of the Knight in the Oriental game deprived himself of four out of 344; whereas the same odds in our game amounts only to the giving up of 3 out of 44. He who gave the odds of the Rook in the former game, gave up 6 out of 344, whereas with us it is only 5 out of 44. It follows, then, that the odds of the Knight in the medieval game was equivalent to that of the Knight, a Pawn, and very nearly half a Pawn in ours. In like manner we find that the odds of the Rook in the former equalled the odds of the Rook and two Pawns in our game. Finally, the odds of the Knight in the Shatranj was very nearly equivalent to that of the Rook in the modern game.

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