The walk-away decision is the only genuinely hard part of the format. Everything else is knowledge; this is arithmetic performed badly under pressure, in front of an audience willing you to gamble.
The arithmetic nobody does on stage
The question is not ‘do I think I know this’ but ‘how often would I be right if this situation repeated a hundred times’. If you would be right seven times in ten, and a wrong answer drops you to a safety net far below your current total, the maths often says stop. A useful rule of thumb: guessing between two options is a coin flip, and a coin flip is only worth taking when the amount you would lose is small relative to the amount you would gain.
Safety nets change everything
Immediately above a safety net, risk is cheap — a wrong answer costs you little because the guaranteed amount is just below you. Immediately below the next one, risk is expensive. Contestants routinely get this backwards, playing cautiously right after a safety net and boldly just before the next.
The pressure to be brave
The audience always wants you to answer. So does the host, and so does the part of you that does not want to look timid on television. None of those parties share your downside. Deciding your threshold before you sit down — ‘I walk if I am not certain above this amount’ — is the only reliable defence against the room.
Nobody remembers the contestant who took a sensible amount home. They also do not have to live with the contestant’s answer, which is the whole point.