Season 16 league 1 playoff results

Final crosstable:

ScorpioNN and Stoofvlees promote to the premier division. Two more NN engines enter the top TCEC division, after starting from the qualification league this season.

Ethereal was still in the race until it lost in the last game of the playoff. 

Notable games:

Game 1, Stoofvlees - ScorpioNN: Stoofvlees had a small eval advantage for over 60 moves, but it lost its queen to a simple knight sacrifice and this was enough for ScorpioNN to win. What a way to start the playoff.

Game 2, Laser - Ethereal: There were almost no exchanges in the game, when the position started to open after 50 moves Laser had an advantage with a bishop pair to Ethereal's knights. Ethereal gave a pawn for some initiative but nothing came out of it. Laser went 3 pawns up and reduced to a winning RB vs RN position. 

Game 4, Stoofvlees - Laser: The black pieces on the king side were almost trapped. Stoofvlees gradually exchanged pieces and when the position opened it was a pawn up in a RN vs RB position. Laser's king was stuck in the corner while the white king came forward, a second pawn gave Stoofvlees the win. 

Game 5, Laser - ScorpioNN: Laser went up a pawn but ScorpioNN had the eval advantage. The black major pieces were strong in the open files, ScorpioNN placed two rooks on the 2nd rank and Laser was forced to give a rook for a knight to block a passer. The RB vs RR position was a win for ScorpioNN.


After RR1: ScorpioNN +2, Stoofvlees 0, Laser Ethereal -1, 4/6 decisive games. A good start for ScorpioNN, Stoofvlees has to be careful with its blunders.

Game 9, Ethereal - ScorpioNN: The game reached a QRB vs QRB position, Ethereal was a pawn up but evals were low. The game seemed to heading for a draw after a long shuffle, then Ethereal captured a second pawn and evals jumped. The black king was threatened and ScorpioNN gave more material to save it, losing the game.

Game 12, Stoofvlees - Ethereal: Stoofvlees gave a rook for a bishop and pawn, the game reached a QRB vs QRR closed position. The engines shuffled and exchanged pawns, Ethereal took a pawn on move 59 and evals jumped. The black king was exposed to attack and Stoofvlees forced a queen exchange, leading to a RB vs RR ending with connected advanced white passers, giving Stoofvlees the win.

After RR2: ScorpioNN Stoofvlees +1, Laser Ethereal -1. The two NN engines are in front, all engines have at least one win and one loss. All 6 game pairs had a 1.5-0.5 score, one decisive game per pair.

Game 16, Stoofvlees - Laser: Stoofvlees gave its queen for two bishops early in the game. Evals stayed low until Laser gave a rook for a knight, evals jumped in favor of Stoofvlees in a RBB vs QN imbalance. Stoofvlees pushed a pawn to the 7th rank and evals came back down, Laser found a perpetual check draw. Probably a missed chance for Stoofvlees.

All games were draws in RR3, no change in the standings. Any decisive game in the last round can have a big effect on the playoff result.

Game 20, Ethereal - Laser: Ethereal was a pawn up with an advanced passer, evals increased as the engines exchanged pieces. Laser tried to counter with an attack on the white king, eventually it captured the passer but lost a knight. The QRN vs QR position was a win for Ethereal.

Laser is 1.5 points behind with 2 games left, it is almost surely out of the race. Ethereal improved its chances, only 0.5 points behind.

Game 21, Ethereal - ScorpioNN: The game reached a RRB vs RRB position with Ethereal a pawn up, but ScorpioNN held the draw.

Game 24, Stoofvlees - Ethereal: Ethereal got into trouble in the opening, its queen attacked alone and captured a pawn on the queen side while Stoofvlees pushed pawns on the king side. Evals jumped high as Stoofvlees captured a knight for pawns, the win was just a matter of time.

Season 16 league 1 statistics

A summary statistics table of previous stages and seasons. 

Draw rate, wins


Final draw rate was 62.5%.


Game termination

The three most common game termination causes were:


29.2% - TCEC draw rule

26.7% - SyzygyTB
22.5% - TCEC win rule


There were 6 crashes in the stage: Booot crashed 3 times and was disqualified, Ginkgo crashed twice and Laser once.

Moves per game


Median= 60.8
Average= 66.6

There were 21 games longer than 100 moves, the longest was 238 moves (Arasan - Ethereal, game 121, Ethereal won).

