I'm not sure if I'm understanding you correctly but you seem to ask, 'What happens if 3 (the second, the thirth and the fourth) of them work together?'
 - Suggesting that 'person one' is the victim.

But then, 'All of that only works under the assumption that three of them work together to cheat the fourth person.'
 - Here 'person four' is the victim.

You're talking about this film, I assume: https://www.youtube.com/watch?v=8zVzw912wPo

At about the 25 minute mark?

If so, your question would be clearer to me if you rephrased it using the names Alice, Bob, Carol and Dave.