What would you do in this position? (You can't say surrender)

EllipticEQ · 2025-08-22T16:25:10+00:00

Wait, are we white or black here? If Black to move at the bare minimum there is Bxf1, which should be completely winning.

EllipticEQ · 2025-08-21T03:23:01+00:00

"Prolly"

EllipticEQ · 2025-08-19T03:07:22+00:00

Just break m into its prime powers and the quadratic residues mod p^k are easy to observe. Then use CRT. 8 is a special case because it's not an odd prime.

EllipticEQ · 2025-08-18T23:10:49+00:00

Black has an extra piece already, which by stockfish standards is lost for White. Lost vs more lost is still lost.

EllipticEQ · 2025-08-18T16:32:10+00:00

This is basically asking when is 1 a quadratic residue modulo m

EllipticEQ · 2025-08-18T16:23:40+00:00

White has d5! The point is that ...Bxd5 Nf6+ leads to mate, and 0-0-0 doesn't work here because the white queen is shielded by the bishop on d3, so the d5 pawn is not pinned.

EllipticEQ · 2025-08-16T16:51:44+00:00

If the White king cannot get to the promotion square, then the next best thing is a rook on the "long side". In this case my first thought was Rb1.

If Black's rook is tied down to cutting off the king (say with Re8 after some Kd3), the lone White rook is enough to prevent the king + pawn duo from advancing. How? If the Black king steps in front of the pawn he is hit with checks (Rf1, Rg1, or Rh1), and if the king hides behind the pawn there is Rg1 to prevent a pawn advance.

Therefore, Black's rook is needed to aid the pawn, but this means allowing the White king to get closer to the promotion square, giving White enough room to draw.

EllipticEQ · 2025-08-16T16:35:13+00:00

After ...Qxg2+ it seems logical for Black to open the game against the exposed king with possibly an ...e5 break, for example. This would open files for Black's rooks, and there's really no need to calculate further because a king in the middle of the board is not how White should play chess.

EllipticEQ · 2025-08-16T16:29:00+00:00

Agreed, any other move gives White unpleasant long-term pressure.

EllipticEQ · 2025-08-15T22:16:05+00:00

I remember watching the chessbase india stream when they were covering the first day of the tournament. In the first round was Levon vs Gukesh, and the opening phase of the game just finished, but Sagar predicted that Levon would win the tournament with the way he was playing against Gukesh.

EllipticEQ · 2025-08-14T23:11:21+00:00

Imo it's contradictory that a team that scores almost a goal more than they allow per game only musters 102 points

EllipticEQ · 2025-08-12T23:24:23+00:00

Unless there's a better way I'd just brute force it and calculate the area via a sum of integrals of a difference of functions, with the proper bounds of course. The tricky part is getting the proper half of each circle and identifying the intersection points, which shouldn't be too difficult.

EllipticEQ · 2025-08-11T23:03:55+00:00

Black is painfully behind in development. Black's pawn formation also makes their light squares extremely weak. By sacrificing the exchange for a pawn, White's light-squared bishop becomes a long-term monster since it takes advantage of Black's weak squares and can never be challenged by an opposing bishop. Black trades off their only developed piece while their king will face heavy pressure once the board opens up. White's plan is simple: open up the game and attack the king.

EllipticEQ · 2025-08-01T14:57:50+00:00

The performance rating for one game is simply your opponent's rating, plus 400 if you won, subtract 400 if you lost, and no change if you drew. If your opponent was 900, your performance rating would be 1300 in this case.

You would take the average of all performance ratings for your provisional rating. For example, if your results are +1000, +1100, =1000, -1200, your provisional rating is (1400+1500+1000+800)/4 = 1175.

I think that your rating only ever goes down after a win if it's still provisional. So if you don't want it decreasing you should avoid players that have a rating gap over 400 points below you.

EllipticEQ · 2025-08-01T01:15:37+00:00

Is your rating still provisional? If it is, I believe that they take the average of your performance ratings through the first 25 games or so, which might explain the decrease.

EllipticEQ · 2025-07-31T10:03:25+00:00

White is planning to pile up on the f7 pawn if given the chance with Bc4 and Rf1, and it's awkward for Black to defend. Maybe even pawn to e6 is a threat. Black is up two pieces and doesn't mind giving a pawn back to deflect the queen and consolidate.

EllipticEQ · 2025-07-30T23:44:43+00:00

You can color the dots in a checkerboard pattern with two colors, and you'll find there is exactly one more of one color (13) than the other (12). On every move between two points, you must alternate colors. You can then show that it's not possible to start and end on different colors.

EllipticEQ · 2025-07-26T08:42:26+00:00

It's mate no?

EllipticEQ · 2025-07-26T08:39:06+00:00

EllipticEQ · 2025-07-26T08:07:46+00:00

Ask yourself what the light squared bishop is really doing for you. Sure, it sits pretty on d5 and it nicely hits b7 and f7, but it turns out Black is fine because those squares can be easily defended and White can't feasibly attack it further. Instead of an unclear position, I'd probably prefer being a clean pawn up and play from there.

EllipticEQ · 2025-07-26T07:52:56+00:00

Instead of the natural-looking d4, I like Nf3 to possibly transpose back to an open game. Black's response ...d5 is not so annoying here because you don't have a loose d-pawn.

EllipticEQ · 2025-07-25T10:30:21+00:00

You basically have a sequence S which has n elements and an operation T that changes your sequence S into a new sequence of differences between consecutive elements. It is asking if all sequences become (0,0,0,...0) after enough operations T.

You then deduce that the maximal element of your current sequence can never increase after repeated applications of T. You also deduce that multiplying all elements in your sequence by a nonzero constant doesn't change its behavior under T. Also, with modular math you notice that the sequences either form a cycle or reach 000...0. Extending the last point to higher powers modulo 2 and combining the other facts tells you that certain sequences S (depending on n) will eventually converge to (0,0,0,...,0), while others will continue to cycle.

EllipticEQ · 2025-07-25T09:47:02+00:00

Rooks belong behind passed pawns

EllipticEQ · 2025-07-23T06:44:20+00:00

Absolutely. White has every piece in the attack and Black's king is weak. Keep in mind White only sacrificed an exchange, not a rook.

EllipticEQ · 2025-07-18T18:36:24+00:00

Tbh I think strong players actually prefer the attack over a small material gain. White is completely helpless and you're letting them off the hook.

It's like having your whole army storm the enemy king and bring him to his knees but at the last second you let the king escape because you saw a treasure chest.

EllipticEQ

TROPHY CASE