Time per game (hours)


Median= 1:30
Average= 1:26

Openings

There were 6-move book openings in this stage chosen by Cato. The first letter of the ECO codes was distributed as follows:


The engines had little freedom to choose the opening variant, 75.8% of the game pairs repeated the same ECO code twice, and 71.7% repeated the same opening variant. In 2.5% of the game pairs the ECO first letter was not repeated twice.

Reverse pairs, wins


Reverse pairs, same moves 


Pairs of reverse games diverged very quickly, 38.3% diverged immediately out of book, 74.2% of the pairs diverged at most after 1 move. The longest repeated sequence of moves was 13 plys (Andscacs - Ethereal games 35 and 155, French Tarasch closed variation, Andscacs won in white)

Season 16 league 1, final results

Final crosstable:
Stoofvlees +10, Laser +6, ScorpioNN Ethereal +5, Chiron Xiphos Andscacs +3, Fizbo Ginkgo +1, ChessBrain -1, rofChade Jonny -2, Arasan -5, Pedone -10, Fire -17, Booot DQ.

Stoofvlees, Laser, ScorpioNN and Ethereal will play a 2-DRR playoff to determine which two engines promote to the premier league. Stoofvlees and ScorpioNN continue on their "qualification to premier" journey, Ethereal and Laser will try to stop at least one of them in the playoff.

Arasan, Pedone, Fire and Booot are relegated to league 2. Arasan and Pedone go back immediately after promoting from league 2. Booot was disqualified after 3 crashes. Fire's new partial NN version was weaker than the original, perhaps it will get stronger and climb back up again next season.

Notable games:

Game 130, Chiron - ChessBrain: ChessBrain had a queen side passer in a closed position. Evals jumped after the king side opened, Chiron gave a rook for a knight to defend its king. ChessBrain pushed the passer and made threats on both sides of the board, Chiron's defense collapsed. 

Game 151, Laser - Ethereal: 3-fold draw after 19 moves.

Game 159, rofChade - Ginkgo: rofChade had connected queen side passers in a RBB vs RBN position. Eventually Ginkgo traded pieces and reduced to a R vs BN ending, but two extra white pawns gave the win to rofChade.


After 20 rounds: Stoofvlees +7, Ethereal +4, ScorpioNN Laser +3, Ginkgo Xiphos Andscacs +2, Chiron +1, ChessBrain Fizbo 0, Jonny -1, Booot Arasan rofChade -2,  Pedone -8, Fire -9. Many engines still in the race for the top 4 places, Stoofvlees firmly in the lead. Pedone and Fire are close to relegation, two more spots still contested. Ginkgo and Booot have two crashes each and are in danger of disqualification.

Game 179, ChessBrain - ScorpioNN: ScorpioNN was close to a win in a queen ending two pawns up, but it couldn't find the winning moves and ChessBrain held the draw.

Game 189, Ethereal - Ginkgo:  Ethereal created an advanced central passer and reduced to a RRN vs RRB position with an extra pawn. Ginkgo eventually lost a piece to stop the pawn, leading to a winning RN vs R ending.

After 24 rounds: Stoofvlees +8, Ethereal +5, Chiron Laser +4, ScorpioNN Xiphos Andscacs +3, Fizbo +1, Ginkgo 0, ChessBrain -1, Jonny rofChade -2, Arasan -3, Pedone -9, Fire -14, Booot DQ. Booot crashes for the third time and is disqualified, its games not considered. With 6 games left there is only one relegation spot open. At the top Chiron joined the race while Ginkgo lost touch with the leaders. There are 6 engines in the race for 3 spots. Top engines that still have to play Booot (effectively these engines have one less game to play): Ethereal, Xiphos, Laser, Andscacs. 

Game 208, ScorpioNN - Stoofvlees: Stoofvlees had an eval advantage in a closed position, the position opened and the game reached a RN vs RR ending. Stoofvlees pushed a passer to the 2nd rank and failed to see an immediate mate threat, it delayed as much as possible but still ScorpioNN mated.

After 27 rounds: Stoofvlees +9, ScorpioNN Laser Ethereal +5, Chiron +4, Xiphos Andscacs +3, Ginkgo +1, Fizbo 0, ChessBrain -1, rofChade Jonny -2, Arasan -5, Pedone -10, Fire -15, Booot DQ. Only 3 games left to play. Arasan is the most probable 4th engine to relegate. At the top ScorpioNN improved its position, the race is still close.

