[Music] [Music] Hello chess friends and welcome to this, an obsessional, and welcome to my Basics in Chess series. So in this series we're following opening principles, middle game strategies, and the endgame strategies. Today we'll talk about some mid game strategies. Again today we'll talk about

a very important topic in chess and it's the so-called positional sacrifice. The positional sacrifice is a sacrifice in which you give up maybe a pawn for a bishop and then get a huge activity with your bishop. Your opponent has troubles to activate his rook although your

opponent would be sort of up the exchange but he has problems to activate his good piece. So the problem about positional sacrifices is when you don't activate the piece. So in order to make this positional sacrifice work, you have to get something out of it. So we need

really a new element in in the positional sacrifice. So the funny thing about this video that I'll show today, I already recorded it but accidentally deleted it from my YouTube channel. So I'm recording again but I'll do that in in the near future also again because I

think I recorded good subjects in chess but the quality of those videos wasn't good. So I am, of course, trying to improve also my YouTube channel. So I'll record many of my videos again because there weren't so many times viewed, I think, by you, but still I wanted to show you them

again because I have now also more subscribers, more viewers, and basically when I started this YouTube channel I wanted to do this kind of thing. So strategies, tactics, opening preparations, so I think now with more viewers we could really make this series work. So today, as I said, we are talking about the

mathematics of positional sacrifices so when we give up maybe a rook for a bishop and a pawn this probably isn't a good sacrifice because you gave up five points and you only got four points but in order to make this positional sacrifice work you need

another element so this another element is not a pawn it's not a knight it's not extra material that they get it's really another great element in chess which could be maybe a piece activity so as I said maybe you could give up a rook for

a bishop and a pawn but this bishop that you got has now a huge huge activity and your opponent has troubles to activate the piece sometimes we could give up a bishop and a pawn for a rook for a bishop and a pawn and create new weaknesses in your opponent's position

so we can maybe split pawns we could maybe create weak squares in your opponent's position we could even get maybe our pawns on the sixth rank we could create maybe central pawn storms with this rook sacrifice we could maybe create a rook sacrifice and then your

opponent's king could be in danger so we really need this other element without this other element this positional sacrifice won't work because your opponent will simplify the position he'll have this rook you'll have the bishop on the board okay you have maybe

an extra pawn but then he gets out of the attack and he loses the game so as I said we need this other element so I'm going to show you now some examples of positional sacrifices now we have our first example it's a game played by

Octavia ESCO against Tigran Petrosian. Tigran Petrosian here with two black pieces and in the game white tried to move the Knight to e3 in order to attack this Rook on c4, so now taking on Patterson, play the move Rxe4.

He gave up the Rook for the Bishop and a pawn, but we have now this new element, as I said, we have now another element in the game and it's now the endangered King because we have now this in danger King position. White it doesn't

have anymore light scope. Bishop and the Queen and the Bishop are building this very powerful battery. So if we, if you could just imagine now a new position in which maybe white would have some pawns in front of the King, if he could protect the light squares, then

this positional sacrifice wouldn't be correct because we wouldn't have this other mo element or in this case this endangered King situation. So that's why you see Tigran Patterson activates his Bishop. This Rook, although you're basically up the exchange, but it's not

about Rooks anymore. I think in this game it's about really this open diagonal and that's why this other element was so important in the game here. Why try tonight to see to in order to defend somehow here we have d5. The patrician

cements his great piece now. Basically this Bishop can be, it cannot be kicked away by any piece. You in order to make maybe something happen you would give up back the exchange. You would have to give up your Rook for the Bishop here. Tonight to d4 was played an hour before so pizza

Patrician attacks the Queen's side further, wants to open the position here for the bishops. We have C takes B8, B takes B8, and now a4, Queen to a7. Woodson discovered attack possibilities on the King. You have to, and now look to see, we have B3. Bishop, we have faked Patterson. He's trying to remain over the Bishop, of course, create new attacking possibilities on dark squares because you should place your bishops diagonally here. We are threatening, of course, to place our Bishop here and combine with this Bishop. The King would be really

vulnerable to this attack. So now we have Knight to B5. Point 286, Queen to D2. I'm not going to explain how all of this moves from this tactical point of view. I just wanted to show you how this rook sacrifice for a bishop

and a pawn was great in order to activate the bishop. So here, Queen to B6 again, a check, King to F1, and now Rook to C3, again a positional sacrifice. We're giving up again a rook for a knight, but we get again, I'm pointing out this

new element. We have now a new element, it's this passed pawn. So now we have a new element. Ever after Knight to, Knight takes C3. B takes C3. You see what white is here, simply on the defensive side. This rook is not great. This pawn will march on.

