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One should Daven Maariv before doing the Bedika if a Minyan is now available and it will be difficult to gather a Minyan later on, or if one usually Davens with a Minyan, and tonight there is no Minyan available, and he will thus be Davening alone. However, if one normally Davens Maariv without a Minyan, then he is to first perform the Bedika and only then Daven Maariv. [However, the Chabad custom is to always Daven Maariv before the Bedika, in all cases.]
 Admur 431:8 “If there are ten people that desire to daven Maariv at its proper time, which is at nightfall, then they should daven immediately at nightfall, and then go to their homes to check the Chametz.”
The reason: The reason for this is because if they first go home to check their Chametz it will be troublesome to re-gather the Minyan to daven afterwards, and the Mitzvah of Davening with a congregation will thus be completely nullified due to having first done the Bedika. However, if they daven Maariv before they do the Bedika, the Bedika will not be nullified, [and thus it is better to first daven]. [Admur ibid]
Appointing a Shliach: Some Poskim rule that one should appoint someone else in his place to check while he Davens, as then he fulfills both of the Mitzvahs. [M”A 431:5; M”B 431:8; Chayeh Adam] Admur omits this ruling. Perhaps this is because it is a greater Mitzvah to check oneself than to appoint a shliach.
 Admur 431:7 “If throughout the year one normally Davens Maariv with a minyan before nightfall, and missed the Minyan on the eve of the 14th, then he should daven immediately upon nightfall, and do the Bedika only after Davening.” Seemingly, the same would apply after nightfall as well
The reason: The reason for this is because since he is not accustomed to Daven Maariv at home, we suspect that [if we were to have him first do the Bedika] then due to his involvement and pursuit of checking for Chametz, he may come to [completely] forget about saying the Shema and praying. [Admur ibid]
Appointing a Shliach: See previous footnote
 Admur 431:6
The reason: Although the reading of Shema of night is a Biblical positive command and is also a constant obligation which applies every single day, twice a day, and the Mitzvah which is more common is to be given precedence, nevertheless, one needs to proceed the checking of Chametz to saying the Shema and Prayer. The reason for this is because the checking for Chametz is a passing mitzvah. As if one does not do the Bedika immediately, then he has transgressed a Rabbinical command, however the reading of the Shema, even though it’s a Mitzvah Min Hamuvchar to read it at the beginning of the night, nevertheless, he is not considered to be transgressing the institution of the sages [by delaying its reading] unless one delays reading it until after midnight, as explained in chapter 235. [Admur ibid]
Other opinions: Some Poskim rule that one should always daven Maariv first, as Maariv is Tadir. [Chok Yaakov 431, brought in Kuntrus Acharon 431; Admur ibid explains why Tadir does not overrule in this case.] Some Poskim rule there is no Rabbinical obligation to check immediately at night, [and it is thus not really understood according to them why one should first do the Bedika rather than daven, which is more Tadir] [M”B 431:1. See also Halacha 4A]
 Hayom Yom 14th Nissan; Letter of Rebbe printed in Shaarei Halacha Uminhag 2:191; Vetzaruch Iyun from the reply of the Rebbe ibid that the Rebbe Rayatz would do the Bedika between Mincha and Maariv, and would then daven Maariv after the Bedika [beyechidus].
The reason: As our custom is to take a long time to do the Bedika. Therefore, we make sure to daven Maariv beforehand [as otherwise we may come to forget to pray, or because we will only get a chance to pray after it is already midnight]. [Rebbe ibid]