Game 218, Fizbo - Chiron: The game reached a RRN vs RRB position, the white king came forward and the movement of the black pieces was restricted. Fizbo captured two pawns and reduced to a winning RN vs RB ending.

In round 28 Ethereal draws Stoofvlees, Chiron takes a step back, Arasan draws Jonny and its chances of escape are low, rofChade beats Fire and is almost surely safe from relegation.

In round 29 all relevant games were draws, Arasan can escape only if Ginkgo crashes, at the top ScorpioNN, Laser and Ethereal are one point clear of the chasing engines. 

In the last round Ginkgo did not crash and Arasan relegates. Xiphos and Chiron drew their games, Andscacs' last game was against Booot, none of them catch up with the leaders. Laser added a win and it finishes in 2nd place.

Season 16 league 1, first half

Standings after 15 rounds:

Stoofvlees +6, Ethereal Ginkgo +3, Chiron Andscacs ScorpioNN +2, Laser +1, Fizbo Xiphos 0, Jonny rofChade Booot -1, ChessBrain Arasan -2, Fire Pedone -6.

I'm back from my vacation, and already 2/3 of league 1 is over. My TCEC backlog is about 160 games and I won't be able to look at them closely. This post will be written gradually over a few days, I'll try to finish it quickly. TCEC waits for no one, and I hate backlogs...

A few remarks:
- Stoofvlees is dominating this league as well, though it sometimes blunders and loses.
- The race at the top of the table is wide open. In this league the top 4 will play a playoff to determine the two qualifiers.
- At the bottom Pedone and Fire seem to be likely relegation candidates. The other two spots are still contested. Fire's new version is an AB-NN hybrid, and it appears to be worse than the AB version.
- Ginkgo, Booot and Laser have each crashed once so far.


Notable games

Game 17, FireNN - Arasan: 3-fold repeat after 15 moves, (including a 6-move book)

Game 18, Xiphos - Ethereal: an even smaller miniature in the next game, 3-fold repeat after only 13 moves.

Game 21, Fizbo - Stoofvlees: In the middle of a series of exchanges Stoofvlees failed to consider Fizbo's queen sacrifice. It realized its mistake too late and Fizbo reached mate on the board.

Game 31, Ethereal - Laser: Ethereal sacrificed material and got a strong attack on the black king. Laser gave the material back but the bishop ending was a win for Ethereal.

Game 35, Andscacs - Ethereal: The game reached a N vs B endgame. Andscacs trapped the bishop with its pawns, then used its knight to capture black pawns. Two connected passers were enough for a win.

Game 43, Stoofvlees - Ginkgo: Ginkgo had a trapped bishop dominated by a white knight. The game reached a RN vs RB position, Ginkgo used a passer to trade its bishop for a rook, however, the forward white king captured black pawns and secured a tablebase win for Stoofvlees.

Game 48, Xiphos - Laser: The game reached a queen ending with Xiphos a pawn up. Laser blundered under time pressure and Xiphos had enough time to find the winning moves.

Game 88, Stoofvlees - ScorpioNN: Stoofvlees gave a rook for a bishop early, yet evals were over 1. The game reached a BN vs RN position, Stoofvlees had passers on the queen side and ScorpioNN couldn't prevent promotion. This was the first ScorpioNN loss in season 16.

Game 90, Pedone - Stoofvlees: Stoofvlees gave a pawn early, then in a QRB vs QRB position it gave a second pawn but failed to see its king was in danger. Pedone won material and reduced to a winning king and pawns endgame.

Game 93, Xiphos - ChessBrain: ChessBrain's bishops were strong in a RR vs RBB endgame. After stopping a white passer and exchanging a pair of rooks ChessBrain's bishops captured enough white pawns for a win.

Game 94, Laser - Ginkgo: The game reached a queen ending, Laser had an eval advantage, the black pawns were scattered and the black king was exposed. However, Laser crashed and Ginkgo got the point.

Game 95, Andscacs - Chiron: Andscacs gave a rook for a knight and pawns.In the N vs R endgame Chiron played better, after a few pawn exchanges the rook was strong enough for a win.

