The accepted stereotype that Mexicans tend to be sloppy and emotional when really intoxicated led to a category of intoxication that can be applied to anyone who meets the criteria of being extremely intoxicated and emotional.
When, to settle a disagreement, two or more people see who can drink more alcohol (usually shots or beer). The person who stays the most sober the longest wins.
"Madison and I couldn't agree on when to go see the movie so we had a Mexican Drink Off."
"Tony and Luke had a Mexican Drink Off to see who got to ask that new foreign girl out."