Support it with this bishop. So here in the game, Rook to C1, we have Queen to B3, simply taking another pawn. We have Rook to C2, C1, and then Bishop to B4. So this pawn is protected again. This is now our another element, as I

said, this pawn is protected again. This is now our another element, as I said, this pawn is protected again. This is now our another element as I

mentioned we have now again the great bishops activity a passport and all of these rocks here are basically used only as the fan of pieces so g4 we have the bishop takes c2 rook takes c2 Queen takes a for f5 here white ones to counter play once at least

maybe to split the pawn structure in front of the King and maybe create some perpetual if the position allows it of course getting maybe a draw here in the game he takes a five-eighth xf v g5 passing through keeping the position in

front of the king compact h4 we have Bishop to c5 the check it's not a check part of me after hte g5 we have Queen to f4 now comes the check and after Queen to King t1 we have Queen to g3 King to d1

we have Queen to g1 attacking Queen to e1 trades of Queens and now after H takes g5 we have a new position in which black can stay with this pawn on the board which is very important you see Petra son gave up his rook here for the night

but has has this passport you cannot take of course because you get Bishop to Bishop to b4 the pin and now it's time maybe to take this pawn and we would have a winning endgame in which we have maybe a bishop against Bishop and three

points against the rook which is of course in our common in relations if we have for instance a bishop and three palms against the rook it's worth six points against our opponents five points so this should be probably again a winning game so let's see now what

happened in the game, King to eat you here, white is forced to get out of the dark horse because, as I said, Bishop to b4 was really a serious threat here in the game. Bishop to d4 protecting the pawn, we have cooked a two, and now simply better

someplace with the King, Bishop to e5, and now after King to f6 we have a new position in which King takes f5 was played and now African 283 here, everything is perfectly protected, we have now three pawns on the board, the bishop, and it's game over here for white.

So okay, this was now a first example. Let's see now another one here is a game played by Garry Kasparov against Alex, a shear of two great technicians in a game. She loves right here 95 and he wants to of course protect his Bishop on

b7, all of these games that I'm using in the video will be in the description below so you can maybe analyze the whole games. I'm just wanted to show you this examples of dispositional sacrifices about this mathematics of positional sacrifices. We have now Knight to c5 and

the hero, Garry, as part of place a great idea, King takes rook, takes Bishop here on b7, Knight takes. And if we evaluate now this position again, we have a new element as a cell, we need new elements in this particular case, the other element is a bad bishop position.

So the only piece that basically was good on the board, the only minor piece was this Bishop on b7 because it attacked of course here the pawn on e4, that's why here Garry Kasparov gets rid of the last piece that has some kind of

an activity and after Knight to b7 we have a new position in which the knights are out of the game, the bishop is out of the game, and here after the move before here Garry Kasparov really locks these two minor pieces, he still has a flexibility to

improve, of course, the position of his bishop, he has the opportunity to play Bishop to c4, Knight to h3, so Garry Kasparov's pieces will find a way into the game. On the other hand, black's pieces are a lot of games, so we have now

this other element, as I said, this other element is the lack of activity by black's pieces, which isn't so easy to handle here for black. How to activate it, where to place our pieces in the game? Bishop to g5 here Shiro tries desperately to find some kind of

an activity, but now 1983 with preparations to play Knight to c4, then attacking here maybe the d6 weakness, so here Karpov played Knight to c4, a5, we have Bishop to d3. You see Karpov as part of piece keeps

the position compact with these pieces, they're all protecting each other. The bishop is, of course, a very nice centralized piece protecting the knight, and c4, 8x, Bc takes b4, and Queen to b8. Now h5h for attacking the bishop in a bishop to

h6, and now Knight to b6 played by Derek Karpov, you see his pieces are dancing all over the board. He's down the exchange, but the positional sacrifice was good because he had this other element. So, root j2, we have Karpov rook to D2, another problem

Queen to f3, we have Queen to a7, and now after 9 - D - it's basically a lost position for Alexei. The problem is that you cannot cover here this, this, uh, this is the problem because you get something like Bishop to b5 also.