Game 103, Stoofvlees - Ethereal: Stoofvlees sacrificed a bishop and exposed the black king. Ethereal's king walked to the center for safety, Stoofvlees placed a strong knight on the 6th rank. Ethereal exchanged pieces until only R vs RN remained, the white rook on the 7th rank and two advanced passers gave Stoofvlees the win.

Game 106, Ethereal - ScorpioNN: ScorpioNN blundered under time pressure in a double bishop ending, Ethereal exchanged a pair of bishops and the remaining black pieces were passive. Ethereal captured a pawn and ScorpioNN could not prevent a white passer from queening.

Game 112, Jonny - Chiron: After long shuffles evals started jumping in a QB vs QB position. Jonny went two pawns up and pushed its pawns slowly. Chiron gave many checks but couldn't force a perpetual check draw to stop the pawns.

Game 118: Stoofvlees - Xiphos: Stoofvlees created a queen side passer, Xiphos gave a rook for a bishop to stop it. Stoofvlees gave the material back to get a winning bishop ending a pawn up.

Season 16 league 2, final results

Final crosstable



Stoofvlees, ScorpioNN, Pedone and Arasan advance to league 1. The two NN engines Stoofvlees and ScorpionNN dominated the league, ScorpioNN had a +7 perfomance in the second half and ended the league without a loss. Arasan barely qualifed after a weak second half. The qualification race continued until the very last game.
 
Wasp, Nirvana, chess22k, Pirarucu, Marvin and Topple relegate down to qualification. The 4 AB qualifiers did not survive league 2. Nirvana had a weak second half performance of -6. Gull managed to stay in the league and it is safe for at least another TCEC season.

Next comes league 1 with Ethereal, Fire, Xiphos, Laser, Andscacs, Fizbo, Jonny, Chiron, Ginkgo, ChessBrain, Booot, rofChade and the 4 qualifying engines from league 2. The games will be longer at 45' per engine.

I will be mostly on vacation in the next two weeks, I'll try to catch up when i get back...


Notable games

Game 121, chess22k - Fritz: The game reached a RN vs RN position, the white king was trapped on the back rank and Fritz had a passer on the 3rd rank. Evals peaked over 2 for black but chess22k managed to hold the draw.

Game 132, Gull - Stoofvlees: Gull seemed to hold in a QN vs QB position. After 50 moves the engines exchanged all pieces and Stoofvlees was up a pawn. Both engines promoted a pawn to get a queen ending, Gull could still hold but without tablebase support it allowed Stoofvlees to reach a won 6-man position.

Game 143, ScorpioNN - Nemorino: ScorpioNN played better in a R vs NN ending two pawns up, Nemorino could not stop the passers on both sides of the board.

Game 147, Nemorino - Stoofvlees: Nemorino was two pawns up in a RRN vs RRB position, Stoofvlees' only counter was a rook on the 2nd rank. Nemorino couldn't find the right path and had to settle for a draw.

Game 149, Gull - Wasp: Gull had an advantage from the start. It won material through a king side attack, the game reached RRN vs RBN position. It took a while but Gull converted the win in the end.

Game 151, Texel - Fritz: The game reached a Q vs RR imbalance and for a long while the engines exchanged pawns until each had two left. Fritz slowly outplayed Texel, it managed to push a pawn forward until Texel was forced to give a piece to stop it, and won the game.

After 20 rounds the table was: Stoofvlees +11, Arasan +8, ScorpioNN +7, Pedone +5, Fritz +4, Nemorino and Texel +3, Vajolet 0. Wasp Gull and Nirvana -2, RubiChess -3, chess22k -5, Pirarucu -7, Topple -10, Marvin -10. With 10 games to go both the top and bottom races are open, though Stoofvlees will probably advance (3.5 points gap) and Topple and Marvin will relegate (4 points gap).

Game 171, Nirvana - Gull: The engines played a RN vs BBN ending for a long time. It took Gull more than 70 moves to create a passer, it gave a bishop but Nirvana gave the material back and more and tried to stop the passer. In the end Gull pushed the passer to promotion and won.

Game 172, Fritz - Pedone: Pedone gave a knight for two pawns and exposed the white king to attack. Fritz found safety for its king and reduced to a winning RB vs R ending.

