You got it totally wrong.hgm wrote:A bet that IMO you already lost, based on the presented evidence. The 7 Knights were shown to win, even in starting positions where they did not protect each other at all, where the Pawns were fully spread out, and even when one resorted to giving them ridiculous other disadvantages, like starting their King in front of the Pawn chan, on g6.
The Bishops, however, seem to do no better than about 50%.
6 Knights also win against 3 Queens, when the side handling the Queens is slightly incompetent (e.g. does not strive for Q vs 2N, or, when it does, has less search depth than the Knights opponent that knows the danger, and thus can succesfully avoid them). 6 Bishops against 3 Queens do not stand a chance when the latter strives for Q-2B trades.
I think the most important difference is that it is very difficult for Bishops to keep them all twice protected, while for Knights this is easy. The Bishops are distributed over different colors, so with 6 you would have 3 on each color, and the only way to let them mutually protect each other twice is to put them on the same diagonal. Where they then sort of become frozen, as it would take several moves during which you are heavily exposed to switch them to another diagonal. And on the diagonal they hardly do anything useful. The opponent simply avoids that diagonal, and perpendicular to it there are only single Bishop attacts, for which single protection by a superior piece is sufficient defense.
A 2-for-1 trade-avoiding strategy for the Bishops against 3 Queens is extremely costly in terms of their usefulness (i.e. causes strong depression of their piece value), while to Knights it comes naturally. (And of course neither of them has to worry about 1-for-1 trades, which would be even more costly to avoid, basically requiring your pieces to remain under lock and key, not doing anything at all.)
The raw tactical power of a cloud of 6 Knights already inflicts a devaluation on the Queens that makes 3 Queens inferior to them. It is just that this situation can be relaxed through Q-for-2N trades that saves the day for the Queens. My prediction is therefore that 8 Knights would beat 4 Queens, despite the fact that the N-to-Q ratio is exactly 2, and Q-2N trades would be a winning path. With 8 Knights the Knights should be able to mutually protect each other well enough that no amount of Queen tactics can force a Q-2N trade. With 8 Bishops against 4 Queens, OTOH, the Bishops should be toast.
Note that mutual protection does not help you win games (although it could be great for drawing them). Essential is how much the pieces are able to do on the side, while protecting each other. The mutual protection is certainly part of the equation, as explained before: it saturates the amount of depression of the higher piece value, because no matter how dysfunctional, a piece is at least worth as much as what you are going to trade it for(*). With Queens versus Archbishops the suppression of the Queens can never get very large, as there is no way the Archbishops are going to avoid 1-on-1 trades. The mutual defense only becomes an issue when the survival of the strong-piece side hinges on 2-for-1 trades.
*) I discovered this when determining the opening value of the Camel (a (3,1) leaper), which is an absolutely worthless piece, that in the end-game is virtually always lost without any compensation at all. Yet its opening value came out very close to that of the other minors, because it has enough forking power to trade it for one when the opponent still has such minors in abundant quantity.
No one ever provided data that 7Ns perform better vs 3Qs than 7Bs would. On the contrary: the scarce evidence we have suggests otherwise.
Bishops excellently protect each other 2 and more times, for example you have black Bc5, d6, e5, d6 is protected by both c5 and e5, and they are on different diagonals, so that this is not a very much redundant control.
Bsihops build excellent diagonal batteries, that knights do not, and they are able to attack from a distance, something that knights do not do.
Bishops complement better, something that knights do not do.
So, basically, there are couple of elements where bishops excel. Where do knights excel?
But even if you run a longer match of TQueeny vs itself in the 2 imbalances with some randomness (although TQueeny is just stronger than Queeny, but not the ultimate choice, as it still makes many mistakes), you will see that the bishops perform relatively better.