Knight to f6 forks on the king and the rook are possible, so that's why here Alexei should have decided to give up back to exchange. If you try to move the rook somewhere else, then you get something like Knight to e7, and we can

take here this f7 pawn. So it's again a lost position for black in the game. Knight takes a knight to d8 was played. ML after Knight to f6, King perfect. And if we validate now this position, now the materials are equal, but we have created a

new great element in the chess game, and it's the passed pawn which is supported. The good thing about this pawn is that it can be placed, of course, on b5 and an effort also on b6. Again, black's pieces are simply too passive. This Bishop is

aiming in soon. I think the knight is out of the game. We can also include this rook into the game, maybe look to see one route to c8 and other ideas. So in after this couple moves, well, Garry Kasparov won the game very, very easily. So let's see now another

example here. We have a great game. It was Deep Blue against Garry Kasparov again. I got a cast part of gaming, or he's really won one of my favorite chess players. Here we have a position in which White has a very nice activity with the pieces.

The main idea could be maybe to occupy, occupy here the weakness on d5. So here, Gary Kasparov has a weak square on d5 in order to solve the raised dispositional problems. Garry Kasparov played again this rook sacrifice: rook takes c3 after b takes c3.

Let's so far calculate what we got. So we have now given up a rook for a bishop, so so far we got only three points for the rook, or Poland got five points. But now we get another element. We have first of all we can take the pawn.

Bishop takes e4 after bishop to c1. We can take king takes bishop takes g to king takes g2. And if we evaluate the position now, okay, we got a pawn and and the bishop for the rook, so so far we have four points. But we have again, I'm pointing

out this other element, this other element is now in Garry Kasparov's case, this pawn central control. So you see black has two centralized pawns. Our main goal is here to advance the pawn on d5 and then get really a nice restriction, because then this two points would

really restrict the four, this four important squares on the board. So that's why I think this positional sacrifice is perfectly fine. So we got three points for the bishop, we got one point for the pawn and a pawn central control. So at least I think black has an equal game.

Although down the exchange, but here Garry Kasparov recognized this possibility to get out of some other positional problems and he managed to get a draw. He didn't win the game, but at against Deep Blue to get a draw. This was played in 2003. This Deep Blue was also

also evolving so that's what I think it was a great accomplishment here by the legendary goddess so let's see now another example here's a very very instructive game it's a Victor Alexander which you blame ski against Mikhail Botvinnik Mikhail Botvinnik with the

black pieces has some troubles here we have to admit it because Mikhail Botvinnik has here four pawns that are weak so these are the main targets of whites black needs to do something in order to get out of this mess although black has of course the power of the

bishop ER but this bishops are not so good this Bishop is blocked out here by the c4 pawn this Bishop is blocked off by the e5 pawn and the knight is a more flexible piece of course the knight will always find a good squares on the board

of course boots on maneuvers the knight will find a way into the game but here Mikhail Botvinnik really a great player played on a positional sacrifice rook to this or he wants to improve his pawn structure he needs to do it because he

doesn't have anything left he has to improve somehow and after night 2 you want to hear Bishop to see it here after Knight takes e4 Knight is default part of me we have C takes d4 and we have now a new position after Bishop to f2 we

have c5 in which ok we got only so far the bishop for the rook of apartment the night for rook but we have now a new strategical element and it's the so called supported passed pawn the supported passed pawn it's really a powerful element

in chess it's really hard now for white to face this pawn structure the bishop is blocked out so basically we have created a new position in which white doesn't have anymore the bishop the bishop is out of game our bishops could not play we could maybe find another way to

include some other bishop this bishop suddenly has a good activity I just wanted to point you out in this particular position this bishop was out of game now basically the light squared bishop of blacks here now is the best minor piece on the board so after knight

takes d4 C takes d4 you see how Mikhail Botvinnik improved the position by a simple rook sacrifice so bishop to c4 c5 rook takes e1 and now f5 now black he's not even scared to open the

position because this bishops are aiming here against White's King so whatever you do if it's right eat X F 5 10 G takes f 5 we would have four connected pawns in the center and as I said another element can be also a central

pawn storm here I have pointed that also also this other element this other great element when you play on positional sacrifices can be really this nice central pawn storm when you get this pawns rolling in the center then of course but a white would have some

troubles here in the game the bishop to g3 was played Whiteley's desperately trying to improve the position of his pieces and now bishop to d7 we have rook to d1 and now f4 kicking away the bishop this bishop is really paralyzed now it's like it's not

even on the board I think here this bishop shouldn't be evaluated at all it's worth several points now so that's why if we evaluate this position we have basically two bishops for a rook which is a great thing so we have g5 by