Game 186, Texel - Gull: Texel opened the position with a rook for pawns sacrifice. Gull slowly exchanged pieces and the 4 extra pawns were not enough. In a RN vs B position Gull's remaining 2 pawns gave it the win.

Game 187, Arasan - Pedone: An advanced passer gave Pedone an advantage when the position opened. The game reached a double rook ending, a second advanced passer gave Pedone the win.

Game 192, Marvin - Stoofvlees: Stoofvlees gave a knight for pawns to create an advanced passer, Marvin blocked it and stayed calm. Stoofvlees then gave a second knight and attacked the white king, the attack failed and instead Marvin found mate.

After 24 rounds the table was: Stoofvlees +12, ScorpioNN +9, Arasan and Pedone +7, Nemorino +6, Fritz +5, Texel +3, Gull  and Vajolet 0, RubiChess -2, Wasp -3, Nirvana -5, chess22k and Pirarucu -8, Marvin -10, Topple -13. Only 6 games left, ScorpioNN improved its position and will probably advance, chess22k and Pirarucu are close to relegation. There is a tight race of 4 engines for two qualifying spots at the top of the table. Gull improved its position and has a good chance of surviving this season.

Game 198, Nemorino - Arasan: The engines mostly shuffled for a long time. Arasan gave a knight and two pawns for a rook, giving Nemorino connected passers in the center in a NN vs RB position. The white king came forward to support the pawns, Arasan had to give a piece to stop a passer and lost the game.

Game 202, Vajolet - Pedone: Vajolet had a space advantage in a closed position. Pedone gave a rook for a bishop and pawn, after the position opened the game reached a Q vs RB opening. The white queen was strong enough to give Vajolet the win.

Game 203, Texel - Nemorino: When the engines opened the position the game reduced to a QR vs QR endgame. The black king was exposed and Texel had an advantage. It slowly improved its position and then exchanged rooks and went up a pawn. The queen ending with an advanced passer was a win for Texel.

Game 209, Wasp - chess22k:The game reached a RRN vs RRN position, the black rooks were strong and the white knight was pinned. chess22k captured two pawns and  reduced to a winning RN vs RN endgame.


After 27 rounds the table was: Stoofvlees +14, ScorpioNN +11, Nemorino Pedone Arasan and Fritz +6, Texel +4, Vajolet +2, Gull and RubiChess -1, Wasp -4, Nirvana -6, chess22k -7, Pirarucu -10, Marvin -11, Topple -15. The bottom of the table is getting clear, only Wasp has a small chance to escape relegation but it has to close the 1.5 points gap in 3 games. At the top 4 engines are tied in the race for two spots, and evel Texel still has a chance.

Game 218, Gull - Nemorino: Gull gave a rook for a bishop and pawn, the game reached a BN vs RB position. Gull created connected passers on the king side and Nemorino gave the rook to stop them, the remaining white pawns were enough for a win.

After 28 rounds the race at the top was: Pedone Arasan and Fritz +6, Nemorino and Texel +5. At the bottom the gap for Wasp is still 1.5 points, two games remaining. 

Game 231, RubiChess - Gull: The game reached a RB vs RB position and seemed to be a draw with the engines shuffling. Then Gull blundered and allowed RubiChess to exchange rooks, the bishops were of opposite colors but RubiChess created advanced passers that were enough to win.

Game 232, Nemorino - Pedone: Pedone was better after the opening, it had a space advantage and it pushed the queen side pawns facing the white king. An advanced passer cost Nemorino a rook and the game.

One round to go. Wasp cannot close the gap after RubiChess won, the relegation race is over. At the top the scores are: Pedone +7, Arasan and Fritz +6, Texel +5, Nemorino +4. Nothing is over but Pedone improved its chances and Nemorino is almost surely out.

Nemorino and Pedone won, Texel lost, as a result Pedone ensured 3rd place and Texel was in 7th place. Arasan drew its game, so Nemorino was out. Fritz needed a win in its last game since Arasan was better on tiebreaks. However, Fritz only drew against Topple, and Arasan qualified.

Season 16 league 2 statistics

A summary statistics table of previous stages and seasons. 

Draw rate, wins


Final draw rate was 50%.


Game termination

The three most common game termination causes were:


30.8% - TCEC win rule
29.2% - SyzygyTB
25.8% - TCEC draw rule

There were 3 crashes in the stage: RubiChess once and chess22k twice. There were 8 games that ended in mate, the evals of ScorpioNN and Stoofvlees were usually not high enough to invoke the win rule.

