Praying While Drunk
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Someone who is "slightly intoxicated,” who referred to as a shatui, is permitted to pray Le'chatchilah. One who is drunk, referred to as a shikor , whose speech is slurred even when using a siddur is forbidden to pray (until he sobers up) however he may recite Birkat Hamazon.
A shatui is defined as still sober enough to conduct a conversation with a person. A shikor refers to one who drinks beyond this measure, and whose speech is slurred even when using a Siddur.
Be'dieved if he prayed in this manner he does not need to repeat the tefillah as long as he could still arrange his words even Be'dochak using a siddur. However, if he is so drunk that he can't arrange his words at all , even when using a siddur, then he needs to repeat the tefillah when he has sobered up.
A person is allowed to decide for himself whether he is a shatui or a shikor , and, by extension, One who prays after drinking any amount of alcohol should be sure to pray from a siddur , and not by heart, in order to better ensure proper concentration.