In today’s cavalcade I’d like to allotment with you a chess aphorism the Spanish IM Michael Rahal is application on his YouTube approach to advice actuate whether a cede will assignment or not.
The aphorism says:
“Sacrifice is achievable if the cardinal of pieces advancing the castled position, additional the cardinal of weaknesses in it, beneath the cardinal of defenders, is greater than 2.”
It can be bidding by the afterward formula,
N = A W – D
N is the aftereffect of calculation,
A is the cardinal of attackers,
W is the cardinal of weaknesses,
D is the cardinal of defenders
First of all, we charge to analyze few concepts:
The castled position, we accredit to the bearings area Baron is primarily either on g8, g7, or h8 and adequate with pawns.
Attackers, abide about of pieces that beforehand the castled position either directly, or aggressive to do so in one move.
Defenders, abide of adversary pieces already attention the castled position, or those able to arise bound to rescue.
Weakness, is harder to define; we accede every assurance beforehand (as able-bodied as a assurance missing) in avant-garde of Baron as a weakness.
Now I am activity to accord an archetype to advice accept the abstraction better:
Steinitz vs. Lasker. Year 1899.
This is position from the Vienna. Atramentous ashen two moves with the Nf3-g5-f3. Lasker was not affectionate and the d accomplished quick
All the attackers are apparent in red.
Let’s accomplish a basic count:
Attackers: Bd6, Bd7, Qd5 and Nh4.
The Re8 can accompany the beforehand apace (with Re6-g6)
The added Amateur doesn’t arise to be able to accompany quickly.
Weaknesses: the h3; the f-pawn is absent.
Therefore, A W = 7
Defenders: f3, Be2, Rf1, Qd1, Bc1 (five in total)
The blueprint gives N = A W – D = 5 2 – 5 = 2, so we charge to anticipate better
The ambush is to see which defenders are not accomplishing a acceptable job to advice the King. Once we alpha artful we can see that Rf1 doesn’t help; what’s more, it is blocking the King’s escape route. The Be2 is a bald spectator, clumsy to avert the atramentous squares to be acclimated by the attackers. Likewise, the Bc1 is additionally abortive and can be larboard out from application (he is arresting g5 and h6). So I would accord the Rf1, Be2 and Bc1 alone one point (instead of three).
In the end, N = 5 2 – 3 = 4 and the cede works
The game, continued:
It can be apparent from the archetype that it’s not that accessible to assignment the cede out. In my view, the best difficult allotment is to actuate whether a allotment can accomplish its arresting assignment or not. A allotment can be far from the King, yet able to help, while sometimes a man in aing adjacency to the Baron can alone do harm, e.g. blocking it.
Now chase some added examples. I allure you to booty a attending at the positions and amount out whether the cede would be correct.
1) This is from a d of abundance (OTB)
I didn’t calculation the queen, because she accustomed too late, and the rook, because it’s blocking the baron and allowance white pieces.
2) N=2 example
3) This one is analized in this blog
N= 5 2-2=5 Alone Charlatan and abbey are defending
N=5 1-2=4 No doubt
5) This is one of the best aggregate i accept anytime apparent
N=5 1-4=2 After seeing the combination, we can see that the white queen is not a arresting allotment till the end, but d8 amateur and b7 abbey are advancing pieces. So absolutely N=7 1-3 and the aphorism works afresh
6) Morphy, of advance
N= 5 1-2= 4 (e8 amateur is useless) In this archetype the cede was adjoin a arresting piece
N= 5 0-3=2 It can work, and it works. f8 abbey is abortive and it is a N=5 0-2=3
N=4 0-2= 2 Before watching the aggregate i didn’t apperceive if e1 is an advancing piece. After watching the aggregate i see that the atramentous baron can escape by e8, and again e6!! opens the amateur column. It could attending like this:
N= 5 0-2=3 Another f8 abortive rook, and f1 abbey and c3 charlatan are advancing pieces!
10) And the aftermost one, additionally serves to absolve posicional barter sacrifices on f6/f3/c3
extra) and archetype of a N>2 that doesnt work. Tal, of advance
N= 6 0-2=4 It should work, but bone However, Tal was winning. The simple move h3 followed by g4 was accoutrement the queen.
Should I cede now in f7?
N=5 1-4 = 2 It should be calculated. In the game, White played h4 (the charlatan can not be eaten because the pieces access through cavalcade h). Atramentous answered Re8, and that acquired them to lose 1 arresting piece, while the belfry of h1 can be aing by h3-g3 Aback N=6 1-3=4 and the cede in f7 is account it.
Finally, I appetite to acknowledgment @RoaringPawn (Momir Radović) for his comment, area he allotment an affinity with warfare.
I accept never been a fan of all those chess “rules”, but all this makes faculty in a way.
A brace of years ago, I wrote on my (now defunct) blog about Mass and Advance arrangement (one of the capital attempt of warfare)
“Commanders accept consistently capital to accept the advantage of numbers. Mass, or the greatest accessible absorption of armament at the absolute point is Clausewitz’s capital assumption of war. The axiological key to accepted warfare, or any appropriate assurance in chess, that increases aition and affairs of victory, is able allotment alignment in the beforehand zone.
Massing is all-important because aegis tends to be the added able anatomy of warfare in agreement of activity bare to bottle and survive. Traditionally, it is affected that arresting force can authority off three times its own cardinal of attackers in a accepted war.That is why the cardinal of pieces complex in the beforehand charge beat arresting possibilities. It’s advance ratio, or offense-defense balance.”
And acknowledgment to him for allowance me advice this cavalcade from spanish
Thanks to the agnostic man dpcarballo. He did not assurance the rule, and I had to use one d of him (OTB) to accord him a assignment
PS: Sorry for my english, I achievement you accept it able-bodied
The Real Reason Behind 1112.1112 Forming Questions In Spanish | 112.112 Forming Questions In Spanish – 2.2 forming questions in spanish
| Encouraged in order to my personal weblog, in this time I’ll explain to you regarding 2.2 forming questions in spanish