When does a hydride shift occur?

To specify, you meant to ask about a 1,2-hydride shift. Those are taught in organic chemistry, first semester.

When you have a reaction that contains a carbocation intermediate (such as an #"S"_N1# reaction of tert-butyl bromide with water), you have to question whether you can achieve a more stable carbocation or not.

CARBOCATION HYPERCONJUGATION

Carbocation stability goes as follows:

#3^@ > 2^@ > 1^@ > "methyl"#

This is due to the #"C"-"H"# bonds on the alkyl groups surrounding the central, cationic carbon.

These #"C"-"H"# bonds can spread their electron density out and share it with the central empty #p# orbital on the cationic carbon, thus stabilizing it. This is called hyperconjugation.

The more alkyl groups surrounding the cationic carbon, the more stable it thus becomes, because an additional #"C"-"H"# bond is available to share more negative charge density and offset the positivity in the central cationic carbon.

1,2-HYDRIDE SHIFTS

Whenever you have a more substituted carbon adjacent to a cationic carbon, a 1,2-hydride shift would shift the positive charge over to a carbon that can better stabilize itself.