Botvinnik G for after F takes G 3 Bishop takes c3 and now Bishop 2 H 3 attacking the rook the rook 2 F 2 was played and now you see Mikhail Botvinnik is just pushing forward trying again to kick

away this Bishop on G 3 we have worked to d2 and now 8 for Bishop to f2 now this rook comes very actively into the game we have a new target and it's of course the weak f3 pawn so in the game

rook to d3 rook to f4 you see how Botvinnik cements his rook basically it's this rooks are not good this rooks are out of game as I said we could we cannot evaluate now this rooks by our

common evaluations this rooks are by white are not worth 5 points I'm not sure how many points should we get get them but here this rooks are basically all of game this rook is active basically what we want to do maybe is

just improve the position of maybe this Bishop on c7 so this bishop needs improvement the Queen as a flexible piece can always of course find a way into the attack so King page 1 we have kingdom h7 root 2 G 1 and now Bishop to

Do you see how both Monique is trying to improve the position of the bishop because now at least this bishop is protecting our g5 and maybe we could sneak in somehow with the Queen into the game. So Quinta - we have Quinta f7, we

have Queen to d1 and now Queen to h4, h5 again another great move because now we could also try maybe to push the pawn on g4, Bishop to e3, Queen to f3 here, Queen takes Queen takes f3 and now after Bishop takes g5, we have Rook to d3,

bishop takes the rook, but another problem here after rook to e3, we have a completely winning endgame. You cannot protect this pawn then again we are having these two extra pawns in the center, so it's game over here for white. Oh great, great game by Botvinnik to come

up with this idea to play rook to d4, basically he was lost here. This as I said, these bishops are all of the game, the pawn structure is the bad, so that's why rook to d4 perfect move. So let's in our last example, it's a gameplay by Samuel

Reshevsky against Patterson again. Again Patterson with the black pieces, the problem here of blacks, of course, by the problem of Petrosian here is that white has here this very nice centralized point. So if white manages to do something like d5 to get this pawn

connected on the fifth rank, then it's game over here for for black. So in order to escape from this very nice attack, Tigran Petrosian, one of the best defenders, finds really great move, he plays the move rook to h6. He gives

US gives up the rook for the exchange after a four move. We have Knight to d7 after Bishop to e6. We're here at the F takes a six. What Tigran Petrosian has gained here is now a new position in which we can play, play on our blockade. So our

pardon me, move this one. So our other element here in this position is now a potential blockade on light-squares. So now basically if we evaluate this bishop activity, this bishop is out of games. So that's why this idea to play the move rook to e6 was a great line by Petrosian.

In the game, Queen to f1 was played. We have Knight to d5 attacking the rook. Rook to f3 and now Bishop to d3. You see how now the pieces are rolling, the pieces are active in this position. Rook to d3

was played by white after C takes D3.  D3 and now B for now at least Patterson managed to improve the position. This game ended in a draw, but if we go back here after the move here, this move Knight to e6 here

played by Petrosian. If you don't play it, White has a really a simple plan to play something like Bishop to f3, then maybe deep d5. So that's why this idea by Petrosian was really a great one in order to escape from this, from White's attack and as I said, he finally

got a draw. So okay, I hope you realize these ideas. Let's go to our text here. So as I said, you should evaluate your pieces by their activity, not by common evaluation. So if you get an active piece, it's probably even better. A good bishop is always better than

a bad rook, so that's why you should sometimes calculate, do I have really another element to have maybe a piece activity? Do I have maybe an endangered king position by my opponent? Can I maybe create a central pawn storm or these other great tactical elements that can

happen in a middle game? And then it really it's time to strike, to play on this positional sacrifice and maybe surprise your opponent in the middle game stage. So okay, I hope that you realize these ideas and I hope that you enjoy these videos. Meanwhile, you can

watch my other basics in chess videos from the series. Here is the link and you can also watch my best chess games of all times if you want to see the best chess games that have been ever played in chess history. See you soon with some more videos and the chess is the best of

The Mathematics in Chess! - The Mathematics of positional Sacrifices

The Mathematics in Chess! - The Mathematics of positional Sacrifices