Moves per game


Median= 63.5
Average= 69.4

There were 27 games longer than 100 moves, the longest was 197 moves (Fritz - Gull, game 46, draw).

Time per game (hours)


Median= 1:03
Average= 1:02

Openings

There were 4-move book openings in this stage chosen by Cato. The first letter of the ECO codes was distributed as follows:


The engines had less freedom to choose the opening variant, 81.7% of the game pairs repeated the same ECO code twice, and 78.3% repeated the same opening variant. In 4.2% of the game pairs the ECO first letter was not repeated twice.

Reverse pairs, wins


Reverse pairs, same moves 


Pairs of reverse games diverged very quickly, 33.3% diverged immediately out of book, 80.8% of the pairs diverged at most after 1 move. The longest repeated sequence of moves was 17 plys (Wasp - Nirvana games 119 and 239, QGA Bogolyubov variation with 4 queens on the board, Wasp won in black) 

Season 16 league 2, first half

Standings after 15 rounds:
Stoofvlees +7, Arasan +6, ScorpioNN and Pedone +4, Fritz and Nemorino +3, Texel +1, Wasp Vajolet and Nirvana 0, chess22k RubiChess and Gull -2, Pirarucu -6, Marvin -7, Topple -9.

The two NN qualifiers, Stoofvlees and ScorpioNN, are doing well in league 2 and have a good chance of moving up again. Stoofvlees has the most wins so far, but it makes mistakes occasionally and loses to weaker opponents. ScorpioNN has no losses so far, but it has many draws against the bottom half of the table.

Arasan is also doing well in this league. It appeared in TCEC at least from season 7, never getting great results. It played the last two seasons in division 3, this time it appears to be better than other engines that were in division 3 last season.

There are 4 qualifiers in this league, the race is still open and there are at least 6 engines with a good chance.

Of the 4 AB qualifiers only Wasp and chess22k have a chance to stay in league 2, Marvin and Topple are on their way back down.

There are 6 engines that will be relegated, and one of these may well be Gull. Gull has been in TCEC at least from season 4, the first season I saw. In season 8 it was 3rd in stage 3 which was the last stage before the superfinal, with a better score than Houdini. It has not been updated since then and it has slowly drifted downward in the divisions. If it relegates it may not play again in TCEC, since engines currently under development are preferred.

Of the other engines at the bottom of the table it is interesting to note that RubiChess has two wins against the table leaders, Arasan and Stoofvlees, and a draw against ScorpioNN. It needs to lose less against the lower ranked engines if it wants to get away from the danger zone.

Notable games


Game 22, Pedone - Stoofvlees: Pedone blundered in a N vs B ending, Stoofvlees was able to capture a pawn. Using zugzwang the black king infiltrated behind the white pawns and won the game.

Game 26, ScorpioNN - RubiChess: ScorpioNN gave two pawns but had a strong king side attack in a closed position. After the position opened RubiChess lost a piece, the game reduced to a RB vs R ending and ScorpioNN could only get a draw.

Game 27, Stoofvlees - Nemorino: Stoofvlees missed a long move sequence by Nemorino and its king got caught in a mating net. Stoofvlees had no tablebase support and it failed to see that the resulting RN vs Q position was a loss.

Game 39, RubiChess - Stoofvlees: Stoofvlees gave a pawn early, then gave more and more material and tried to attack the white king. RubiChess held on, the white king escaped and the material advantage gave RubiChess an easy win.

Game 63, Arasan - Gull: The game reached a QN vs QR position with Arasan three pawns up. Gull thought it was safe enough to exchange rook and knight, without tablebase support it didn't realize the queen ending was a win for Arasan.

Game 84, RubiChess - Arasan: RubiChess gave a bishop for a crushing attack on the black king. Arasan gave the piece back, the game reduced to a BN vs BN ending and the white king charged forward and cleared the black queen side pawns. This created a passer that won the game for RubiChess.

Game 108, Arasan - Stoofvlees: In a position with a closed center Arasan opened the queen side and neglected the long black pawn line closing on its king on the king side. Stoofvlees used a pawn on g3 to open the king side and win material, reaching a BN vs Q imbalance that was enough to win the game.