頼み

1. Origins, structure, and basic meaning

• Structure: 頼み, read たのみ, means a request or something one relies on.
• Basic usage: In 君に一つ頼みがあるんだ。, the speaker has one favor to ask of the other person.

2. Common pitfalls and similar expressions

• A request and a source of hope
  • 頼みがある means having a favor to ask, whereas 頼みの綱 figuratively names a last source of hope or support. In the letter example, it is the remaining hope when contact is otherwise impossible.