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I don't think the win was entirely down to luck. Even though Arsenal faced considerable pressure from Tottenham but they indeed have a solid defense. Arteta knows they cannot afford to play an open and offensive game because, without Odegaard and Declan Rice, their rhythm would not have developed optimally. Therefore, they tend to play defensive football and wait for a good opportunity to counter-attack. That patience paid off, when Tottenham was so frustrated in chasing goals, it was Arsenal who broke the deadlock.
Yes, it was a good strategy from Arsenal and they succeeded in it. Winning a match full of pressure like a derby match is very difficult for both teams, but Arsenal, which has a good defense, is able to reduce so many attacks and maximize opportunities to score goals against Tottenham. Commentators said that usually derby matches have a higher possibility of penalties as usual, but not in this match.
Thanks to Arsenal's victory over Tottenham, Arsenal managed to stick closely to Manchester City with a gap of 2 points. Arsenal is in second place, followed by Newcastle with the same points (10 points) after beating Wolves away from home. Newcastle have appeared convincing so far and they are one of 3 Premier League teams who are unbeaten in 4 consecutive matches so far.