There is always one. The friend who loves the party, laughs at everyone else's turn, and absolutely refuses to take one of their own. Pushing them harder never works. It just makes the spotlight they are afraid of feel even hotter.
Understand what they are actually afraid of
Shy people are rarely afraid of singing. They are afraid of being watched while they decide what to do, of the silent moment where all eyes are on them and they have to choose and commit. The fear lives in the pause, not the performance. If you can remove the pause, you remove most of the fear.
Take away the choices
The cruelest thing you can do to a nervous friend is ask "so what do you want to sing?" Now they have to make a decision, in public, with an audience waiting. Games that assign the turn and the task remove this completely. When the game says "you are up" and hands you the word, there is nothing to decide and nowhere to hide, and paradoxically that is a relief. The scary freedom is gone.
Make everyone else look silly first
Nobody wants to be the first to look foolish. So do not let your shy friend go first. Let them watch three or four other people be gloriously, loudly imperfect. Once the room has established that looking ridiculous is the whole point and nobody is being judged, the barrier to joining drops through the floor. This is the same principle behind beating stage fright: shared, low-stakes exposure shrinks the fear fast.
Why the format matters
Grab The Phone Karaoke is unusually good at this. The turns are assigned, so there is no volunteering. The clip is fifteen seconds, so there is no long exposure. And the whole group is playing, so no single person is ever the sole focus for long. A shy friend can go from "I'm just watching" to grabbing the phone without ever having to make the terrifying decision to put themselves forward. The game makes the decision for them.
The one rule that seals it
Cheer the reluctant ones the loudest. When your quiet friend finally takes a turn, however small, the room should erupt. That single burst of warmth is usually all it takes. By the next round they are not the shy one anymore. They are just another player, and they will thank you for it later, even if they never admit they were nervous at all.